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Title: A System of Logic: Ratiocinative and Inductive - 7th Edition, Vol. II
Author: Mill, John Stuart, 1806-1873
Language: English
As this book started as an ASCII text book there are no pictures available.

*** Start of this LibraryBlog Digital Book "A System of Logic: Ratiocinative and Inductive - 7th Edition, Vol. II" ***
















  ON INDUCTION.--(_Continued._)

  CHAPTER XIV. _Of the Limits to the Explanation of Laws of
  Nature; and of Hypotheses._

  § 1. Can all the sequences in nature be resolvable into one law?    3

    2. Ultimate laws cannot be less numerous than the
       distinguishable feelings of our nature                         4

    3. In what sense ultimate facts can be explained                  7

    4. The proper use of scientific hypotheses                        8

    5. Their indispensableness                                       16

    6. Legitimate, how distinguished from illegitimate hypotheses    18

    7. Some inquiries apparently hypothetical are really inductive   25

  CHAPTER XV. _Of Progressive Effects; and of the Continued
              Action of Causes._

  § 1. How a progressive effect results from the simple continuance
       of the cause                                                  29

    2. --and from the progressiveness of the cause                   33

    3. Derivative laws generated from a single ultimate law          36

  CHAPTER XVI. _Of Empirical Laws._

  § 1. Definition of an empirical law                                38

    2. Derivative laws commonly depend on collocations               39

    3. The collocations of the permanent causes are not reducible
       to any law                                                    41

    4. Hence empirical laws cannot be relied on beyond the limits
       of actual experience                                          41

    5. Generalizations which rest only on the Method of Agreement
       can only be received as empirical laws                        43

    6. Signs from which an observed uniformity of sequence may be
       presumed to be resolvable                                     44

    7. Two kinds of empirical laws                                   47

  CHAPTER XVII. _Of Chance, and its Elimination._

  § 1. The proof of empirical laws depends on the theory of chance   49

    2. Chance defined and characterized                              50

    3. The elimination of chance                                     55

    4. Discovery of residual phenomena by eliminating chance         57

    5. The doctrine of chances                                       59

  CHAPTER XVIII. _Of the Calculation of Chances._

  § 1. Foundation of the doctrine of chances, as taught by
       mathematics                                                   61

    2. The doctrine tenable                                          63

    3. On what foundation it really rests                            64

    4. Its ultimate dependence on causation                          68

    5. Theorem of the doctrine of chances which relates to the
       cause of a given event                                        72

    6. How applicable to the elimination of chance                   74

  CHAPTER XIX. _Of the Extension of Derivative Laws to Adjacent

  § 1. Derivative laws, when not casual, are almost always
       contingent on collocations                                    78

    2. On what grounds they can be extended to cases beyond the
       bounds of actual experience                                   80

    3. Those cases must be adjacent cases                            82

  CHAPTER XX. _Of Analogy._

  § 1. Various senses of the word analogy                            86

    2. Nature of analogical evidence                                 87

    3. On what circumstances its value depends                       91

  CHAPTER XXI. _Of the Evidence of the Law of Universal

  § 1. The law of causality does not rest on an instinct             95

    2. But on an induction by simple enumeration                    100

    3. In what cases such induction is allowable                    102

    4. The universal prevalence of the law of causality, on what
       grounds admissible                                           105

  CHAPTER XXII. _Of Uniformities of Coexistence not dependent
  on Causation._

  § 1. Uniformities of coexistence which result from laws of
       sequence                                                     110

    2. The properties of Kinds are uniformities of coexistence      111

    3. Some are derivative, others ultimate                         113

    4. No universal axiom of coexistence                            114

    5. The evidence of uniformities of coexistence, how measured    117

    6. When derivative, their evidence is that of empirical laws    117

    7. So also when ultimate                                        119

    8. The evidence stronger in proportion as the law is more
       general                                                      120

    9. Every distinct Kind must be examined                         121

  CHAPTER XXIII. _Of Approximate Generalizations, and Probable

  § 1. The inferences called probable, rest on approximate
       generalizations                                              124

    2. Approximate generalizations less useful in science than
       in life                                                      124

    3. In what cases they may be resorted to                        126

    4. In what manner proved                                        127

    5. With what precautions employed                               130

    6. The two modes of combining probabilities                     131

    7. How approximate generalizations may be converted into
       accurate generalizations equivalent to them                  136

  CHAPTER XXIV. _Of the Remaining Laws of Nature._

  § 1. Propositions which assert mere existence                     139

    2. Resemblance, considered as a subject of science              141

    3. The axioms and theorems of mathematics comprise the
       principal laws of resemblance                                143

    4. --and those of order in place, and rest on induction by
       simple enumeration                                           145

    5. The propositions of arithmetic affirm the modes of formation
       of some given number                                         146

    6. Those of algebra affirm the equivalence of different modes
       of formation of numbers generally                            151

    7. The propositions of geometry are laws of outward nature      154

    8. Why geometry is almost entirely deductive                    156

    9. Function of mathematical truths in the other sciences, and
       limits of that function                                      158

  CHAPTER XXV. _Of the Grounds of Disbelief._

  § 1. Improbability and impossibility                              161

    2. Examination of Hume's doctrine of miracles                   162

    3. The degrees of improbability correspond to differences in
       the nature of the generalization with which an assertion
       conflicts                                                    166

    4. A fact is not incredible because the chances are against it  170

    5. Are coincidences less credible than other facts?             172

    6. An opinion of Laplace examined                               175



  CHAPTER I. _Of Observation and Description._

  § 1. Observation, how far a subject of logic                      183

    2. A great part of what seems observation is really inference   184

    3. The description of an observation affirms more than is
       contained in the observation                                 187

    4. --namely an agreement among phenomena; and the comparison
       of phenomena to ascertain such agreements is a preliminary
       to induction                                                 190

  CHAPTER II. _Of Abstraction, or the Formation of

  § 1. The comparison which is a preliminary to induction implies
       general conceptions                                          193

    2. --but these need not be pre-existent                         194

    3. A general conception, originally the result of a comparison,
       becomes itself the type of comparison                        198

    4. What is meant by appropriate conceptions                     200

    5. --and by clear conceptions                                   203

    6. Further illustration of the subject                          205

  CHAPTER III. _Of Naming, as subsidiary to Induction._

  § 1. The fundamental property of names as an instrument of
       thought                                                      209

    2. Names are not indispensable to induction                     210

    3. In what manner subservient to it                             211

    4. General names not a mere contrivance to economize the
       use of language                                              213

  CHAPTER IV. _Of the Requisites of a Philosophical Language,
  and the Principles of Definition._

  § 1. First requisite of philosophical language, a steady and
       determinate meaning for every general name                   215

    2. Names in common use have often a loose connotation           215

    3. --which the logician should fix, with as little alteration
       as possible                                                  218

    4. Why definition is often a question not of words but of
       things                                                       220

    5. How the logician should deal with the transitive
       applications of words                                        224

    6. Evil consequences of casting off any portion of the
       customary connotation of words                               229

  CHAPTER V. _On the Natural History of the Variations in
  the Meaning of Terms._

  § 1. How circumstances originally accidental become incorporated
       into the meaning of words                                    236

    2. --and sometimes become the whole meaning                     238

    3. Tendency of words to become generalized                      240

    4. --and to become specialized                                  243

  CHAPTER VI. _The Principles of a Philosophical Language
  further considered._

  § 1. Second requisite of philosophical language, a name for
       every important meaning                                      248

    2. --viz. first, an accurate descriptive terminology            248

    3. --secondly, a name for each of the more important results
       of scientific abstraction                                    252

    4. --thirdly, a nomenclature, or system of the names of
       Kinds                                                        255

    5. Peculiar nature of the connotation of names which belong
       to a nomenclature                                            257

    6. In what cases language may, and may not, be used
       mechanically                                                 259

  CHAPTER VII. _Of Classification, as subsidiary to

  § 1. Classification as here treated of, wherein different from
       the classification implied in naming                         266

    2. Theory of natural groups                                     267

    3. Are natural groups given by type, or by definition?          271

    4. Kinds are natural groups                                     274

    5. How the names of Kinds should be constructed                 280

  CHAPTER VIII. _Of Classification by Series._

  § 1. Natural groups should be arranged in a natural series        284

    2. The arrangement should follow the degrees of the main
       phenomenon                                                   285

    3. --which implies the assumption of a type-species             287

    4. How the divisions of the series should be determined         288

    5. Zoology affords the completest type of scientific
       classification                                               289



  CHAPTER I. _Of Fallacies in General._

  § 1. Theory of fallacies a necessary part of logic                295

    2. Casual mistakes are not fallacies                            297

    3. The moral sources of erroneous opinion, how related to
       the intellectual                                             297

  CHAPTER II. _Classification of Fallacies._

  § 1. On what criteria a classification of fallacies should be
       grounded                                                     301

    2. The five classes of fallacies                                302

    3. The reference of a fallacy to one or another class is
       sometimes arbitrary                                          305

  CHAPTER III. _Fallacies of Simple Inspection, or à priori

  § 1. Character of this class of Fallacies                         309

    2. Natural prejudice of mistaking subjective laws for
       objective, exemplified in popular superstitions              310

    3. Natural prejudices, that things which we think of together
       must exist together, and that what is inconceivable
       must be false                                                314

    4. Natural prejudice, of ascribing objective existence to
       abstractions                                                 321

    5. Fallacy of the Sufficient Reason                             322

    6. Natural prejudice, that the differences in nature correspond
       to the distinctions in language                              325

    7. Prejudice, that a phenomenon cannot have more than one
       cause                                                        329

    8. Prejudice, that the conditions of a phenomenon must
       resemble the phenomenon                                      332

  CHAPTER IV. _Fallacies of Observation._

  § 1. Non-observation, and Mal-observation                         341

    2. Non-observation of instances, and non-observation of
       circumstances                                                341

    3. Examples of the former                                       342

    4. --and of the latter                                          347

    5. Mal-observation characterized and exemplified                352

  CHAPTER V. _Fallacies of Generalization._

  § 1. Character of the class                                       356

    2. Certain kinds of generalization must always be groundless    356

    3. Attempts to resolve phenomena radically different into
       the same                                                     357

    4. Fallacy of mistaking empirical for causal laws               359

    5. _Post hoc, ergo propter hoc_; and the deductive fallacy
       corresponding to it                                          364

    6. Fallacy of False Analogies                                   366

    7. Function of metaphors in reasoning                           373

    8. How fallacies of generalization grow out of bad
       classification                                               375

  CHAPTER VI. _Fallacies of Ratiocination._

  § 1. Introductory Remarks                                         377

    2. Fallacies in the conversion and æquipollency of
       propositions                                                 377

    3. Fallacies in the syllogistic process                         379

    4. Fallacy of changing the premises                             379

  CHAPTER VII. _Fallacies of Confusion._

  § 1. Fallacy of Ambiguous Terms                                   384

    2. Fallacy of Petitio Principii                                 396

    3. Fallacy of Ignoratio Elenchi                                 405



  CHAPTER I. _Introductory Remarks._

  § 1. The backward state of the Moral Sciences can only be
       remedied by applying to them the methods of Physical
       Science, duly extended and generalized                       413

    2. How far this can be attempted in the present work            415

  CHAPTER II. _Of Liberty and Necessity._

  § 1. Are human actions subject to the law of causality?           417

    2. The doctrine commonly called Philosophical Necessity, in
       what sense true                                              418

    3. Inappropriateness and pernicious effect of the term
       Necessity                                                    420

    4. A motive not always the anticipation of a pleasure or a
       pain                                                         424

  CHAPTER III. _That there is, or may be, a Science of
  Human Nature._

  § 1. There may be sciences which are not exact sciences           426

    2. To what scientific type the Science of Human Nature
       corresponds                                                  429

  CHAPTER IV. _Of the Laws of Mind._

  § 1. What is meant by Laws of Mind                                432

    2. Is there a science of Psychology?                            433

    3. The principal investigations of Psychology characterized     435

    4. Relation of mental facts to physical conditions              440

  CHAPTER V. _Of Ethology, or the Science of the Formation of

  § 1. The Empirical Laws of Human Nature                           445

    2. --are merely approximate generalizations. The universal
       laws are those of the formation of character                 447

    3. The laws of the formation of character cannot be ascertained
       by observation and experiment                                449

    4. --but must be studied deductively                            454

    5. The Principles of Ethology are the _axiomata media_ of
       mental science                                               455

    6. Ethology characterized                                       459

  CHAPTER VI. _General Considerations on the Social Science._

  § 1. Are Social Phenomena a subject of Science?                   461

    2. Of what nature the Social Science must be                    463

  CHAPTER VII. _Of the Chemical, or Experimental, Method in the
  Social Science._

  § 1. Characters of the mode of thinking which deduces political
       doctrines from specific experience                           466

    2. In the Social Science experiments are impossible             468

    3. --the Method of Difference inapplicable                      469

    4. --and the Methods of Agreement, and of Concomitant
       Variations, inconclusive                                     471

    5. The Method of Residues also inconclusive, and presupposes
       Deduction                                                    472

  CHAPTER VIII. _Of the Geometrical, or Abstract Method._

  § 1. Characters of this mode of thinking                          476

    2. Examples of the Geometrical Method                           478

    3. The interest-philosophy of the Bentham school                479

  CHAPTER IX. _Of the Physical, or Concrete Deductive Method._

  § 1. The Direct and Inverse Deductive Methods                     486

    2. Difficulties of the Direct Deductive Method in the Social
       Science                                                      489

    3. To what extent the different branches of sociological
       speculation can be studied apart. Political Economy
       characterized                                                492

    4. Political Ethology, or the science of national character     497

    5. The Empirical Laws of the Social Science                     500

    6. The Verification of the Social Science                       502

  CHAPTER X. _Of the Inverse Deductive, or Historical Method._

  § 1. Distinction between the general Science of Society, and
       special sociological inquiries                               506

    2. What is meant by a State of Society?                         506

    3. The Progressiveness of Man and Society                       508

    4. The laws of the succession of states of society can only
       be ascertained by the Inverse Deductive Method               511

    5. Social Statics, or the science of the Coexistences of
       Social Phenomena                                             513

    6. Social Dynamics, or the science of the Successions of Social
       Phenomena                                                    521

    7. Outlines of the Historical Method                            522

    8. Future prospects of Sociological Inquiry                     525

  CHAPTER XI. _Additional Elucidations of the Science of History._

  § 1. The subjection of historical facts to uniform laws is
       verified by statistics                                       529

    2. --does not imply the insignificance of moral causes          532

    3. --nor the inefficacy of the characters of individuals and
       of the acts of governments                                   535

    4. The historical importance of eminent men and of the
       policy of governments illustrated                            540

  CHAPTER XII. _Of the Logic of Practice, or Art; including
  Morality and Policy._

  § 1. Morality not a science, but an Art                           544

    2. Relation between rules of art and the theorems of the
       corresponding science                                        544

    3. What is the proper function of rules of art?                 546

    4. Art cannot be Deductive                                      548

    5. Every Art consists of truths of Science, arranged in the
       order suitable for some practical use                        549

    6. Teleology, or the Doctrine of Ends                           550

    7. Necessity of an ultimate standard, or first principle of
       Teleology                                                    552

    8. Conclusion                                                   554




"In such cases the inductive and deductive methods of inquiry may be
said to go hand in hand, the one verifying the conclusions deduced by
the other; and the combination of experiment and theory, which may thus
be brought to bear in such cases, forms an engine of discovery
infinitely more powerful than either taken separately. This state of any
department of science is perhaps of all others the most interesting, and
that which promises the most to research."--SIR J. HERSCHEL, _Discourse
on the Study of Natural Philosophy_.



§ 1. The preceding considerations have led us to recognise a distinction
between two kinds of laws, or observed uniformities in nature: ultimate
laws, and what may be termed derivative laws. Derivative laws are such
as are deducible from, and may, in any of the modes which we have
pointed out, be resolved into, other and more general ones. Ultimate
laws are those which cannot. We are not sure that any of the
uniformities with which we are yet acquainted are ultimate laws; but we
know that there must be ultimate laws; and that every resolution of a
derivative law into more general laws, brings us nearer to them.

Since we are continually discovering that uniformities, not previously
known to be other than ultimate, are derivative, and resolvable into
more general laws; since (in other words) we are continually discovering
the explanation of some sequence which was previously known only as a
fact; it becomes an interesting question whether there are any necessary
limits to this philosophical operation, or whether it may proceed until
all the uniform sequences in nature are resolved into some one universal
law. For this seems, at first sight, to be the ultimatum towards which
the progress of induction, by the Deductive Method resting on a basis of
observation and experiment, is tending. Projects of this kind were
universal in the infancy of philosophy; any speculations which held out
a less brilliant prospect, being in those early times deemed not worth
pursuing. And the idea receives so much apparent countenance from the
nature of the most remarkable achievements of modern science, that
speculators are even now frequently appearing, who profess either to
have solved the problem, or to suggest modes in which it may one day be
solved. Even where pretensions of this magnitude are not made, the
character of the solutions which are given or sought of particular
classes of phenomena, often involves such conceptions of what
constitutes explanation, as would render the notion of explaining all
phenomena whatever by means of some one cause or law, perfectly

§ 2. It is therefore useful to remark, that the ultimate Laws of Nature
cannot possibly be less numerous than the distinguishable sensations or
other feelings of our nature;--those, I mean, which are distinguishable
from one another in quality, and not merely in quantity or degree. For
example; since there is a phenomenon _sui generis_, called colour, which
our consciousness testifies to be not a particular degree of some other
phenomenon, as heat or odour or motion, but intrinsically unlike all
others, it follows that there are ultimate laws of colour; that though
the facts of colour may admit of explanation, they never can be
explained from laws of heat or odour alone, or of motion alone, but that
however far the explanation may be carried, there will always remain in
it a law of colour. I do not mean that it might not possibly be shown
that some other phenomenon, some chemical or mechanical action for
example, invariably precedes, and is the cause of, every phenomenon of
colour. But though this, if proved, would be an important extension of
our knowledge of nature, it would not explain how or why a motion, or a
chemical action, can produce a sensation of colour; and however diligent
might be our scrutiny of the phenomena, whatever number of hidden links
we might detect in the chain of causation terminating in the colour, the
last link would still be a law of colour, not a law of motion, nor of
any other phenomenon whatever. Nor does this observation apply only to
colour, as compared with any other of the great classes of sensations;
it applies to every particular colour, as compared with others. White
colour can in no manner be explained exclusively by the laws of the
production of red colour. In any attempt to explain it, we cannot but
introduce, as one element of the explanation, the proposition that some
antecedent or other produces the sensation of white.

The ideal limit, therefore, of the explanation of natural phenomena
(towards which as towards other ideal limits we are constantly tending,
without the prospect of ever completely attaining it) would be to show
that each distinguishable variety of our sensations, or other states of
consciousness, has only one sort of cause; that, for example, whenever
we perceive a white colour, there is some one condition or set of
conditions which is always present, and the presence of which always
produces in us that sensation. As long as there are several known modes
of production of a phenomenon, (several different substances, for
instance, which have the property of whiteness, and between which we
cannot trace any other resemblance,) so long it is not impossible that
one of these modes of production may be resolved into another, or that
all of them may be resolved into some more general mode of production
not hitherto recognised. But when the modes of production are reduced to
one, we cannot, in point of simplification, go any further. This one may
not, after all, be the ultimate mode; there may be other links to be
discovered between the supposed cause and the effect; but we can only
further resolve the known law, by introducing some other law hitherto
unknown; which will not diminish the number of ultimate laws.

In what cases, accordingly, has science been most successful in
explaining phenomena, by resolving their complex laws into laws of
greater simplicity and generality? Hitherto chiefly in cases of the
propagation of various phenomena through space: and, first and
principally, the most extensive and important of all facts of that
description, the fact of motion. Now this is exactly what might be
expected from the principles here laid down. Not only is motion one of
the most universal of all phenomena, it is also (as might be expected
from that circumstance) one of those which, apparently at least, are
produced in the greatest number of ways; but the phenomenon itself is
always, to our sensations, the same in every respect but degree.
Differences of duration, or of velocity, are evidently differences in
degree only; and differences of direction in space, which alone has any
semblance of being a distinction in kind, entirely disappear (so far as
our sensations are concerned) by a change in our own position; indeed
the very same motion appears to us, according to our position, to take
place in every variety of direction, and motions in every different
direction to take place in the same. And again, motion in a straight
line and in a curve are no otherwise distinct than that the one is
motion continuing in the same direction, the other is motion which at
each instant changes its direction. There is, therefore, according to
the principles I have stated, no absurdity in supposing that all motion
may be produced in one and the same way; by the same kind of cause.
Accordingly, the greatest achievements in physical science have
consisted in resolving one observed law of the production of motion into
the laws of other known modes of production, or the laws of several such
modes into one more general mode; as when the fall of bodies to the
earth, and the motions of the planets, were brought under the one law of
the mutual attraction of all particles of matter; when the motions said
to be produced by magnetism were shown to be produced by electricity;
when the motions of fluids in a lateral direction, or even contrary to
the direction of gravity, were shown to be produced by gravity; and the
like. There is an abundance of distinct causes of motion still
unresolved into one another; gravitation, heat, electricity, chemical
action, nervous action, and so forth; but whether the efforts of the
present generation of savans to resolve all these different modes of
production into one, are ultimately successful or not, the attempt so to
resolve them is perfectly legitimate. For though these various causes
produce, in other respects, sensations intrinsically different, and are
not, therefore, capable of being resolved into one another, yet in so
far as they all produce motion, it is quite possible that the immediate
antecedent of the motion may in all these different cases be the same;
nor is it impossible that these various agencies themselves may, as the
new doctrines assert, all of them have for their own immediate
antecedent, modes of molecular motion.

We need not extend our illustration to other cases, as for instance to
the propagation of light, sound, heat, electricity, &c. through space,
or any of the other phenomena which have been found susceptible of
explanation by the resolution of their observed laws into more general
laws. Enough has been said to display the difference between the kind of
explanation and resolution of laws which is chimerical, and that of
which the accomplishment is the great aim of science; and to show into
what sort of elements the resolution must be effected, if at all.

§ 3. As, however, there is scarcely any one of the principles of a true
method of philosophizing which does not require to be guarded against
errors on both sides, I must enter a caveat against another
misapprehension, of a kind directly contrary to the preceding. M. Comte,
among other occasions on which he has condemned, with some asperity, any
attempt to explain phenomena which are "evidently primordial," (meaning,
apparently, no more than that every peculiar phenomenon must have at
least one peculiar and therefore inexplicable law,) has spoken of the
attempt to furnish any explanation of the colour belonging to each
substance, "la couleur élémentaire propre à chaque substance," as
essentially illusory. "No one," says he, "in our time attempts to
explain the particular specific gravity of each substance or of each
structure. Why should it be otherwise as to the specific colour, the
notion of which is undoubtedly no less primordial?"[1]

Now although, as he elsewhere observes, a colour must always remain a
different thing from a weight or a sound, varieties of colour might
nevertheless follow, or correspond to, given varieties of weight, or
sound, or some other phenomenon as different as these are from colour
itself. It is one question what a thing is, and another what it depends
on; and though to ascertain the conditions of an elementary phenomenon
is not to obtain any new insight into the nature of the phenomenon
itself, that is no reason against attempting to discover the conditions.
The interdict against endeavouring to reduce distinctions of colour to
any common principle, would have held equally good against a like
attempt on the subject of distinctions of sound; which nevertheless have
been found to be immediately preceded and caused by distinguishable
varieties in the vibrations of elastic bodies: though a sound, no doubt,
is quite as different as a colour is from any motion of particles,
vibratory or otherwise. We might add, that, in the case of colours,
there are strong positive indications that they are not ultimate
properties of the different kinds of substances, but depend on
conditions capable of being superinduced upon all substances; since
there is no substance which cannot, according to the kind of light
thrown upon it, be made to assume almost any colour; and since almost
every change in the mode of aggregation of the particles of the same
substance, is attended with alterations in its colour, and in its
optical properties generally.

The real defect in the attempts which have been made to account for
colours by the vibrations of a fluid, is not that the attempt itself is
unphilosophical, but that the existence of the fluid, and the fact of
its vibratory motion, are not proved; but are assumed, on no other
ground than the facility they are supposed to afford of explaining the
phenomena. And this consideration leads to the important question of the
proper use of scientific hypotheses; the connexion of which with the
subject of the explanation of the phenomena of nature, and of the
necessary limits to that explanation, needs not be pointed out.

§ 4. An hypothesis is any supposition which we make (either without
actual evidence, or on evidence avowedly insufficient) in order to
endeavour to deduce from it conclusions in accordance with facts which
are known to be real; under the idea that if the conclusions to which
the hypothesis leads are known truths, the hypothesis itself either must
be, or at least is likely to be, true. If the hypothesis relates to the
cause, or mode of production of a phenomenon, it will serve, if
admitted, to explain such facts as are found capable of being deduced
from it. And this explanation is the purpose of many, if not most,
hypotheses. Since explaining, in the scientific sense, means resolving
an uniformity which is not a law of causation, into the laws of
causation from which it results, or a complex law of causation into
simpler and more general ones from which it is capable of being
deductively inferred; if there do not exist any known laws which fulfil
this requirement, we may feign or imagine some which would fulfil it;
and this is making an hypothesis.

An hypothesis being a mere supposition, there are no other limits to
hypotheses than those of the human imagination; we may, if we please,
imagine, by way of accounting for an effect, some cause of a kind
utterly unknown, and acting according to a law altogether fictitious.
But as hypotheses of this sort would not have any of the plausibility
belonging to those which ally themselves by analogy with known laws of
nature, and besides would not supply the want which arbitrary hypotheses
are generally invented to satisfy, by enabling the imagination to
represent to itself an obscure phenomenon in a familiar light; there is
probably no hypothesis in the history of science in which both the agent
itself and the law of its operation were fictitious. Either the
phenomenon assigned as the cause is real, but the law according to which
it acts, merely supposed; or the cause is fictitious, but is supposed to
produce its effects according to laws similar to those of some known
class of phenomena. An instance of the first kind is afforded by the
different suppositions made respecting the law of the planetary central
force, anterior to the discovery of the true law, that the force varies
as the inverse square of the distance; which also suggested itself to
Newton, in the first instance, as an hypothesis, and was verified by
proving that it led deductively to Kepler's laws. Hypotheses of the
second kind are such as the vortices of Descartes, which were
fictitious, but were supposed to obey the known laws of rotatory motion;
or the two rival hypotheses respecting the nature of light, the one
ascribing the phenomena to a fluid emitted from all luminous bodies, the
other (now generally received) attributing them to vibratory motions
among the particles of an ether pervading all space. Of the existence of
either fluid there is no evidence, save the explanation they are
calculated to afford of some of the phenomena; but they are supposed to
produce their effects according to known laws; the ordinary laws of
continued locomotion in the one case, and in the other, those of the
propagation of undulatory movements among the particles of an elastic

According to the foregoing remarks, hypotheses are invented to enable
the Deductive Method to be earlier applied to phenomena. But[2] in order
to discover the cause of any phenomenon by the Deductive Method, the
process must consist of three parts; induction, ratiocination, and
verification. Induction, (the place of which, however, may be supplied
by a prior deduction,) to ascertain the laws of the causes;
ratiocination, to compute from those laws, how the causes will operate
in the particular combination known to exist in the case in hand;
verification, by comparing this calculated effect with the actual
phenomenon. No one of these three parts of the process can be dispensed
with. In the deduction which proves the identity of gravity with the
central force of the solar system, all the three are found. First, it is
proved from the moon's motions, that the earth attracts her with a force
varying as the inverse square of the distance. This (though partly
dependent on prior deductions) corresponds to the first, or purely
inductive, step, the ascertainment of the law of the cause. Secondly,
from this law, and from the knowledge previously obtained of the moon's
mean distance from the earth, and of the actual amount of her deflexion
from the tangent, it is ascertained with what rapidity the earth's
attraction would cause the moon to fall, if she were no further off, and
no more acted upon by extraneous forces, than terrestrial bodies are:
that is the second step, the ratiocination. Finally, this calculated
velocity being compared with the observed velocity with which all heavy
bodies fall, by mere gravity, towards the surface of the earth, (sixteen
feet in the first second, forty-eight in the second, and so forth, in
the ratio of the odd numbers, 1, 3, 5, &c.,) the two quantities are
found to agree. The order in which the steps are here presented, was not
that of their discovery; but it is their correct logical order, as
portions of the proof that the same attraction of the earth which causes
the moon's motion, causes also the fall of heavy bodies to the earth: a
proof which is thus complete in all its parts.

Now, the Hypothetical Method suppresses the first of the three steps,
the induction to ascertain the law; and contents itself with the other
two operations, ratiocination and verification; the law which is
reasoned from, being assumed, instead of proved.

This process may evidently be legitimate on one supposition, namely, if
the nature of the case be such that the final step, the verification,
shall amount to, and fulfil the conditions of, a complete induction. We
want to be assured that the law we have hypothetically assumed is a true
one; and its leading deductively to true results will afford this
assurance, provided the case be such that a false law cannot lead to a
true result; provided no law, except the very one which we have assumed,
can lead deductively to the same conclusions which that leads to. And
this proviso is often realized. For example, in the very complete
specimen of deduction which we just cited, the original major premise of
the ratiocination, the law of the attractive force, was ascertained in
this mode; by this legitimate employment of the Hypothetical Method.
Newton began by an assumption, that the force which at each instant
deflects a planet from its rectilineal course, and makes it describe a
curve round the sun, is a force tending directly towards the sun. He
then proved that if this be so, the planet will describe, as we know by
Kepler's first law that it does describe, equal areas in equal times;
and, lastly, he proved that if the force acted in any other direction
whatever, the planet would not describe equal areas in equal times. It
being thus shown that no other hypothesis would accord with the facts,
the assumption was proved; the hypothesis became an inductive truth. Not
only did Newton ascertain by this hypothetical process the direction of
the deflecting force; he proceeded in exactly the same manner to
ascertain the law of variation of the quantity of that force. He assumed
that the force varied inversely as the square of the distance; showed
that from this assumption the remaining two of Kepler's laws might be
deduced; and finally, that any other law of variation would give results
inconsistent with those laws, and inconsistent, therefore, with the real
motions of the planets, of which Kepler's laws were known to be a
correct expression.

I have said that in this case the verification fulfils the conditions of
an induction: but an induction of what sort? On examination we find that
it conforms to the canon of the Method of Difference. It affords the two
instances, A B C, _a b c_, and B C, _b c_. A represents central force; A
B C, the planets _plus_ a central force; B C, the planets apart from a
central force. The planets with a central force give _a_, areas
proportional to the times; the planets without a central force give _b
c_ (a set of motions) without _a_, or with something else instead of
_a_. This is the Method of Difference in all its strictness. It is true,
the two instances which the method requires are obtained in this case,
not by experiment, but by a prior deduction. But that is of no
consequence. It is immaterial what is the nature of the evidence from
which we derive the assurance that A B C will produce _a b c_, and B C
only _b c_; it is enough that we have that assurance. In the present
case, a process of reasoning furnished Newton with the very instances,
which, if the nature of the case had admitted of it, he would have
sought by experiment.

It is thus perfectly possible, and indeed is a very common occurrence,
that what was an hypothesis at the beginning of the inquiry, becomes a
proved law of nature before its close. But in order that this should
happen, we must be able, either by deduction or experiment, to obtain
_both_ the instances which the Method of Difference requires. That we
are able from the hypothesis to deduce the known facts, gives only the
affirmative instance, A B C, _a b c_. It is equally necessary that we
should be able to obtain, as Newton did, the negative instance B C, _b
c_; by showing that no antecedent, except the one assumed in the
hypothesis, would in conjunction with B C produce _a_.

Now it appears to me that this assurance cannot be obtained, when the
cause assumed in the hypothesis is an unknown cause, imagined solely to
account for _a_. When we are only seeking to determine the precise law
of a cause already ascertained, or to distinguish the particular agent
which is in fact the cause, among several agents of the same kind, one
or other of which it is already known to be, we may then obtain the
negative instance. An inquiry, which of the bodies of the solar system
causes by its attraction some particular irregularity in the orbit or
periodic time of some satellite or comet, would be a case of the second
description. Newton's was a case of the first. If it had not been
previously known that the planets were hindered from moving in straight
lines by some force tending towards the interior of their orbit, though
the exact direction was doubtful; or if it had not been known that the
force increased in some proportion or other as the distance diminished,
and diminished as it increased; Newton's argument would not have proved
his conclusion. These facts, however, being already certain, the range
of admissible suppositions was limited to the various possible
directions of a line, and the various possible numerical relations
between the variations of the distance, and the variations of the
attractive force: now among these it was easily shown that different
suppositions could not lead to identical consequences.

Accordingly, Newton could not have performed his second great scientific
operation, that of identifying terrestrial gravity with the central
force of the solar system, by the same hypothetical method. When the law
of the moon's attraction had been proved from the data of the moon
itself, then on finding the same law to accord with the phenomena of
terrestrial gravity, he was warranted in adopting it as the law of those
phenomena likewise; but it would not have been allowable for him,
without any lunar data, to assume that the moon was attracted towards
the earth with a force as the inverse square of the distance, merely
because that ratio would enable him to account for terrestrial gravity:
for it would have been impossible for him to prove that the observed law
of the fall of heavy bodies to the earth could not result from any
force, save one extending to the moon, and proportional to the inverse

It appears, then, to be a condition of a genuinely scientific
hypothesis, that it be not destined always to remain an hypothesis, but
be of such a nature as to be either proved or disproved by comparison
with observed facts. This condition is fulfilled when the effect is
already known to depend on the very cause supposed, and the hypothesis
relates only to the precise mode of dependence; the law of the variation
of the effect according to the variations in the quantity or in the
relations of the cause. With these may be classed the hypotheses which
do not make any supposition with regard to causation, but only with
regard to the law of correspondence between facts which accompany each
other in their variations, though there may be no relation of cause and
effect between them. Such were the different false hypotheses which
Kepler made respecting the law of the refraction of light. It was known
that the direction of the line of refraction varied with every variation
in the direction of the line of incidence, but it was not known how;
that is, what changes of the one corresponded to the different changes
of the other. In this case any law, different from the true one, must
have led to false results. And, lastly, we must add to these, all
hypothetical modes of merely representing, or _describing_, phenomena;
such as the hypothesis of the ancient astronomers that the heavenly
bodies moved in circles; the various hypotheses of excentrics,
deferents, and epicycles, which were added to that original hypothesis;
the nineteen false hypotheses which Kepler made and abandoned respecting
the form of the planetary orbits; and even the doctrine in which he
finally rested, that those orbits are ellipses, which was but an
hypothesis like the rest until verified by facts.

In all these cases, verification is proof; if the supposition accords
with the phenomena there needs no other evidence of it. But in order
that this may be the case, I conceive it to be necessary, when the
hypothesis relates to causation, that the supposed cause should not only
be a real phenomenon, something actually existing in nature, but should
be already known to exercise, or at least to be capable of exercising,
an influence of some sort over the effect. In any other case, it is no
evidence of the truth of the hypothesis that we are able to deduce the
real phenomena from it.

Is it, then, never allowable, in a scientific hypothesis, to assume a
cause; but only to ascribe an assumed law to a known cause? I do not
assert this. I only say, that in the latter case alone can the
hypothesis be received as true merely because it explains the phenomena:
in the former case it is only useful by suggesting a line of
investigation which may possibly terminate in obtaining real proof. For
this purpose, as is justly remarked by M. Comte, it is indispensable
that the cause suggested by the hypothesis should be in its own nature
susceptible of being proved by other evidence. This seems to be the
philosophical import of Newton's maxim, (so often cited with approbation
by subsequent writers,) that the cause assigned for any phenomenon must
not only be such as if admitted would explain the phenomenon, but must
also be a _vera causa_. What he meant by a _vera causa_ Newton did not
indeed very explicitly define; and Dr. Whewell, who dissents from the
propriety of any such restriction upon the latitude of framing
hypotheses, has had little difficulty in showing[3] that his conception
of it was neither precise nor consistent with itself: accordingly his
optical theory was a signal instance of the violation of his own rule.
It is certainly not necessary that the cause assigned should be a cause
already known; else how could we ever become acquainted with any new
cause? But what is true in the maxim is, that the cause, though not
known previously, should be capable of being known thereafter; that its
existence should be capable of being detected, and its connexion with
the effect ascribed to it should be susceptible of being proved, by
independent evidence. The hypothesis, by suggesting observations and
experiments, puts us on the road to that independent evidence if it be
really attainable; and till it be attained, the hypothesis ought not to
count for more than a conjecture.

§ 5. This function, however, of hypotheses, is one which must be
reckoned absolutely indispensable in science. When Newton said,
"Hypotheses non fingo," he did not mean that he deprived himself of the
facilities of investigation afforded by assuming in the first instance
what he hoped ultimately to be able to prove. Without such assumptions,
science could never have attained its present state: they are necessary
steps in the progress to something more certain; and nearly everything
which is now theory was once hypothesis. Even in purely experimental
science, some inducement is necessary for trying one experiment rather
than another; and though it is abstractedly possible that all the
experiments which have been tried, might have been produced by the mere
desire to ascertain what would happen in certain circumstances, without
any previous conjecture as to the result; yet, in point of fact, those
unobvious, delicate, and often cumbrous and tedious processes of
experiment, which have thrown most light upon the general constitution
of nature, would hardly ever have been undertaken by the persons or at
the time they were, unless it had seemed to depend on them whether some
general doctrine or theory which had been suggested, but not yet proved,
should be admitted or not. If this be true even of merely experimental
inquiry, the conversion of experimental into deductive truths could
still less have been effected without large temporary assistance from
hypotheses. The process of tracing regularity in any complicated, and at
first sight confused set of appearances, is necessarily tentative: we
begin by making any supposition, even a false one, to see what
consequences will follow from it; and by observing how these differ from
the real phenomena, we learn what corrections to make in our assumption.
The simplest supposition which accords with the more obvious facts, is
the best to begin with; because its consequences are the most easily
traced. This rude hypothesis is then rudely corrected, and the operation
repeated; and the comparison of the consequences deducible from the
corrected hypothesis, with the observed facts, suggests still further
correction, until the deductive results are at last made to tally with
the phenomena. "Some fact is as yet little understood, or some law is
unknown: we frame on the subject an hypothesis as accordant as possible
with the whole of the data already possessed; and the science, being
thus enabled to move forward freely, always ends by leading to new
consequences capable of observation, which either confirm or refute,
unequivocally, the first supposition." Neither induction nor deduction
would enable us to understand even the simplest phenomena, "if we did
not often commence by anticipating on the results; by making a
provisional supposition, at first essentially conjectural, as to some of
the very notions which constitute the final object of the inquiry."[4]
Let any one watch the manner in which he himself unravels a complicated
mass of evidence; let him observe how, for instance, he elicits the true
history of any occurrence from the involved statements of one or of many
witnesses: he will find that he does not take all the items of evidence
into his mind at once, and attempt to weave them together: he
extemporises, from a few of the particulars, a first rude theory of the
mode in which the facts took place, and then looks at the other
statements one by one, to try whether they can be reconciled with that
provisional theory, or what alterations or additions it requires to make
it square with them. In this way, which has been justly compared to the
Methods of Approximation of mathematicians, we arrive, by means of
hypotheses, at conclusions not hypothetical.[5]

§ 6. It is perfectly consistent with the spirit of the method, to
assume in this provisional manner not only an hypothesis respecting the
law of what we already know to be the cause, but an hypothesis
respecting the cause itself. It is allowable, useful, and often even
necessary, to begin by asking ourselves what cause _may_ have produced
the effect, in order that we may know in what direction to look out for
evidence to determine whether it actually _did_. The vortices of
Descartes would have been a perfectly legitimate hypothesis, if it had
been possible, by any mode of exploration which we could entertain the
hope of ever possessing, to bring the reality of the vortices, as a fact
in nature, conclusively to the test of observation. The hypothesis was
vicious, simply because it could not lead to any course of investigation
capable of converting it from an hypothesis into a proved fact. It might
chance to be _dis_proved, either by some want of correspondence with the
phenomena it purported to explain, or (as actually happened) by some
extraneous fact. "The free passage of comets through the spaces in which
these vortices should have been, convinced men that these vortices did
not exist."[6] But the hypothesis would have been false, though no such
direct evidence of its falsity had been procurable. Direct evidence of
its truth there could not be.

The prevailing hypothesis of a luminiferous ether, in other respects not
without analogy to that of Descartes, is not in its own nature entirely
cut off from the possibility of direct evidence in its favour. It is
well known that the difference between the calculated and the observed
times of the periodical return of Encke's comet, has led to a conjecture
that a medium capable of opposing resistance to motion is diffused
through space. If this surmise should be confirmed, in the course of
ages, by the gradual accumulation of a similar variance in the case of
the other bodies of the solar system, the luminiferous ether would have
made a considerable advance towards the character of a _vera causa_,
since the existence would have been ascertained of a great cosmical
agent, possessing some of the attributes which the hypothesis assumes;
though there would still remain many difficulties, and the
identification of the ether with the resisting medium would even, I
imagine, give rise to new ones. At present, however, this supposition
cannot be looked upon as more than a conjecture; the existence of the
ether still rests on the possibility of deducing from its assumed laws a
considerable number of the phenomena of light; and this evidence I
cannot regard as conclusive, because we cannot have, in the case of such
an hypothesis, the assurance that if the hypothesis be false it must
lead to results at variance with the true facts.

Accordingly, most thinkers of any degree of sobriety allow, that an
hypothesis of this kind is not to be received as probably true because
it accounts for all the known phenomena; since this is a condition
sometimes fulfilled tolerably well by two conflicting hypotheses; while
there are probably a thousand more which are equally possible, but
which, for want of anything analogous in our experience, our minds are
unfitted to conceive. But it seems to be thought that an hypothesis of
the sort in question is entitled to a more favourable reception, if,
besides accounting for all the facts previously known, it has led to the
anticipation and prediction of others which experience afterwards
verified; as the undulatory theory of light led to the prediction,
subsequently realized by experiment, that two luminous rays might meet
each other in such a manner as to produce darkness. Such predictions and
their fulfilment are, indeed, well calculated to impress the uninformed,
whose faith in science rests solely on similar coincidences between its
prophecies and what comes to pass. But it is strange that any
considerable stress should be laid upon such a coincidence by persons of
scientific attainments. If the laws of the propagation of light accord
with those of the vibrations of an elastic fluid in as many respects as
is necessary to make the hypothesis afford a correct expression of all
or most of the phenomena known at the time, it is nothing strange that
they should accord with each other in one respect more. Though twenty
such coincidences should occur, they would not prove the reality of the
undulatory ether; it would not follow that the phenomena of light were
results of the laws of elastic fluids, but at most that they are
governed by laws partially identical with these; which, we may observe,
is already certain, from the fact that the hypothesis in question could
be for a moment tenable.[7] Cases may be cited, even in our imperfect
acquaintance with nature, where agencies that we have good reason to
consider as radically distinct, produce their effects, or some of their
effects, according to laws which are identical. The law, for example, of
the inverse square of the distance, is the measure of the intensity not
only of gravitation, but (it is believed) of illumination, and of heat
diffused from a centre. Yet no one looks upon this identity as proving
similarity in the mechanism by which the three kinds of phenomena are

According to Dr. Whewell, the coincidence of results predicted from an
hypothesis, with facts afterwards observed, amounts to a conclusive
proof of the truth of the theory. "If I copy a long series of letters,
of which the last half dozen are concealed, and if I guess these aright,
as is found to be the case when they are afterwards uncovered, this must
be because I have made out the import of the inscription. To say, that
because I have copied all that I could see, it is nothing strange that I
should guess those which I cannot see, would be absurd, without
supposing such a ground for guessing."[8] If any one, from examining the
greater part of a long inscription, can interpret the characters so that
the inscription gives a rational meaning in a known language, there is a
strong presumption that his interpretation is correct; but I do not
think the presumption much increased by his being able to guess the few
remaining letters without seeing them: for we should naturally expect
(when the nature of the case excludes chance) that even an erroneous
interpretation which accorded with all the visible parts of the
inscription would accord also with the small remainder; as would be the
case, for example, if the inscription had been designedly so contrived
as to admit of a double sense. I assume that the uncovered characters
afford an amount of coincidence too great to be merely casual: otherwise
the illustration is not a fair one. No one supposes the agreement with
the phenomena of light with the theory of undulations to be merely
fortuitous. It must arise from the actual identity of some of the laws
of undulations with some of those of light: and if there be that
identity, it is reasonable to suppose that its consequences would not
end with the phenomena which first suggested the identification, nor be
even confined to such phenomena as were known at the time. But it does
not follow, because some of the laws agree with those of undulations,
that there are any actual undulations; no more than it followed because
some (though not so many) of the same laws agreed with those of the
projection of particles, that there was actual emission of particles.
Even the undulatory hypothesis does not account for all the phenomena of
light. The natural colours of objects, the compound nature of the solar
ray, the absorption of light, and its chemical and vital action, the
hypothesis leaves as mysterious as it found them; and some of these
facts are, at least apparently, more reconcileable with the emission
theory than with that of Young and Fresnel. Who knows but that some
third hypothesis, including all these phenomena, may in time leave the
undulatory theory as far behind as that has left the theory of Newton
and his successors?

To the statement, that the condition of accounting for all the known
phenomena is often fulfilled equally well by two conflicting hypotheses,
Dr. Whewell makes answer that he knows "of no such case in the history
of science, where the phenomena are at all numerous and complicated."[9]
Such an affirmation, by a writer of Dr. Whewell's minute acquaintance
with the history of science, would carry great authority, if he had
not, a few pages before, taken pains to refute it,[10] by maintaining
that even the exploded scientific hypotheses might always, or almost
always, have been so modified as to make them correct representations of
the phenomena. The hypothesis of vortices, he tells us, was, by
successive modifications, brought to coincide in its results with the
Newtonian theory and with the facts. The vortices did not indeed explain
all the phenomena which the Newtonian theory was ultimately found to
account for, such as the precession of the equinoxes; but this
phenomenon was not, at the time, in the contemplation of either party,
as one of the facts to be accounted for. All the facts which they did
contemplate, we may believe on Dr. Whewell's authority to have accorded
as accurately with the Cartesian hypothesis, in its finally improved
state, as with Newton's.

But it is not, I conceive, a valid reason for accepting any given
hypothesis, that we are unable to imagine any other which will account
for the facts. There is no necessity for supposing that the true
explanation must be one which, with only our present experience, we
could imagine. Among the natural agents with which we are acquainted,
the vibrations of an elastic fluid may be the only one whose laws bear a
close resemblance to those of light; but we cannot tell that there does
not exist an unknown cause, other than an elastic ether diffused through
space, yet producing effects identical in some respects with those which
would result from the undulations of such an ether. To assume that no
such cause can exist, appears to me an extreme case of assumption
without evidence.

I do not mean to condemn those who employ themselves in working out into
detail this sort of hypotheses; it is useful to ascertain what are the
known phenomena, to the laws of which those of the subject of inquiry
bear the greatest, or even a great analogy, since this may suggest (as
in the case of the luminiferous ether it actually did) experiments to
determine whether the analogy which goes so far does not extend still
further. But that, in doing this, we should imagine ourselves to be
seriously inquiring whether the hypothesis of an ether, an electric
fluid, or the like, is true; that we should fancy it possible to obtain
the assurance that the phenomena are produced in that way and no other;
seems to me, I confess, unworthy of the present improved conceptions of
the methods of physical science. And at the risk of being charged with
want of modesty, I cannot help expressing astonishment that a
philosopher of Dr. Whewell's abilities and attainments should have
written an elaborate treatise on the philosophy of induction, in which
he recognises absolutely no mode of induction except that of trying
hypothesis after hypothesis until one is found which fits the phenomena;
which one, when found, is to be assumed as true, with no other
reservation than that if on re-examination it should appear to assume
more than is needful for explaining the phenomena, the superfluous part
of the assumption should be cut off. And this without the slightest
distinction between the cases in which it may be known beforehand that
two different hypotheses cannot lead to the same result, and those in
which, for aught we can ever know, the range of suppositions, all
equally consistent with the phenomena, may be infinite.[11]

§ 7. It is necessary, before quitting the subject of hypotheses, to
guard against the appearance of reflecting upon the scientific value of
several branches of physical inquiry, which, though only in their
infancy, I hold to be strictly inductive. There is a great difference
between inventing agencies to account for classes of phenomena, and
endeavouring, in conformity with known laws, to conjecture what former
collocations of known agents may have given birth to individual facts
still in existence. The latter is the legitimate operation of inferring
from an observed effect, the existence, in time past, of a cause similar
to that by which we know it to be produced in all cases in which we have
actual experience of its origin. This, for example, is the scope of the
inquiries of geology; and they are no more illogical or visionary than
judicial inquiries, which also aim at discovering a past event by
inference from those of its effects which still subsist. As we can
ascertain whether a man was murdered or died a natural death, from the
indications exhibited by the corpse, the presence or absence of signs of
struggling on the ground or on the adjacent objects, the marks of
blood, the footsteps of the supposed murderers, and so on, proceeding
throughout on uniformities ascertained by a perfect induction without
any mixture of hypothesis; so if we find, on and beneath the surface of
our planet, masses exactly similar to deposits from water, or to results
of the cooling of matter melted by fire, we may justly conclude that
such has been their origin; and if the effects, though similar in kind,
are on a far larger scale than any which are now produced, we may
rationally, and without hypothesis, conclude either that the causes
existed formerly with greater intensity, or that they have operated
during an enormous length of time. Further than this no geologist of
authority has, since the rise of the present enlightened school of
geological speculation, attempted to go.

In many geological inquiries it doubtless happens that though the laws
to which the phenomena are ascribed are known laws, and the agents known
agents, those agents are not known to have been present in the
particular case. In the speculation respecting the igneous origin of
trap or granite, the fact does not admit of direct proof, that those
substances have been actually subjected to intense heat. But the same
thing might be said of all judicial inquiries which proceed on
circumstantial evidence. We can conclude that a man was murdered, though
it is not proved by the testimony of eye-witnesses that some person who
had the intention of murdering him was present on the spot. It is
enough, for most purposes, if no other known cause could have generated
the effects shown to have been produced.

The celebrated speculation of Laplace concerning the origin of the earth
and planets, participates essentially in the inductive character of
modern geological theory. The speculation is, that the atmosphere of the
sun originally extended to the present limits of the solar system; from
which, by the process of cooling, it has contracted to its present
dimensions; and since, by the general principles of mechanics, the
rotation of the sun and of its accompanying atmosphere must increase in
rapidity as its volume diminishes, the increased centrifugal force
generated by the more rapid rotation, overbalancing the action of
gravitation, has caused the sun to abandon successive rings of vaporous
matter, which are supposed to have condensed by cooling, and to have
become the planets. There is in this theory no unknown substance
introduced on supposition, nor any unknown property or law ascribed to a
known substance. The known laws of matter authorize us to suppose that a
body which is constantly giving out so large an amount of heat as the
sun is, must be progressively cooling, and that, by the process of
cooling, it must contract; if, therefore, we endeavour, from the present
state of that luminary, to infer its state in a time long past, we must
necessarily suppose that its atmosphere extended much farther than at
present, and we are entitled to suppose that it extended as far as we
can trace effects such as it might naturally leave behind it on
retiring; and such the planets are. These suppositions being made, it
follows from known laws that successive zones of the solar atmosphere
might be abandoned; that these would continue to revolve round the sun
with the same velocity as when they formed part of its substance; and
that they would cool down, long before the sun itself, to any given
temperature, and consequently to that at which the greater part of the
vaporous matter of which they consisted would become liquid or solid.
The known law of gravitation would then cause them to agglomerate in
masses, which would assume the shape our planets actually exhibit; would
acquire, each about its own axis, a rotatory movement; and would in that
state revolve, as the planets actually do, about the sun, in the same
direction with the sun's rotation, but with less velocity, because in
the same periodic time which the sun's rotation occupied when his
atmosphere extended to that point. There is thus, in Laplace's theory,
nothing, strictly speaking, hypothetical: it is an example of legitimate
reasoning from a present effect to a possible past cause, according to
the known laws of that cause. The theory therefore is, as I have said,
of a similar character to the theories of geologists; but considerably
inferior to them in point of evidence. Even if it were proved (which it
is not) that the conditions necessary for determining the breaking off
of successive rings would certainly occur; there would still be a much
greater chance of error in assuming that the existing laws of nature are
the same which existed at the origin of the solar system, than in merely
presuming (with geologists) that those laws have lasted through a few
revolutions and transformations of a single one among the bodies of
which that system is composed.



§ 1. In the last four chapters we have traced the general outlines of
the theory of the generation of derivative laws from ultimate ones. In
the present chapter our attention will be directed to a particular case
of the derivation of laws from other laws, but a case so general, and so
important, as not only to repay, but to require, a separate examination.
This is, the case of a complex phenomenon resulting from one simple law,
by the continual addition of an effect to itself.

There are some phenomena, some bodily sensations for example, which are
essentially instantaneous, and whose existence can only be prolonged by
the prolongation of the existence of the cause by which they are
produced. But most phenomena are in their own nature permanent; having
begun to exist, they would exist for ever unless some cause intervened
having a tendency to alter or destroy them. Such, for example, are all
the facts or phenomena which we call bodies. Water, once produced, will
not of itself relapse into a state of hydrogen and oxygen; such a change
requires some agent having the power of decomposing the compound. Such,
again, are the positions in space, and the movements, of bodies. No
object at rest alters its position without the intervention of some
conditions extraneous to itself; and when once in motion, no object
returns to a state of rest, or alters either its direction or its
velocity, unless some new external conditions are superinduced. It,
therefore, perpetually happens that a temporary cause gives rise to a
permanent effect. The contact of iron with moist air for a few hours,
produces a rust which may endure for centuries; or a projectile force
which launches a cannon ball into space, produces a motion which would
continue for ever unless some other force counteracted it.

Between the two examples which we have here given, there is a difference
worth pointing out. In the former (in which the phenomenon produced is a
substance, and not a motion of a substance), since the rust remains for
ever and unaltered unless some new cause supervenes, we may speak of the
contact of air a hundred years ago as even the proximate cause of the
rust which has existed from that time until now. But when the effect is
motion, which is itself a change, we must use a different language. The
permanency of the effect is now only the permanency of a series of
changes. The second foot, or inch, or mile of motion, is not the mere
prolonged duration of the first foot, or inch, or mile, but another fact
which succeeds, and which may in some respects be very unlike the
former, since it carries the body through a different region of space.
Now, the original projectile force which set the body moving is the
remote cause of all its motion, however long continued, but the
proximate cause of no motion except that which took place at the first
instant. The motion at any subsequent instant is proximately caused by
the motion which took place at the instant preceding. It is on that, and
not on the original moving cause, that the motion at any given moment
depends. For, suppose that the body passes through some resisting
medium, which partially counteracts the effect of the original impulse,
and retards the motion: this counteraction (it needs scarcely here be
repeated) is as strict an example of obedience to the law of the
impulse, as if the body had gone on moving with its original velocity;
but the motion which results is different, being now a compound of the
effects of two causes acting in contrary directions, instead of the
single effect of one cause. Now, what cause does the body obey in its
subsequent motion? The original cause of motion, or the actual motion at
the preceding instant? The latter: for when the object issues from the
resisting medium, it continues moving, not with its original, but with
its retarded velocity. The motion having once been diminished, all that
which follows is diminished. The effect changes, because the cause which
it really obeys, the proximate cause, the real cause in fact, has
changed. This principle is recognised by mathematicians when they
enumerate among the causes by which the motion of a body is at any
instant determined, the _force generated_ by the previous motion; an
expression which would be absurd if taken to imply that this "force" was
an intermediate link between the cause and the effect, but which really
means only the previous motion itself, considered as a cause of further
motion. We must, therefore, if we would speak with perfect precision,
consider each link in the succession of motions as the effect of the
link preceding it. But if, for the convenience of discourse, we speak of
the whole series as one effect, it must be as an effect produced by the
original impelling force; a permanent effect produced by an
instantaneous cause, and possessing the property of self-perpetuation.

Let us now suppose that the original agent or cause, instead of being
instantaneous, is permanent. Whatever effect has been produced up to a
given time, would (unless prevented by the intervention of some new
cause) subsist permanently, even if the cause were to perish. Since,
however, the cause does not perish, but continues to exist and to
operate, it must go on producing more and more of the effect; and
instead of an uniform effect, we have a progressive series of effects,
arising from the accumulated influence of a permanent cause. Thus, the
contact of iron with the atmosphere causes a portion of it to rust; and
if the cause ceased, the effect already produced would be permanent, but
no further effect would be added. If, however, the cause, namely,
exposure to moist air, continues, more and more of the iron becomes
rusted, until all which is exposed is converted into a red powder, when
one of the conditions of the production of rust, namely, the presence of
unoxidized iron, has ceased, and the effect cannot any longer be
produced. Again, the earth causes bodies to fall towards it, that is,
the existence of the earth at a given instant, causes an unsupported
body to move towards it at the succeeding instant: and if the earth were
annihilated, as much of the effect as is already produced would
continue; the object would go on moving in the same direction, with its
acquired velocity, until intercepted by some body or deflected by some
other force. The earth, however, not being annihilated, goes on
producing in the second instant an effect similar and of equal amount
with the first, which two effects being added together, there results an
accelerated velocity; and this operation being repeated at each
successive instant, the mere permanence of the cause, though without
increase, gives rise to a constant progressive increase of the effect,
so long as all the conditions, negative and positive, of the production
of that effect, continue to be realized.

It is obvious that this state of things is merely a case of the
Composition of Causes. A cause which continues in action, must on a
strict analysis be considered as a number of causes exactly similar,
successively introduced, and producing by their combination the sum of
the effects which they would severally produce if they acted singly. The
progressive rusting of the iron is in strictness the sum of the effects
of many particles of air acting in succession upon corresponding
particles of iron. The continued action of the earth upon a falling body
is equivalent to a series of forces, applied in successive instants,
each tending to produce a certain constant quantity of motion; and the
motion at each instant is the sum of the effects of the new force
applied at the preceding instant, and the motion already acquired. In
each instant, a fresh effect, of which gravity is the proximate cause,
is added to the effect of which it was the remote cause: or (to express
the same thing in another manner) the effect produced by the earth's
influence at the instant last elapsed, is added to the sum of the
effects of which the remote causes were the influences exerted by the
earth at all the previous instants since the motion began. The case,
therefore, comes under the principle of a concurrence of causes
producing an effect equal to the sum of their separate effects. But as
the causes come into play not all at once, but successively, and as the
effect at each instant is the sum of the effects of those causes only
which have come into action up to that instant, the result assumes the
form of an ascending series; a succession of sums, each greater than
that which preceded it; and we have thus a progressive effect from the
continued action of a cause.

Since the continuance of the cause influences the effect only by adding
to its quantity, and since the addition takes place according to a fixed
law (equal quantities in equal times), the result is capable of being
computed on mathematical principles. In fact, this case, being that of
infinitesimal increments, is precisely the case which the differential
calculus was invented to meet. The questions, what effect will result
from the continual addition of a given cause to itself, and what amount
of the cause, being continually added to itself, will produce a given
amount of the effect, are evidently mathematical questions, and to be
treated, therefore, deductively. If, as we have seen, cases of the
Composition of Causes are seldom adapted for any other than deductive
investigation, this is especially true in the case now examined, the
continual composition of a cause with its own previous effects; since
such a case is peculiarly amenable to the deductive method, while the
undistinguishable manner in which the effects are blended with one
another and with the causes, must make the treatment of such an instance
experimentally, still more chimerical than in any other case.

§ 2. We shall next advert to a rather more intricate operation of the
same principle, namely, when the cause does not merely continue in
action, but undergoes, during the same time, a progressive change in
those of its circumstances which contribute to determine the effect. In
this case, as in the former, the total effect goes on accumulating by
the continual addition of a fresh effect to that already produced, but
it is no longer by the addition of equal quantities in equal times; the
quantities added are unequal, and even the quality may now be different.
If the change in the state of the permanent cause be progressive, the
effect will go through a double series of changes, arising partly from
the accumulated action of the cause, and partly from the changes in its
action. The effect is still a progressive effect, produced however, not
by the mere continuance of a cause, but by its continuance and its
progressiveness combined.

A familiar example is afforded by the increase of the temperature as
summer advances, that is, as the sun draws nearer to a vertical
position, and remains a greater number of hours above the horizon. This
instance exemplifies in a very interesting manner the twofold operation
on the effect, arising from the continuance of the cause, and from its
progressive change. When once the sun has come near enough to the
zenith, and remains above the horizon long enough, to give more warmth
during one diurnal rotation than the counteracting cause, the earth's
radiation, can carry off, the mere continuance of the cause would
progressively increase the effect, even if the sun came no nearer and
the days grew no longer; but in addition to this, a change takes place
in the accidents of the cause (its series of diurnal positions), tending
to increase the quantity of the effect. When the summer solstice has
passed, the progressive change in the cause begins to take place the
reverse way; but, for some time, the accumulating effect of the mere
continuance of the cause exceeds the effect of the changes in it, and
the temperature continues to increase.

Again, the motion of a planet is a progressive effect, produced by
causes at once permanent and progressive. The orbit of a planet is
determined (omitting perturbations) by two causes: first, the action of
the central body, a permanent cause, which alternately increases and
diminishes as the planet draws nearer to or goes further from its
perihelion, and which acts at every point in a different direction; and,
secondly, the tendency of the planet to continue moving in the direction
and with the velocity which it has already acquired. This force also
grows greater as the planet draws nearer to its perihelion, because as
it does so its velocity increases; and less, as it recedes from its
perihelion: and this force as well as the other acts at each point in a
different direction, because at every point the action of the central
force, by deflecting the planet from its previous direction, alters the
line in which it tends to continue moving. The motion at each instant is
determined by the amount and direction of the motion, and the amount
and direction of the sun's action, at the previous instant: and if we
speak of the entire revolution of the planet as one phenomenon (which,
as it is periodical and similar to itself, we often find it convenient
to do,) that phenomenon is the progressive effect of two permanent and
progressive causes, the central force and the acquired motion. Those
causes happening to be progressive in the particular way which is called
periodical, the effect necessarily is so too; because the quantities to
be added together returning in a regular order, the same sums must also
regularly return.

This example is worthy of consideration also in another respect. Though
the causes themselves are permanent, and independent of all conditions
known to us, the changes which take place in the quantities and
relations of the causes are actually caused by the periodical changes in
the effects. The causes, as they exist at any moment, having produced a
certain motion, that motion, becoming itself a cause, reacts upon the
causes, and produces a change in them. By altering the distance and
direction of the central body relatively to the planet, and the
direction and quantity of the force in the direction of the tangent, it
alters the elements which determine the motion at the next succeeding
instant. This change renders the next motion somewhat different; and
this difference, by a fresh reaction upon the causes, renders the next
motion again different, and so on. The original state of the causes
might have been such, that this series of actions modified by reactions
would not have been periodical. The sun's action, and the original
impelling force, might have been in such a ratio to one another, that
the reaction of the effect would have been such as to alter the causes
more and more, without ever bringing them back to what they were at any
former time. The planet would then have moved in a parabola, or an
hyperbola, curves not returning into themselves. The quantities of the
two forces were, however, originally such, that the successive reactions
of the effect bring back the causes, after a certain time, to what they
were before; and from that time all the variations continue to recur
again and again in the same periodical order, and must so continue
while the causes subsist and are not counteracted.

§ 3. In all cases of progressive effects, whether arising from the
accumulation of unchanging or of changing elements, there is an
uniformity of succession not merely between the cause and the effect,
but between the first stages of the effect and its subsequent stages.
That a body _in vacuo_ falls sixteen feet in the first second,
forty-eight in the second, and so on in the ratio of the odd numbers, is
as much an uniform sequence as that when the supports are removed the
body falls. The sequence of spring and summer is as regular and
invariable as that of the approach of the sun and spring: but we do not
consider spring to be the cause of summer; it is evident that both are
successive effects of the heat received from the sun, and that,
considered merely in itself, spring might continue for ever, without
having the slightest tendency to produce summer. As we have so often
remarked, not the conditional, but the unconditional invariable
antecedent is termed the cause. That which would not be followed by the
effect unless something else had preceded, is not the cause, however
invariable the sequence may in fact be.

It is in this way that most of those uniformities of succession are
generated, which are not cases of causation. When a phenomenon goes on
increasing, or periodically increases and diminishes, or goes through
any continued and unceasing process of variation reducible to an uniform
rule or law of succession, we do not on this account presume that any
two successive terms of the series are cause and effect. We presume the
contrary; we expect to find that the whole series originates either from
the continued action of fixed causes, or from causes which go through a
corresponding process of continuous change. A tree grows from half an
inch high to a hundred feet; and some trees will generally grow to that
height, unless prevented by some counteracting cause. But we do not call
the seedling the cause of the full-grown tree; the invariable antecedent
it certainly is, and we know very imperfectly on what other antecedents
the sequence is contingent, but we are convinced that it is contingent
on something; because the homogeneousness of the antecedent with the
consequent, the close resemblance of the seedling to the tree in all
respects except magnitude, and the graduality of the growth, so exactly
resembling the progressively accumulating effect produced by the long
action of some one cause, leave no possibility of doubting that the
seedling and the tree are two terms in a series of that description, the
first term of which is yet to seek. The conclusion is further confirmed
by this, that we are able to prove by strict induction the dependence of
the growth of the tree, and even of the continuance of its existence,
upon the continued repetition of certain processes of nutrition, the
rise of the sap, the absorptions and exhalations by the leaves, &c.; and
the same experiments would probably prove to us that the growth of the
tree is the accumulated sum of the effects of these continued processes,
were we not, for want of sufficiently microscopic eyes, unable to
observe correctly and in detail what those effects are.

This supposition by no means requires that the effect should not, during
its progress, undergo many modifications besides those of quantity, or
that it should not sometimes appear to undergo a very marked change of
character. This may be either because the unknown cause consists of
several component elements or agents, whose effects, accumulating
according to different laws, are compounded in different proportions at
different periods in the existence of the organized being; or because,
at certain points in its progress, fresh causes or agencies come in, or
are evolved, which intermix their laws with those of the prime agent.



§ 1. Scientific inquirers give the name of Empirical Laws to those
uniformities which observation or experiment has shown to exist, but on
which they hesitate to rely in cases varying much from those which have
been actually observed, for want of seeing any reason _why_ such a law
should exist. It is implied, therefore, in the notion of an empirical
law, that it is not an ultimate law; that if true at all, its truth is
capable of being, and requires to be, accounted for. It is a derivative
law, the derivation of which is not yet known. To state the explanation,
the _why_, of the empirical law, would be to state the laws from which
it is derived; the ultimate causes on which it is contingent. And if we
knew these, we should also know what are its limits; under what
conditions it would cease to be fulfilled.

The periodical return of eclipses, as originally ascertained by the
persevering observation of the early eastern astronomers, was an
empirical law, until the general laws of the celestial motions had
accounted for it. The following are empirical laws still waiting to be
resolved into the simpler laws from which they are derived. The local
laws of the flux and reflux of the tides in different places: the
succession of certain kinds of weather to certain appearances of sky:
the apparent exceptions to the almost universal truth that bodies expand
by increase of temperature: the law that breeds, both animal and
vegetable, are improved by crossing: that gases have a strong tendency
to permeate animal membranes: that substances containing a very high
proportion of nitrogen (such as hydrocyanic acid and morphia) are
powerful poisons: that when different metals are fused together, the
alloy is harder than the various elements: that the number of atoms of
acid required to neutralize one atom of any base, is equal to the number
of atoms of oxygen in the base: that the solubility of substances in one
another, depends[12] (at least in some degree) on the similarity of
their elements.

An empirical law, then, is an observed uniformity, presumed to be
resolvable into simpler laws, but not yet resolved into them. The
ascertainment of the empirical laws of phenomena often precedes by a
long interval the explanation of those laws by the Deductive Method; and
the verification of a deduction usually consists in the comparison of
its results with empirical laws previously ascertained.

§ 2. From a limited number of ultimate laws of causation, there are
necessarily generated a vast number of derivative uniformities, both of
succession and of coexistence. Some are laws of succession or of
coexistence between different effects of the same cause: of these we had
examples in the last chapter. Some are laws of succession between
effects and their remote causes; resolvable into the laws which connect
each with the intermediate link. Thirdly, when causes act together and
compound their effects, the laws of those causes generate the
fundamental law of the effect, namely, that it depends on the
coexistence of those causes. And, finally, the order of succession or of
coexistence which obtains among effects, necessarily depends on their
causes. If they are effects of the same cause, it depends on the laws of
that cause; if on different causes, it depends on the laws of those
causes severally, and on the circumstances which determine their
coexistence. If we inquire further when and how the causes will
coexist, that, again, depends on _their_ causes: and we may thus trace
back the phenomena higher and higher, until the different series of
effects meet in a point, and the whole is shown to have depended
ultimately on some common cause; or until, instead of converging to one
point, they terminate in different points, and the order of the effects
is proved to have arisen from the collocation of some of the primeval
causes, or natural agents. For example, the order of succession and of
coexistence among the heavenly motions, which is expressed by Kepler's
laws, is derived from the coexistence of two primeval causes, the sun,
and the original impulse or projectile force belonging to each
planet.[13] Kepler's laws are resolved into the laws of these causes and
the fact of their coexistence.

Derivative laws, therefore, do not depend solely on the ultimate laws
into which they are resolvable: they mostly depend on those ultimate
laws, and an ultimate fact; namely, the mode of coexistence of some of
the component elements of the universe. The ultimate laws of causation
might be the same as at present, and yet the derivative laws completely
different, if the causes coexisted in different proportions, or with any
difference in those of their relations by which the effects are
influenced. If, for example, the sun's attraction, and the original
projectile force, had existed in some other ratio to one another than
they did (and we know of no reason why this should not have been the
case), the derivative laws of the heavenly motions might have been quite
different from what they are. The proportions which exist happen to be
such as to produce regular elliptical motions; any other proportions
would have produced different ellipses, or circular, or parabolic, or
hyperbolic motions, but still regular ones; because the effects of each
of the agents accumulate according to an uniform law; and two regular
series of quantities, when their corresponding terms are added, must
produce a regular series of some sort, whatever the quantities
themselves are.

§ 3. Now this last-mentioned element in the resolution of a derivative
law, the element which is not a law of causation, but a collocation of
causes, cannot itself be reduced to any law. There is (as formerly
remarked[14]) no uniformity, no _norma_, principle, or rule, perceivable
in the distribution of the primeval natural agents through the universe.
The different substances composing the earth, the powers that pervade
the universe, stand in no constant relation to one another. One
substance is more abundant than others, one power acts through a larger
extent of space than others, without any pervading analogy that we can
discover. We not only do not know of any reason why the sun's attraction
and the force in the direction of the tangent coexist in the exact
proportion they do, but we can trace no coincidence between it and the
proportions in which any other elementary powers in the universe are
intermingled. The utmost disorder is apparent in the combination of the
causes; which is consistent with the most regular order in their
effects; for when each agent carries on its own operations according to
an uniform law, even the most capricious combination of agencies will
generate a regularity of some sort; as we see in the kaleidoscope, where
any casual arrangement of coloured bits of glass produces by the laws of
reflection a beautiful regularity in the effect.

§ 4. In the above considerations lies the justification of the limited
degree of reliance which scientific inquirers are accustomed to place in
empirical laws.

A derivative law which results wholly from the operation of some one
cause, will be as universally true as the laws of the cause itself; that
is, it will always be true except where some one of those effects of the
cause, on which the derivative law depends, is defeated by a
counteracting cause. But when the derivative law results not from
different effects of one cause, but from effects of several causes, we
cannot be certain that it will be true under any variation in the mode
of coexistence of those causes, or of the primitive natural agents on
which the causes ultimately depend. The proposition that coal beds rest
on certain descriptions of strata exclusively, though true on the earth
so far as our observation has reached, cannot be extended to the moon or
the other planets, supposing coal to exist there; because we cannot be
assured that the original constitution of any other planet was such as
to produce the different depositions in the same order as in our globe.
The derivative law in this case depends not solely on laws, but on a
collocation; and collocations cannot be reduced to any law.

Now it is the very nature of a derivative law which has not yet been
resolved into its elements, in other words, an empirical law, that we do
not know whether it results from the different effects of one cause, or
from effects of different causes. We cannot tell whether it depends
wholly on laws, or partly on laws and partly on a collocation. If it
depends on a collocation, it will be true in all the cases in which that
particular collocation exists. But, since we are entirely ignorant, in
case of its depending on a collocation, what the collocation is, we are
not safe in extending the law beyond the limits of time and place in
which we have actual experience of its truth. Since within those limits
the law has always been found true, we have evidence that the
collocations, whatever they are, on which it depends, do really exist
within those limits. But, knowing of no rule or principle to which the
collocations themselves conform, we cannot conclude that because a
collocation is proved to exist within certain limits of place or time,
it will exist beyond those limits. Empirical laws, therefore, can only
be received as true within the limits of time and place in which they
have been found true by observation: and not merely the limits of time
and place, but of time, place, and circumstance: for since it is the
very meaning of an empirical law that we do not know the ultimate laws
of causation on which it is dependent, we cannot foresee, without actual
trial, in what manner or to what extent the introduction of any new
circumstance may affect it.

§ 5. But how are we to know that an uniformity, ascertained by
experience, is only an empirical law? Since, by the supposition, we have
not been able to resolve it into any other laws, how do we know that it
is not an ultimate law of causation?

I answer, that no generalization amounts to more than an empirical law
when the only proof on which it rests is that of the Method of
Agreement. For it has been seen that by that method alone we never can
arrive at causes. The utmost that the Method of Agreement can do is, to
ascertain the whole of the circumstances common to all cases in which a
phenomenon is produced: and this aggregate includes not only the cause
of the phenomenon, but all phenomena with which it is connected by any
derivative uniformity, whether as being collateral effects of the same
cause, or effects of any other cause which, in all the instances we have
been able to observe, coexisted with it. The method affords no means of
determining which of these uniformities are laws of causation, and which
are merely derivative laws, resulting from those laws of causation and
from the collocation of the causes. None of them, therefore, can be
received in any other character than that of derivative laws, the
derivation of which has not been traced; in other words, empirical laws:
in which light, all results obtained by the Method of Agreement (and
therefore almost all truths obtained by simple observation without
experiment) must be considered, until either confirmed by the Method of
Difference, or explained deductively, in other words accounted for _à

These empirical laws may be of greater or less authority, according as
there is reason to presume that they are resolvable into laws only, or
into laws and collocations together. The sequences which we observe in
the production and subsequent life of an animal or a vegetable, resting
on the Method of Agreement only, are mere empirical laws; but though the
antecedents in those sequences may not be the causes of the consequents,
both the one and the other are doubtless, in the main, successive stages
of a progressive effect originating in a common cause, and therefore
independent of collocations. The uniformities, on the other hand, in the
order of superposition of strata on the earth, are empirical laws of a
much weaker kind, since they not only are not laws of causation, but
there is no reason to believe that they depend on any common cause: all
appearances are in favour of their depending on the particular
collocation of natural agents which at some time or other existed on our
globe, and from which no inference can be drawn as to the collocation
which exists or has existed in any other portion of the universe.

§ 6. Our definition of an empirical law including not only those
uniformities which are not known to be laws of causation, but also those
which are, provided there be reason to presume that they are not
ultimate laws; this is the proper place to consider by what signs we may
judge that even if an observed uniformity be a law of causation, it is
not an ultimate but a derivative law.

The first sign is, if between the antecedent _a_ and the consequent _b_
there be evidence of some intermediate link; some phenomenon of which we
can surmise the existence, though from the imperfection of our senses or
of our instruments we are unable to ascertain its precise nature and
laws. If there be such a phenomenon (which may be denoted by the letter
_x_), it follows that even if _a_ be the cause of _b_, it is but the
remote cause, and that the law, _a_ causes _b_, is resolvable into at
least two laws, _a_ causes _x_, and _x_ causes _b_. This is a very
frequent case, since the operations of nature mostly take place on so
minute a scale, that many of the successive steps are either
imperceptible, or very indistinctly perceived.

Take, for example, the laws of the chemical composition of substances;
as that hydrogen and oxygen being combined, water is produced. All we
see of the process is, that the two gases being mixed in certain
proportions, and heat or electricity being applied, an explosion takes
place, the gases disappear, and water remains. There is no doubt about
the law, or about its being a law of causation. But between the
antecedent (the gases in a state of mechanical mixture, heated or
electrified), and the consequent (the production of water), there must
be an intermediate process which we do not see. For if we take any
portion whatever of the water, and subject it to analysis, we find that
it always contains hydrogen and oxygen; nay, the very same proportions
of them, namely, two thirds, in volume, of hydrogen, and one third
oxygen. This is true of a single drop; it is true of the minutest
portion which our instruments are capable of appreciating. Since, then,
the smallest perceptible portion of the water contains both those
substances, portions of hydrogen and oxygen smaller than the smallest
perceptible must have come together in every such minute portion of
space; must have come closer together than when the gases were in a
state of mechanical mixture, since (to mention no other reasons) the
water occupies far less space than the gases. Now, as we cannot see this
contact or close approach of the minute particles, we cannot observe
with what circumstances it is attended, or according to what laws it
produces its effects. The production of water, that is, of the sensible
phenomena which characterize the compound, may be a very remote effect
of those laws. There may be innumerable intervening links; and we are
sure that there must be some. Having full proof that corpuscular action
of some kind takes place previous to any of the great transformations in
the sensible properties of substances, we can have no doubt that the
laws of chemical action, as at present known, are not ultimate but
derivative laws; however ignorant we may be, and even though we should
for ever remain ignorant, of the nature of the laws of corpuscular
action from which they are derived.

In like manner, all the processes of vegetative life, whether in the
vegetable properly so called or in the animal body, are corpuscular
processes. Nutrition is the addition of particles to one another,
sometimes merely replacing other particles separated and excreted,
sometimes occasioning an increase of bulk or weight, so gradual, that
only after a long continuance does it become perceptible. Various
organs, by means of peculiar vessels, secrete from the blood, fluids,
the component particles of which must have been in the blood, but which
differ from it most widely both in mechanical properties and in chemical
composition. Here, then, are abundance of unknown links to be filled up;
and there can be no doubt that the laws of the phenomena of vegetative
or organic life are derivative laws, dependent on properties of the
corpuscles, and of those elementary tissues which are comparatively
simple combinations of corpuscles.

The first sign, then, from which a law of causation, though hitherto
unresolved, may be inferred to be a derivative law, is any indication of
the existence of an intermediate link or links between the antecedent
and the consequent. The second is, when the antecedent is an extremely
complex phenomenon, and its effects therefore, probably, in part at
least, compounded of the effects of its different elements; since we
know that the case in which the effect of the whole is not made up of
the effects of its parts, is exceptional, the Composition of Causes
being by far the more ordinary case.

We will illustrate this by two examples, in one of which the antecedent
is the sum of many homogeneous, in the other of heterogeneous, parts.
The weight of a body is made up of the weights of its minute particles:
a truth which astronomers express in its most general terms, when they
say that bodies, at equal distances, gravitate to one another in
proportion to their quantity of matter. All true propositions,
therefore, which can be made concerning gravity, are derivative laws;
the ultimate law into which they are all resolvable being, that every
particle of matter attracts every other. As our second example, we may
take any of the sequences observed in meteorology: for instance, a
diminution of the pressure of the atmosphere (indicated by a fall of the
barometer) is followed by rain. The antecedent is here a complex
phenomenon, made up of heterogeneous elements; the column of the
atmosphere over any particular place consisting of two parts, a column
of air, and a column of aqueous vapour mixed with it; and the change in
the two together manifested by a fall of the barometer, and followed by
rain, must be either a change in one of these, or in the other, or in
both. We might, then, even in the absence of any other evidence, form a
reasonable presumption, from the invariable presence of both these
elements in the antecedent, that the sequence is probably not an
ultimate law, but a result of the laws of the two different agents; a
presumption only to be destroyed when we had made ourselves so well
acquainted with the laws of both, as to be able to affirm that those
laws could not by themselves produce the observed result.

There are but few known cases of succession from very complex
antecedents, which have not either been actually accounted for from
simpler laws, or inferred with great probability (from the ascertained
existence of intermediate links of causation not yet understood) to be
capable of being so accounted for. It is, therefore, highly probable
that all sequences from complex antecedents are thus resolvable, and
that ultimate laws are in all cases comparatively simple. If there were
not the other reasons already mentioned for believing that the laws of
organized nature are resolvable into simpler laws, it would be almost a
sufficient reason that the antecedents in most of the sequences are so
very complex.

§ 7. In the preceding discussion we have recognised two kinds of
empirical laws: those known to be laws of causation, but presumed to be
resolvable into simpler laws; and those not known to be laws of
causation at all. Both these kinds of laws agree in the demand which
they make for being explained by deduction, and agree in being the
appropriate means of verifying such deduction, since they represent the
experience with which the result of the deduction must be compared. They
agree, further, in this, that until explained, and connected with the
ultimate laws from which they result, they have not attained the highest
degree of certainty of which laws are susceptible. It has been shown on
a former occasion that laws of causation which are derivative, and
compounded of simpler laws, are not only, as the nature of the case
implies, less general, but even less certain, than the simpler laws
from which they result; not in the same degree to be relied on as
universally true. The inferiority of evidence, however, which attaches
to this class of laws, is trifling, compared with that which is inherent
in uniformities not known to be laws of causation at all. So long as
these are unresolved, we cannot tell on how many collocations, as well
as laws, their truth may be dependent; we can never, therefore, extend
them with any confidence to cases in which we have not assured
ourselves, by trial, that the necessary collocation of causes, whatever
it may be, exists. It is to this class of laws alone that the property,
which philosophers usually consider as characteristic of empirical laws,
belongs in all its strictness; the property of being unfit to be relied
on beyond the limits of time, place, and circumstance, in which the
observations have been made. These are empirical laws in a more emphatic
sense; and when I employ that term (except where the context manifestly
indicates the reverse) I shall generally mean to designate those
uniformities only, whether of succession or of coexistence, which are
not known to be laws of causation.



§ 1. Considering then as empirical laws only those observed uniformities
respecting which the question whether they are laws of causation must
remain undecided until they can be explained deductively, or until some
means are found of applying the Method of Difference to the case, it has
been shown in the preceding chapter, that until an uniformity can, in
one or the other of these modes, be taken out of the class of empirical
laws, and brought either into that of laws of causation or of the
demonstrated results of laws of causation, it cannot with any assurance
be pronounced true beyond the local and other limits within which it has
been found so by actual observation. It remains to consider how we are
to assure ourselves of its truth even within those limits; after what
quantity of experience a generalization which rests solely on the Method
of Agreement, can be considered sufficiently established, even as an
empirical law. In a former chapter, when treating of the Methods of
Direct Induction, we expressly reserved this question,[15] and the time
is now come for endeavouring to solve it.

We found that the Method of Agreement has the defect of not proving
causation, and can therefore only be employed for the ascertainment of
empirical laws. But we also found that besides this deficiency, it
labours under a characteristic imperfection, tending to render uncertain
even such conclusions as it is in itself adapted to prove. This
imperfection arises from Plurality of Causes. Although two or more cases
in which the phenomenon _a_ has been met with, may have no common
antecedent except A, this does not prove that there is any connexion
between _a_ and A, since _a_ may have many causes, and may have been
produced, in these different instances, not by anything which the
instances had in common, but by some of those elements in them which
were different. We nevertheless observed, that in proportion to the
multiplication of instances pointing to A as the antecedent, the
characteristic uncertainty of the method diminishes, and the existence
of a law of connexion between A and _a_ more nearly approaches to
certainty. It is now to be determined, after what amount of experience
this certainty may be deemed to be practically attained, and the
connexion between A and _a_ may be received as an empirical law.

This question may be otherwise stated in more familiar terms:--After how
many and what sort of instances may it be concluded, that an observed
coincidence between two phenomena is not the effect of chance?

It is of the utmost importance for understanding the logic of induction,
that we should form a distinct conception of what is meant by chance,
and how the phenomena which common language ascribes to that abstraction
are really produced.

§ 2. Chance is usually spoken of in direct antithesis to law; whatever
(it is supposed) cannot be ascribed to any law, is attributed to chance.
It is, however, certain, that whatever happens is the result of some
law; is an effect of causes, and could have been predicted from a
knowledge of the existence of those causes, and from their laws. If I
turn up a particular card, that is a consequence of its place in the
pack. Its place in the pack was a consequence of the manner in which the
cards were shuffled, or of the order in which they were played in the
last game; which, again, were effects of prior causes. At every stage,
if we had possessed an accurate knowledge of the causes in existence, it
would have been abstractedly possible to foretell the effect.

An event occurring by chance, may be better described as a coincidence
from which we have no ground to infer an uniformity: the occurrence of a
phenomenon in certain circumstances, without our having reason on that
account to infer that it will happen again in those circumstances. This,
however, when looked closely into, implies that the enumeration of the
circumstances is not complete. Whatever the fact be, since it has
occurred once, we may be sure that if _all_ the same circumstances were
repeated, it would occur again; and not only if all, but there is some
particular portion of those circumstances, on which the phenomenon is
invariably consequent. With most of them, however, it is not connected
in any permanent manner: its conjunction with those is said to be the
effect of chance, to be merely casual. Facts casually conjoined are
separately the effects of causes, and therefore of laws; but of
different causes, and causes not connected by any law.

It is incorrect, then, to say that any phenomenon is produced by chance;
but we may say that two or more phenomena are conjoined by chance, that
they coexist or succeed one another only by chance: meaning that they
are in no way related through causation; that they are neither cause and
effect, nor effects of the same cause, nor effects of causes between
which there subsists any law of coexistence, nor even effects of the
same collocation of primeval causes.

If the same casual coincidence never occurred a second time, we should
have an easy test for distinguishing such from the coincidences which
are the results of a law. As long as the phenomena had been found
together only once, so long, unless we knew some more general laws from
which the coincidence might have resulted, we could not distinguish it
from a casual one; but if it occurred twice, we should know that the
phenomena so conjoined must be in some way connected through their

There is, however, no such test. A coincidence may occur again and
again, and yet be only casual. Nay, it would be inconsistent with what
we know of the order of nature, to doubt that every casual coincidence
will sooner or later be repeated, as long as the phenomena between which
it occurred do not cease to exist, or to be reproduced. The recurrence,
therefore, of the same coincidence more than once, or even its frequent
recurrence, does not prove that it is an instance of any law; does not
prove that it is not casual, or, in common language, the effect of

And yet, when a coincidence cannot be deduced from known laws, nor
proved by experiment to be itself a case of causation, the frequency of
its occurrence is the only evidence from which we can infer that it is
the result of a law. Not, however, its absolute frequency. The question
is not whether the coincidence occurs often or seldom, in the ordinary
sense of those terms; but whether it occurs more often than chance will
account for; more often than might rationally be expected if the
coincidence were casual. We have to decide, therefore, what degree of
frequency in a coincidence, chance will account for. And to this there
can be no general answer. We can only state the principle by which the
answer must be determined: the answer itself will be different in every
different case.

Suppose that one of the phenomena, A, exists always, and the other
phenomenon, B, only occasionally: it follows that every instance of B
will be an instance of its coincidence with A, and yet the coincidence
will be merely casual, not the result of any connexion between them. The
fixed stars have been constantly in existence since the beginning of
human experience, and all phenomena that have come under human
observation have, in every single instance, coexisted with them; yet
this coincidence, though equally invariable with that which exists
between any of those phenomena and its own cause, does not prove that
the stars are its cause, nor that they are in anywise connected with it.
As strong a case of coincidence, therefore, as can possibly exist, and a
much stronger one in point of mere frequency than most of those which
prove laws, does not here prove a law: why? because, since the stars
exist always, they _must_ coexist with every other phenomenon, whether
connected with them by causation or not. The uniformity, great though it
be, is no greater than would occur on the supposition that no such
connexion exists.

On the other hand, suppose that we were inquiring whether there be any
connexion between rain and any particular wind. Rain, we know,
occasionally occurs with every wind; therefore the connexion, if it
exists, cannot be an actual law; but still, rain may be connected with
some particular wind through causation; that is, though they cannot be
always effects of the same cause (for if so they would regularly
coexist), there may be some causes common to the two, so that in so far
as either is produced by those common causes, they will, from the laws
of the causes, be found to coexist. How, then, shall we ascertain this?
The obvious answer is, by observing whether rain occurs with one wind
more frequently than with any other. That, however, is not enough; for
perhaps that one wind blows more frequently than any other; so that its
blowing more frequently in rainy weather is no more than would happen,
although it had no connexion with the causes of rain, provided it were
not connected with causes adverse to rain. In England, westerly winds
blow during about twice as great a portion of the year as easterly. If,
therefore, it rains only twice as often with a westerly, as with an
easterly wind, we have no reason to infer that any law of nature is
concerned in the coincidence. If it rains more than twice as often, we
may be sure that some law is concerned; either there is some cause in
nature which, in this climate, tends to produce both rain and a westerly
wind, or a westerly wind has itself some tendency to produce rain. But
if it rains less than twice as often, we may draw a directly opposite
inference: the one, instead of being a cause, or connected with causes,
of the other, must be connected with causes adverse to it, or with the
absence of some cause which produces it; and though it may still rain
much oftener with a westerly wind than with an easterly, so far would
this be from proving any connexion between the phenomena, that the
connexion proved would be between rain and an easterly wind, to which,
in mere frequency of coincidence, it is less allied.

Here, then, are two examples: in one, the greatest possible frequency of
coincidence, with no instance whatever to the contrary, does not prove
that there is any law; in the other, a much less frequency of
coincidence, even when non-coincidence is still more frequent, does
prove that there is a law. In both cases the principle is the same. In
both we consider the positive frequency of the phenomena themselves, and
how great frequency of coincidence that must of itself bring about,
without supposing any connexion between them, provided there be no
repugnance; provided neither be connected with any cause tending to
frustrate the other. If we find a greater frequency of coincidence than
this, we conclude that there is some connexion; if a less frequency,
that there is some repugnance. In the former case, we conclude that one
of the phenomena can under some circumstances cause the other, or that
there exists something capable of causing them both; in the latter, that
one of them, or some cause which produces one of them, is capable of
counteracting the production of the other. We have thus to deduct from
the observed frequency of coincidence, as much as may be the effect of
chance, that is, of the mere frequency of the phenomena themselves; and
if anything remains, what does remain is the residual fact which proves
the existence of a law.

The frequency of the phenomena can only be ascertained within definite
limits of space and time; depending as it does on the quantity and
distribution of the primeval natural agents, of which we can know
nothing beyond the boundaries of human observation, since no law, no
regularity, can be traced in it, enabling us to infer the unknown from
the known. But for the present purpose this is no disadvantage, the
question being confined within the same limits as the data. The
coincidences occurred in certain places and times, and within those we
can estimate the frequency with which such coincidences would be
produced by chance. If, then, we find from observation that A exists in
one case out of every two, and B in one case out of every three; then if
there be neither connexion nor repugnance between them, or between any
of their causes, the instances in which A and B will both exist, that is
to say will coexist, will be one case in every six. For A exists in
three cases out of six: and B, existing in one case out of every three
without regard to the presence or absence of A, will exist in one case
out of those three. There will therefore be, of the whole number of
cases, two in which A exists without B; one case of B without A; two in
which neither B nor A exists, and one case out of six in which they both
exist. If then, in point of fact, they are found to coexist oftener than
in one case out of six; and, consequently, A does not exist without B so
often as twice in three times, nor B without A so often as once in every
twice; there is some cause in existence which tends to produce a
conjunction between A and B.

Generalizing the result, we may say, that if A occurs in a larger
proportion of the cases where B is, than of the cases where B is not;
then will B also occur in a larger proportion of the cases where A is,
than of the cases where A is not; and there is some connexion, through
causation, between A and B. If we could ascend to the causes of the two
phenomena, we should find, at some stage, either proximate or remote,
some cause or causes common to both; and if we could ascertain what
these are, we could frame a generalization which would be true without
restriction of place or time: but until we can do so, the fact of a
connexion between the two phenomena remains an empirical law.

§ 3. Having considered in what manner it may be determined whether any
given conjunction of phenomena is casual, or the result of some law; to
complete the theory of chance, it is necessary that we should now
consider those effects which are partly the result of chance and partly
of law, or, in other words, in which the effects of casual conjunctions
of causes are habitually blended in one result with the effects of a
constant cause.

This is a case of Composition of Causes; and the peculiarity of it is,
that instead of two or more causes intermixing their effects in a
regular manner with those of one another, we have now one constant
cause, producing an effect which is successively modified by a series of
variable causes. Thus, as summer advances, the approach of the sun to a
vertical position tends to produce a constant increase of temperature;
but with this effect of a constant cause, there are blended the effects
of many variable causes, winds, clouds, evaporation, electric agencies
and the like, so that the temperature of any given day depends in part
on these fleeting causes, and only in part on the constant cause. If the
effect of the constant cause is always accompanied and disguised by
effects of variable causes, it is impossible to ascertain the law of the
constant cause in the ordinary manner, by separating it from all other
causes and observing it apart. Hence arises the necessity of an
additional rule of experimental inquiry.

When the action of a cause A is liable to be interfered with, not
steadily by the same cause or causes, but by different causes at
different times, and when these are so frequent, or so indeterminate,
that we cannot possibly exclude all of them from any experiment, though
we may vary them; our resource is, to endeavour to ascertain what is the
effect of all the variable causes taken together. In order to do this,
we make as many trials as possible, preserving A invariable. The results
of these different trials will naturally be different, since the
indeterminate modifying causes are different in each: if, then, we do
not find these results to be progressive, but, on the contrary, to
oscillate about a certain point, one experiment giving a result a little
greater, another a little less, one a result tending a little more in
one direction, another a little more in the contrary direction; while
the average or middle point does not vary, but different sets of
experiments (taken in as great a variety of circumstances as possible)
yield the same mean, provided only they be sufficiently numerous; then
that mean or average result, is the part, in each experiment, which is
due to the cause A, and is the effect which would have been obtained if
A could have acted alone: the variable remainder is the effect of
chance, that is, of causes the coexistence of which with the cause A was
merely casual. The test of the sufficiency of the induction in this case
is, when any increase of the number of trials from which the average is
struck, does not materially alter the average.

This kind of elimination, in which we do not eliminate any one
assignable cause, but the multitude of floating unassignable ones, may
be termed the Elimination of Chance. We afford an example of it when we
repeat an experiment, in order, by taking the mean of different results,
to get rid of the effects of the unavoidable errors of each individual
experiment. When there is no permanent cause such as would produce a
tendency to error peculiarly in one direction, we are warranted by
experience in assuming that the errors on one side will, in a certain
number of experiments, about balance the errors on the contrary side. We
therefore repeat the experiment, until any change which is produced in
the average of the whole by further repetition, falls within limits of
error consistent with the degree of accuracy required by the purpose we
have in view.[16]

§ 4. In the supposition hitherto made, the effect of the constant cause
A has been assumed to form so great and conspicuous a part of the
general result, that its existence never could be a matter of
uncertainty, and the object of the eliminating process was only to
ascertain _how much_ is attributable to that cause; what is its exact
law. Cases, however, occur in which the effect of a constant cause is so
small, compared with that of some of the changeable causes with which
it is liable to be casually conjoined, that of itself it escapes
notice, and the very existence of any effect arising from a constant
cause is first learnt, by the process which in general serves only for
ascertaining the quantity of that effect. This case of induction may be
characterized as follows. A given effect is known to be chiefly, and not
known not to be wholly, determined by changeable causes. If it be wholly
so produced, then if the aggregate be taken of a sufficient number of
instances, the effects of these different causes will cancel one
another. If, therefore, we do not find this to be the case, but, on the
contrary, after such a number of trials has been made that no further
increase alters the average result, we find that average to be, not
zero, but some other quantity, about which, though small in comparison
with the total effect, the effect nevertheless oscillates, and which is
the middle point in its oscillation; we may conclude this to be the
effect of some constant cause: which cause, by some of the methods
already treated of, we may hope to detect. This may be called _the
discovery of a residual phenomenon by eliminating the effects of

It is in this manner, for example, that loaded dice may be discovered.
Of course no dice are so clumsily loaded that they must always throw
certain numbers; otherwise the fraud would be instantly detected. The
loading, a constant cause, mingles with the changeable causes which
determine what cast will be thrown in each individual instance. If the
dice were not loaded, and the throw were left to depend entirely on the
changeable causes, these in a sufficient number of instances would
balance one another, and there would be no preponderant number of throws
of any one kind. If, therefore, after such a number of trials that no
further increase of their number has any material effect upon the
average, we find a preponderance in favour of a particular throw; we may
conclude with assurance that there is some constant cause acting in
favour of that throw, or in other words, that the dice are not fair; and
the exact amount of the unfairness. In a similar manner, what is called
the diurnal variation of the barometer, which is very small compared
with the variations arising from the irregular changes in the state of
the atmosphere, was discovered by comparing the average height of the
barometer at different hours of the day. When this comparison was made,
it was found that there was a small difference, which on the average was
constant, however the absolute quantities might vary, and which
difference, therefore, must be the effect of a constant cause. This
cause was afterwards ascertained, deductively, to be the rarefaction of
the air, occasioned by the increase of temperature as the day advances.

§ 5. After these general remarks on the nature of chance, we are
prepared to consider in what manner assurance may be obtained that a
conjunction between two phenomena, which has been observed a certain
number of times, is not casual, but a result of causation, and to be
received therefore as one of the uniformities of nature, though (until
accounted for _à priori_) only as an empirical law.

We will suppose the strongest case, namely, that the phenomenon B has
never been observed except in conjunction with A. Even then, the
probability that they are connected is not measured by the total number
of instances in which they have been found together, but by the excess
of that number above the number due to the absolute frequency of A. If,
for example, A exists always, and therefore coexists with everything, no
number of instances of its coexistence with B would prove a connexion;
as in our example of the fixed stars. If A be a fact of such common
occurrence that it may be presumed to be present in half of all the
cases that occur, and therefore in half the cases in which B occurs, it
is only the proportional excess above half, that is to be reckoned as
evidence towards proving a connexion between A and B.

In addition to the question, What is the number of coincidences which,
on an average of a great multitude of trials, may be expected to arise
from chance alone? there is also another question, namely, Of what
extent of deviation from that average is the occurrence credible, from
chance alone, in some number of instances smaller than that required
for striking a fair average? It is not only to be considered what is the
general result of the chances in the long run, but also what are the
extreme limits of variation from the general result, which may
occasionally be expected as the result of some smaller number of

The consideration of the latter question, and any consideration of the
former beyond that already given to it, belong to what mathematicians
term the doctrine of chances, or, in a phrase of greater pretension, the
Theory of Probabilities.



§ 1. "Probability," says Laplace,[17] "has reference partly to our
ignorance, partly to our knowledge. We know that among three or more
events, one, and only one, must happen; but there is nothing leading us
to believe that any one of them will happen rather than the others. In
this state of indecision, it is impossible for us to pronounce with
certainty on their occurrence. It is, however, probable that any one of
these events, selected at pleasure, will not take place; because we
perceive several cases, all equally possible, which exclude its
occurrence, and only one which favours it.

"The theory of chances consists in reducing all events of the same kind
to a certain number of cases equally possible, that is, such that we are
_equally undecided_ as to their existence; and in determining the number
of these cases which are favourable to the event of which the
probability is sought. The ratio of that number to the number of all the
possible cases, is the measure of the probability; which is thus a
fraction, having for its numerator the number of cases favourable to the
event, and for its denominator the number of all the cases which are

To a calculation of chances, then, according to Laplace, two things are
necessary: we must know that of several events some one will certainly
happen, and no more than one; and we must not know, nor have any reason
to expect, that it will be one of these events rather than another. It
has been contended that these are not the only requisites, and that
Laplace has overlooked, in the general theoretical statement, a
necessary part of the foundation of the doctrine of chances. To be able
(it has been said) to pronounce two events equally probable, it is not
enough that we should know that one or the other must happen, and should
have no grounds for conjecturing which. Experience must have shown that
the two events are of equally frequent occurrence. Why, in tossing up a
halfpenny, do we reckon it equally probable that we shall throw cross or
pile? Because we know that in any great number of throws, cross and pile
are thrown about equally often; and that the more throws we make, the
more nearly the equality is perfect. We may know this if we please by
actual experiment; or by the daily experience which life affords of
events of the same general character; or deductively, from the effect of
mechanical laws on a symmetrical body acted upon by forces varying
indefinitely in quantity and direction. We may know it, in short, either
by specific experience, or on the evidence of our general knowledge of
nature. But, in one way or the other, we must know it, to justify us in
calling the two events equally probable; and if we knew it not, we
should proceed as much at haphazard in staking equal sums on the result,
as in laying odds.

This view of the subject was taken in the first edition of the present
work: but I have since become convinced, that the theory of chances, as
conceived by Laplace and by mathematicians generally, has not the
fundamental fallacy which I had ascribed to it.

We must remember that the probability of an event is not a quality of
the event itself, but a mere name for the degree of ground which we, or
some one else, have for expecting it. The probability of an event to one
person is a different thing from the probability of the same event to
another, or to the same person after he has acquired additional
evidence. The probability to me, that an individual of whom I know
nothing but his name, will die within the year, is totally altered by my
being told, the next minute, that he is in the last stage of a
consumption. Yet this makes no difference in the event itself, nor in
any of the causes on which it depends. Every event is in itself certain,
not probable: if we knew all, we should either know positively that it
will happen, or positively that it will not. But its probability to us
means the degree of expectation of its occurrence, which we are
warranted in entertaining by our present evidence.

Bearing this in mind, I think it must be admitted, that even when we
have no knowledge whatever to guide our expectations, except the
knowledge that what happens must be some one of a certain number of
possibilities, we may still reasonably judge, that one supposition is
more probable _to us_ than another supposition; and if we have any
interest at stake, we shall best provide for it by acting conformably to
that judgment.

§ 2. Suppose that we are required to take a ball from a box, of which we
only know that it contains balls both black and white, and none of any
other colour. We know that the ball we select will be either a black or
a white ball; but we have no ground for expecting black rather than
white, or white rather than black. In that case, if we are obliged to
make a choice, and to stake something on one or the other supposition,
it will, as a question of prudence, be perfectly indifferent which; and
we shall act precisely as we should have acted if we had known
beforehand that the box contained an equal number of black and white
balls. But though our conduct would be the same, it would not be founded
on any surmise that the balls were in fact thus equally divided; for we
might, on the contrary, know, by authentic information, that the box
contained ninety-nine balls of one colour, and only one of the other;
still, if we are not told which colour has only one, and which has
ninety-nine, the drawing of a white and of a black ball will be equally
probable to us; we shall have no reason for staking anything on the one
event rather than on the other; the option between the two will be a
matter of indifference; in other words it will be an even chance.

But let it now be supposed that instead of two there are three
colours--white, black, and red; and that we are entirely ignorant of the
proportion in which they are mingled. We should then have no reason for
expecting one more than another, and if obliged to bet, should venture
our stake on red, white, or black, with equal indifference. But should
we be indifferent whether we betted for or against some one colour, as,
for instance, white? Surely not. From the very fact that black and red
are each of them separately equally probable to us with white, the two
together must be twice as probable. We should in this case expect
not-white rather than white, and so much rather, that we would lay two
to one upon it. It is true, there might for aught we knew be more white
balls than black and red together; and if so, our bet would, if we knew
more, be seen to be a disadvantageous one. But so also, for aught we
knew, might there be more red balls than black and white, or more black
balls than white and red, and in such case the effect of additional
knowledge would be to prove to us that our bet was more advantageous
than we had supposed it to be. There is in the existing state of our
knowledge a rational probability of two to one against white; a
probability fit to be made a basis of conduct. No reasonable person
would lay an even wager in favour of white, against black and red;
though against black alone, or red alone, he might do so without

The common theory, therefore, of the calculation of chances, appears to
be tenable. Even when we know nothing except the number of the possible
and mutually excluding contingencies, and are entirely ignorant of their
comparative frequency, we may have grounds, and grounds numerically
appreciable, for acting on one supposition rather than on another; and
this is the meaning of Probability.

§ 3. The principle, however, on which the reasoning proceeds, is
sufficiently evident. It is the obvious one, that when the cases which
exist are shared among several kinds, it is impossible that _each_ of
those kinds should be a majority of the whole: on the contrary, there
must be a majority against each kind, except one at most; and if any
kind has more than its share in proportion to the total number, the
others collectively must have less. Granting this axiom, and assuming
that we have no ground for selecting any one kind as more likely than
the rest to surpass the average proportion, it follows that we cannot
rationally presume this of any; which we should do, if we were to bet in
favour of it, receiving less odds than in the ratio of the number of the
other kinds. Even, therefore, in this extreme case of the calculation of
probabilities, which does not rest on special experience at all, the
logical ground of the process is our knowledge, such knowledge as we
then have, of the laws governing the frequency of occurrence of the
different cases; but in this case the knowledge is limited to that
which, being universal and axiomatic, does not require reference to
specific experience, or to any considerations arising out of the special
nature of the problem under discussion.

Except, however, in such cases as games of chance, where the very
purpose in view requires ignorance instead of knowledge, I can conceive
no case in which we ought to be satisfied with such an estimate of
chances as this; an estimate founded on the absolute minimum of
knowledge respecting the subject. It is plain that, in the case of the
coloured balls, a very slight ground of surmise that the white balls
were really more numerous than either of the other colours, would
suffice to vitiate the whole of the calculations made in our previous
state of indifference. It would place us in that position of more
advanced knowledge, in which the probabilities, to us, would be
different from what they were before; and in estimating these new
probabilities we should have to proceed on a totally different set of
data, furnished no longer by mere counting of possible suppositions, but
by specific knowledge of facts. Such data it should always be our
endeavour to obtain; and in all inquiries, unless on subjects equally
beyond the range of our means of knowledge and our practical uses, they
may be obtained, if not good, at least better than none at all.[18]

It is obvious, too, that even when the probabilities are derived from
observation and experiment, a very slight improvement in the data, by
better observations, or by taking into fuller consideration the special
circumstances of the case, is of more use than the most elaborate
application of the calculus to probabilities founded on the data in
their previous state of inferiority. The neglect of this obvious
reflection has given rise to misapplications of the calculus of
probabilities which have made it the real opprobrium of mathematics. It
is sufficient to refer to the applications made of it to the credibility
of witnesses, and to the correctness of the verdicts of juries. In
regard to the first, common sense would dictate that it is impossible to
strike a general average of the veracity, and other qualifications for
true testimony, of mankind, or of any class of them; and even if it were
possible, the employment of it for such a purpose implies a
misapprehension of the use of averages: which serve indeed to protect
those whose interest is at stake, against mistaking the general result
of large masses of instances, but are of extremely small value as
grounds of expectation in any one individual instance, unless the case
be one of those in which the great majority of individual instances do
not differ much from the average. In the case of a witness, persons of
common sense would draw their conclusions from the degree of consistency
of his statements, his conduct under cross-examination, and the relation
of the case itself to his interests, his partialities, and his mental
capacity, instead of applying so rude a standard (even if it were
capable of being verified) as the ratio between the number of true and
the number of erroneous statements which he may be supposed to make in
the course of his life.

Again, on the subject of juries, or other tribunals, some mathematicians
have set out from the proposition that the judgment of any one judge, or
juryman, is, at least in some small degree, more likely to be right than
wrong, and have concluded that the chance of a number of persons
concurring in a wrong verdict is diminished, the more the number is
increased; so that if the judges are only made sufficiently numerous,
the correctness of the judgment may be reduced almost to certainty. I
say nothing of the disregard shown to the effect produced on the moral
position of the judges by multiplying their numbers; the virtual
destruction of their individual responsibility, and weakening of the
application of their minds to the subject. I remark only the fallacy of
reasoning from a wide average, to cases necessarily differing greatly
from any average. It may be true that taking all causes one with
another, the opinion of any one of the judges would be oftener right
than wrong; but the argument forgets that in all but the more simple
cases, in all cases in which it is really of much consequence what the
tribunal is, the proposition might probably be reversed; besides which,
the cause of error, whether arising from the intricacy of the case or
from some common prejudice or mental infirmity, if it acted upon one
judge, would be extremely likely to affect all the others in the same
manner, or at least a majority, and thus render a wrong instead of a
right decision more probable, the more the number was increased.

These are but samples of the errors frequently committed by men who,
having made themselves familiar with the difficult formulæ which algebra
affords for the estimation of chances under suppositions of a complex
character, like better to employ those formulæ in computing what are the
probabilities to a person half informed about a case, than to look out
for means of being better informed. Before applying the doctrine of
chances to any scientific purpose, the foundation must be laid for an
evaluation of the chances, by possessing ourselves of the utmost
attainable amount of positive knowledge. The knowledge required is that
of the comparative frequency with which the different events in fact
occur. For the purposes, therefore, of the present work, it is allowable
to suppose, that conclusions respecting the probability of a fact of a
particular kind, rest on our knowledge of the proportion between the
cases in which facts of that kind occur, and those in which they do not
occur: this knowledge being either derived from specific experiment, or
deduced from our knowledge of the causes in operation which tend to
produce, compared with those which tend to prevent, the fact in

Such calculation of chances is grounded on an induction; and to render
the calculation legitimate, the induction must be a valid one. It is not
less an induction, though it does not prove that the event occurs in all
cases of a given description, but only that out of a given number of
such cases, it occurs in about so many. The fraction which
mathematicians use to designate the probability of an event, is the
ratio of these two numbers; the ascertained proportion between the
number of cases in which the event occurs, and the sum of all the cases,
those in which it occurs and in which it does not occur taken together.
In playing at cross and pile, the description of cases concerned are
throws, and the probability of cross is one-half, because if we throw
often enough, cross is thrown about once in every two throws. In the
cast of a die, the probability of ace is one-sixth; not simply because
there are six possible throws, of which ace is one, and because we do
not know any reason why one should turn up rather than another; though I
have admitted the validity of this ground in default of a better; but
because we do actually know, either by reasoning or by experience, that
in a hundred, or a million of throws, ace is thrown about one-sixth of
that number, or once in six times.

§ 4. I say, "either by reasoning or by experience;" meaning specific
experience. But in estimating probabilities, it is not a matter of
indifference from which of these two sources we derive our assurance.
The probability of events as calculated from their mere frequency in
past experience, affords a less secure basis for practical guidance,
than their probability as deduced from an equally accurate knowledge of
the frequency of occurrence of their causes.

The generalization, that an event occurs in ten out of every hundred
cases of a given description, is as real an induction as if the
generalization were that it occurs in all cases. But when we arrive at
the conclusion by merely counting instances in actual experience, and
comparing the number of cases in which A has been present with the
number in which it has been absent, the evidence is only that of the
method of Agreement, and the conclusion amounts only to an empirical
law. We can make a step beyond this when we can ascend to the causes on
which the occurrence of A or its non-occurrence will depend, and form an
estimate of the comparative frequency of the causes favourable and of
those unfavourable to the occurrence. These are data of a higher order,
by which the empirical law derived from a mere numerical comparison of
affirmative and negative instances will be either corrected or
confirmed, and in either case we shall obtain a more correct measure of
probability than is given by that numerical comparison. It has been well
remarked that in the kind of examples by which the doctrine of chances
is usually illustrated, that of balls in a box, the estimate of
probabilities is supported by reasons of causation, stronger than
specific experience. "What is the reason that in a box where there are
nine black balls and one white, we expect to draw a black ball nine
times as much (in other words, nine times as often, frequency being the
gauge of intensity in expectation) as a white? Obviously because the
local conditions are nine times as favourable, because the hand may
alight in nine places and get a black ball, while it can only alight in
one place and find a white ball; just for the same reason that we do not
expect to succeed in finding a friend in a crowd, the conditions in
order that we and he should come together being many and difficult. This
of course would not hold to the same extent were the white balls of
smaller size than the black, neither would the probability remain the
same: the larger ball would be much more likely to meet the hand."[19]

It is, in fact, evident, that when once causation is admitted as an
universal law, our expectation of events can only be rationally grounded
on that law. To a person who recognises that every event depends on
causes, a thing's having happened once is a reason for expecting it to
happen again, only because proving that there exists, or is liable to
exist, a cause adequate to produce it.[20] The frequency of the
particular event, apart from all surmise respecting its cause, can give
rise to no other induction than that _per enumerationem simplicem_; and
the precarious inferences derived from this, are superseded, and
disappear from the field, as soon as the principle of causation makes
its appearance there.

Notwithstanding, however, the abstract superiority of an estimate of
probability grounded on causes, it is a fact that in almost all cases in
which chances admit of estimation sufficiently precise to render their
numerical appreciation of any practical value, the numerical data are
not drawn from knowledge of the causes, but from experience of the
events themselves. The probabilities of life at different ages, or in
different climates; the probabilities of recovery from a particular
disease; the chances of the birth of male or female offspring; the
chances of the destruction of houses or other property by fire; the
chances of the loss of a ship in a particular voyage; are deduced from
bills of mortality, returns from hospitals, registers of births, of
shipwrecks, &c., that is, from the observed frequency not of the causes,
but of the effects. The reason is, that in all these classes of facts,
the causes are either not amenable to direct observation at all, or not
with the requisite precision, and we have no means of judging of their
frequency except from the empirical law afforded by the frequency of the
effects. The inference does not the less depend on causation alone. We
reason from an effect to a similar effect by passing through the cause.
If the actuary of an insurance office infers from his tables that among
a hundred persons now living, of a particular age, five on the average
will attain the age of seventy, his inference is legitimate, not for the
simple reason that this is the proportion who have lived till seventy in
times past, but because the fact of their having so lived shows that
this is the proportion existing, at that place and time, between the
causes which prolong life to the age of seventy, and those tending to
bring it to an earlier close.[21]

§ 5. From the preceding principles it is easy to deduce the
demonstration of that theorem of the doctrine of probabilities, which is
the foundation of its application to inquiries for ascertaining the
occurrence of a given event, or the reality of an individual fact. The
signs or evidences by which a fact is usually proved, are some of its
consequences: and the inquiry hinges upon determining what cause is most
likely to have produced a given effect. The theorem applicable to such
investigations is the Sixth Principle in Laplace's _Essai Philosophique
sur les Probabilités_, which is described by him as the "fundamental
principle of that branch of the Analysis of Chances, which consists in
ascending from events to their causes."[22]

Given an effect to be accounted for, and there being several causes
which might have produced it, but of the presence of which in the
particular case nothing is known; the probability that the effect was
produced by any one of these causes _is as the antecedent probability of
the cause, multiplied by the probability that the cause, if it existed,
would have produced the given effect_.

Let M be the effect, and A, B, two causes, by either of which it might
have been produced. To find the probability that it was produced by the
one and not by the other, ascertain which of the two is most likely to
have existed, and which of them, if it did exist, was most likely to
produce the effect M: the probability sought is a compound of these two

CASE I. Let the causes be both alike in the second respect; either A or
B, when it exists, being supposed equally likely (or equally certain) to
produce M; but let A be in itself twice as likely as B to exist, that
is, twice as frequent a phenomenon. Then it is twice as likely to have
existed in this case, and to have been the cause which produced M.

For, since A exists in nature twice as often as B; in any 300 cases in
which one or other existed, A has existed 200 times and B 100. But
either A or B must have existed wherever M is produced: therefore in 300
times that M is produced, A was the producing cause 200 times, B only
100, that is, in the ratio of 2 to 1. Thus, then, if the causes are
alike in their capacity of producing the effect, the probability as to
which actually produced it, is in the ratio of their antecedent

CASE II. Reversing the last hypothesis, let us suppose that the causes
are equally frequent, equally likely to have existed, but not equally
likely, if they did exist, to produce M: that in three times in which A
occurs, it produces that effect twice, while B, in three times, produces
it only once. Since the two causes are equally frequent in their
occurrence; in every six times that either one or the other exists, A
exists three times and B three times. A, of its three times, produces M
in two; B, of its three times, produces M in one. Thus, in the whole six
times, M is only produced thrice; but of that thrice it is produced
twice by A, once only by B. Consequently, when the antecedent
probabilities of the causes are equal, the chances that the effect was
produced by them are in the ratio of the probabilities that if they did
exist they would produce the effect.

CASE III. The third case, that in which the causes are unlike in both
respects, is solved by what has preceded. For, when a quantity depends
on two other quantities, in such a manner that while either of them
remains constant it is proportional to the other, it must necessarily be
proportional to the product of the two quantities, the product being the
only function of the two which obeys that law of variation. Therefore,
the probability that M was produced by either cause, is as the
antecedent probability of the cause, multiplied by the probability that
if it existed it would produce M. Which was to be demonstrated.

Or we may prove the third case as we proved the first and second. Let A
be twice as frequent as B; and let them also be unequally likely, when
they exist, to produce M: let A produce it twice in four times, B thrice
in four times. The antecedent probability of A is to that of B as 2 to
1; the probabilities of their producing M are as 2 to 3; the product of
these ratios is the ratio of 4 to 3: and this will be the ratio of the
probabilities that A or B was the producing cause in the given instance.
For, since A is twice as frequent as B, out of twelve cases in which one
or other exists, A exists in 8 and B in 4. But of its eight cases, A, by
the supposition, produces M in only 4, while B of its four cases
produces M in 3. M, therefore, is only produced at all in seven of the
twelve cases; but in four of these it is produced by A, in three by B;
hence, the probabilities of its being produced by A and by B are as 4 to
3, and are expressed by the fractions 4/7 and 3/7. Which was to be

§ 6. It remains to examine the bearing of the doctrine of chances on the
peculiar problem which occupied us in the preceding chapter, namely, how
to distinguish coincidences which are casual from those which are the
result of law; from those in which the facts which accompany or follow
one another are somehow connected through causation.

The doctrine of chances affords means by which, if we knew the _average_
number of coincidences to be looked for between two phenomena connected
only casually, we could determine how often any given deviation from
that average will occur by chance. If the probability of any casual
coincidence, considered in itself, be _1/m_, the probability that the
same coincidence will be repeated _n_ times in succession is _1/m^n_.
For example, in one throw of a die the probability of ace being 1/6; the
probability of throwing ace twice in succession will be 1 divided by the
square of 6, or 1/36. For ace is thrown at the first throw once in six,
or six in thirty-six times, and of those six, the die being cast again,
ace will be thrown but once; being altogether once in thirty-six times.
The chance of the same cast three times successively is, by a similar
reasoning, 1/6^3 or 1/216: that is, the event will happen, on a large
average, only once in two hundred and sixteen throws.

We have thus a rule by which to estimate the probability that any given
series of coincidences arises from chance; provided we can measure
correctly the probability of a single coincidence. If we can obtain an
equally precise expression for the probability that the same series of
coincidences arises from causation, we should only have to compare the
numbers. This however, can rarely be done. Let us see what degree of
approximation can practically be made to the necessary precision.

The question falls within Laplace's sixth principle, just demonstrated.
The given fact, that is to say, the series of coincidences, may have
originated either in a casual conjunction of causes, or in a law of
nature. The probabilities, therefore, that the fact originated in these
two modes, are as their antecedent probabilities, multiplied by the
probabilities that if they existed they would produce the effect. But
the particular combination of chances, if it occurred, or the law of
nature if real, would certainly produce the series of coincidences. The
probabilities, therefore, that the coincidences are produced by the two
causes in question, are as the antecedent probabilities of the causes.
One of these, the antecedent probability of the combination of mere
chances which would produce the given result, is an appreciable
quantity. The antecedent probability of the other supposition may be
susceptible of a more or less exact estimation, according to the nature
of the case.

In some cases, the coincidence, supposing it to be the result of
causation at all, must be the result of a known cause: as the succession
of aces, if not accidental, must arise from the loading of the die. In
such cases we may be able to form a conjecture as to the antecedent
probability of such a circumstance, from the characters of the parties
concerned, or other such evidence; but it would be impossible to
estimate that probability with anything like numerical precision. The
counter-probability, however, that of the accidental origin of the
coincidence, dwindling so rapidly as it does at each new trial; the
stage is soon reached at which the chance of unfairness in the die,
however small in itself, must be greater than that of a casual
coincidence: and on this ground, a practical decision can generally be
come to without much hesitation, if there be the power of repeating the

When, however, the coincidence is one which cannot be accounted for by
any known cause, and the connexion between the two phenomena, if
produced by causation, must be the result of some law of nature hitherto
unknown; which is the case we had in view in the last chapter; then,
though the probability of a casual coincidence may be capable of
appreciation, that of the counter-supposition, the existence of an
undiscovered law of nature, is clearly unsusceptible of even an
approximate valuation. In order to have the data which such a case would
require, it would be necessary to know what proportion of all the
individual sequences or coexistences occurring in nature are the result
of law, and what proportion are mere casual coincidences. It being
evident that we cannot form any plausible conjecture as to this
proportion, much less appreciate it numerically, we cannot attempt any
precise estimation of the comparative probabilities. But of this we are
sure, that the detection of an unknown law of nature--of some previously
unrecognised constancy of conjunction among phenomena--is no uncommon
event. If, therefore, the number of instances in which a coincidence is
observed, over and above that which would arise on the average from the
mere concurrence of chances, be such that so great an amount of
coincidences from accident alone would be an extremely uncommon event;
we have reason to conclude that the coincidence is the effect of
causation, and may be received (subject to correction from further
experience) as an empirical law. Further than this, in point of
precision, we cannot go; nor, in most cases, is greater precision
required, for the solution of any practical doubt.[23]



§ 1. We have had frequent occasion to notice the inferior generality of
derivative laws, compared with the ultimate laws from which they are
derived. This inferiority, which affects not only the extent of the
propositions themselves, but their degree of certainty within that
extent, is most conspicuous in the uniformities of coexistence and
sequence obtaining between effects which depend ultimately on different
primeval causes. Such uniformities will only obtain where there exists
the same collocation of those primeval causes. If the collocation
varies, though the laws themselves remain the same, a totally different
set of derivative uniformities may, and generally will, be the result.

Even where the derivative uniformity is between different effects of the
same cause, it will by no means obtain as universally as the law of the
cause itself. If _a_ and _b_ accompany or succeed one another as effects
of the cause A, it by no means follows that A is the only cause which
can produce them, or that if there be another cause, as B, capable of
producing _a_, it must produce _b_ likewise. The conjunction therefore
of _a_ and _b_ perhaps does not hold universally, but only in the
instances in which _a_ arises from A. When it is produced by a cause
other than A, _a_ and _b_ may be dissevered. Day (for example) is always
in our experience followed by night; but day is not the cause of night;
both are successive effects of a common cause, the periodical passage of
the spectator into and out of the earth's shadow, consequent on the
earth's rotation, and on the illuminating property of the sun. If,
therefore, day is ever produced by a different cause or set of causes
from this, day will not, or at least may not, be followed by night. On
the sun's own surface, for instance, this may be the case.

Finally, even when the derivative uniformity is itself a law of
causation (resulting from the combination of several causes), it is not
altogether independent of collocations. If a cause supervenes, capable
of wholly or partially counteracting the effect of any one of the
conjoined causes, the effect will no longer conform to the derivative
law. While, therefore, each ultimate law is only liable to frustration
from one set of counteracting causes, the derivative law is liable to it
from several. Now, the possibility of the occurrence of counteracting
causes which do not arise from any of the conditions involved in the law
itself, depends on the original collocations.

It is true that (as we formerly remarked) laws of causation, whether
ultimate or derivative, are, in most cases, fulfilled even when
counteracted; the cause produces its effect, though that effect is
destroyed by something else. That the effect may be frustrated, is,
therefore, no objection to the universality of laws of causation. But it
is fatal to the universality of the sequences or coexistences of
effects, which compose the greater part of the derivative laws flowing
from laws of causation. When, from the law of a certain combination of
causes, there results a certain order in the effects; as from the
combination of a single sun with the rotation of an opaque body round
its axis, there results, on the whole surface of that opaque body, an
alternation of day and night; then if we suppose one of the combined
causes counteracted, the rotation stopped, the sun extinguished, or a
second sun superadded, the truth of that particular law of causation is
in no way affected; it is still true that one sun shining on an opaque
revolving body will alternately produce day and night; but since the sun
no longer does shine on such a body, the derivative uniformity, the
succession of day and night on the given planet, is no longer true.
Those derivative uniformities, therefore, which are not laws of
causation, are (except in the rare case of their depending on one cause
alone, not on a combination of causes,) always more or less contingent
on collocations; and are hence subject to the characteristic infirmity
of empirical laws, that of being admissible only where the collocations
are known by experience to be such as are requisite for the truth of the
law, that is, only within the conditions of time and place confirmed by
actual observation.

§ 2. This principle, when stated in general terms, seems clear and
indisputable; yet many of the ordinary judgments of mankind, the
propriety of which is not questioned, have at least the semblance of
being inconsistent with it. On what grounds, it may be asked, do we
expect that the sun will rise to-morrow? To-morrow is beyond the limits
of time comprehended in our observations. They have extended over some
thousands of years past, but they do not include the future. Yet we
infer with confidence that the sun will rise to-morrow; and nobody
doubts that we are entitled to do so. Let us consider what is the
warrant for this confidence.

In the example in question, we know the causes on which the derivative
uniformity depends. They are, the sun giving out light, the earth in a
state of rotation and intercepting light. The induction which shows
these to be the real causes, and not merely prior effects of a common
cause, being complete; the only circumstances which could defeat the
derivative law are such as would destroy or counteract one or other of
the combined causes. While the causes exist, and are not counteracted,
the effect will continue. If they exist and are not counteracted
to-morrow, the sun will rise to-morrow.

Since the causes, namely the sun and the earth, the one in the state of
giving out light, the other in a state of rotation, will exist until
something destroys them; all depends on the probabilities of their
destruction, or of their counteraction. We know by observation (omitting
the inferential proofs of an existence for thousands of ages anterior),
that these phenomena have continued for (say) five thousand years.
Within that time there has existed no cause sufficient to diminish them
appreciably; nor which has counteracted their effect in any appreciable
degree. The chance, therefore, that the sun may not rise to-morrow,
amounts to the chance that some cause, which has not manifested itself
in the smallest degree during five thousand years, will exist to-morrow
in such intensity as to destroy the sun or the earth, the sun's light or
the earth's rotation, or to produce an immense disturbance in the effect
resulting from those causes.

Now, if such a cause will exist to-morrow, or at any future time, some
cause, proximate or remote, of that cause must exist now, and must have
existed during the whole of the five thousand years. If, therefore, the
sun do not rise to-morrow, it will be because some cause has existed,
the effects of which though during five thousand years they have not
amounted to a perceptible quantity, will in one day become overwhelming.
Since this cause has not been recognised during such an interval of
time, by observers stationed on our earth, it must, if it exist, be
either some agent whose effects develop themselves gradually and very
slowly, or one which existed in regions beyond our observation, and is
now on the point of arriving in our part of the universe. Now all causes
which we have experience of, act according to laws incompatible with the
supposition that their effects, after accumulating so slowly as to be
imperceptible for five thousand years, should start into immensity in a
single day. No mathematical law of proportion between an effect and the
quantity or relations of its cause, could produce such contradictory
results. The sudden development of an effect of which there was no
previous trace, always arises from the coming together of several
distinct causes, not previously conjoined; but if such sudden
conjunction is destined to take place, the causes, or _their_ causes,
must have existed during the entire five thousand years; and their not
having once come together during that period, shows how rare that
particular combination is. We have, therefore, the warrant of a rigid
induction for considering it probable, in a degree undistinguishable
from certainty, that the known conditions requisite for the sun's rising
will exist to-morrow.

§ 3. But this extension of derivative laws, not causative, beyond the
limits of observation, can only be to _adjacent_ cases. If instead of
to-morrow we had said this day twenty thousand years, the inductions
would have been anything but conclusive. That a cause which, in
opposition to very powerful causes, produced no perceptible effect
during five thousand years, should produce a very considerable one by
the end of twenty thousand, has nothing in it which is not in conformity
with our experience of causes. We know many agents, the effect of which
in a short period does not amount to a perceptible quantity, but by
accumulating for a much longer period becomes considerable. Besides,
looking at the immense multitude of the heavenly bodies, their vast
distances, and the rapidity of the motion of such of them as are known
to move, it is a supposition not at all contradictory to experience that
some body may be in motion towards us, or we towards it, within the
limits of whose influence we have not come during five thousand years,
but which in twenty thousand more may be producing effects upon us of
the most extraordinary kind. Or the fact which is capable of preventing
sunrise may be, not the cumulative effect of one cause, but some new
combination of causes; and the chances favourable to that combination,
though they have not produced it once in five thousand years, may
produce it once in twenty thousand. So that the inductions which
authorize us to expect future events, grow weaker and weaker the further
we look into the future, and at length become inappreciable.

We have considered the probabilities of the sun's rising to-morrow, as
derived from the real laws, that is, from the laws of the causes on
which that uniformity is dependent. Let us now consider how the matter
would have stood if the uniformity had been known only as an empirical
law; if we had not been aware that the sun's light, and the earth's
rotation (or the sun's motion), were the causes on which the periodical
occurrence of daylight depends. We could have extended this empirical
law to cases adjacent in time, though not to so great a distance of time
as we can now. Having evidence that the effects had remained unaltered
and been punctually conjoined for five thousand years, we could infer
that the unknown causes on which the conjunction is dependent had
existed undiminished and uncounteracted during the same period. The same
conclusions, therefore, would follow as in the preceding case; except
that we should only know that during five thousand years nothing had
occurred to defeat perceptibly this particular effect; while, when we
know the causes, we have the additional assurance, that during that
interval no such change has been noticeable in the causes themselves, as
by any degree of multiplication or length of continuance could defeat
the effect.

To this must be added, that when we know the causes, we may be able to
judge whether there exists any known cause capable of counteracting
them; while as long as they are unknown, we cannot be sure but that if
we did know them, we could predict their destruction from causes
actually in existence. A bedridden savage, who had never seen the
cataract of Niagara, but who lived within hearing of it, might imagine
that the sound he heard would endure for ever; but if he knew it to be
the effect of a rush of waters over a barrier of rock which is
progressively wearing away, he would know that within a number of ages
which may be calculated, it will be heard no more. In proportion,
therefore, to our ignorance of the causes on which the empirical law
depends, we can be less assured that it will continue to hold good; and
the farther we look into futurity, the less improbable is it that some
one of the causes, whose coexistence gives rise to the derivative
uniformity, may be destroyed or counteracted. With every prolongation of
time, the chances multiply of such an event, that is to say, its
non-occurrence hitherto becomes a less guarantee of its not occurring
within the given time. If, then, it is only to cases which in point of
time are adjacent (or nearly adjacent) to those which we have actually
observed, that _any_ derivative law, not of causation, can be extended
with an assurance equivalent to certainty, much more is this true of a
merely empirical law. Happily, for the purposes of life it is to such
cases alone that we can almost ever have occasion to extend them.

In respect of place, it might seem that a merely empirical law could
not be extended even to adjacent cases; that we could have no assurance
of its being true in any place where it has not been specially observed.
The past duration of a cause is a guarantee for its future existence,
unless something occurs to destroy it; but the existence of a cause in
one or any number of places, is no guarantee for its existence in any
other place, since there is no uniformity in the collocations of
primeval causes. When, therefore, an empirical law is extended beyond
the local limits within which it has been found true by observation, the
cases to which it is thus extended must be such as are presumably within
the influence of the same individual agents. If we discover a new planet
within the known bounds of the solar system (or even beyond those
bounds, but indicating its connexion with the system by revolving round
the sun), we may conclude, with great probability, that it revolves on
its axis. For all the known planets do so; and this uniformity points to
some common cause, antecedent to the first records of astronomical
observation: and though the nature of this cause can only be matter of
conjecture, yet if it be, as is not unlikely, and as Laplace's theory
supposes, not merely the same kind of cause, but the same individual
cause (such as an impulse given to all the bodies at once), that cause,
acting at the extreme points of the space occupied by the sun and
planets, is likely, unless defeated by some counteracting cause, to have
acted at every intermediate point, and probably somewhat beyond; and
therefore acted, in all probability, upon the supposed newly-discovered

When, therefore, effects which are always found conjoined, can be traced
with any probability to an identical (and not merely a similar) origin,
we may with the same probability extend the empirical law of their
conjunction to all places within the extreme local boundaries within
which the fact has been observed; subject to the possibility of
counteracting causes in some portion of the field. Still more
confidently may we do so when the law is not merely empirical; when the
phenomena which we find conjoined are effects of ascertained causes,
from the laws of which the conjunction of their effects is deducible. In
that case, we may both extend the derivative uniformity over a larger
space, and with less abatement for the chance of counteracting causes.
The first, because instead of the local boundaries of our observation of
the fact itself, we may include the extreme boundaries of the
ascertained influence of its causes. Thus the succession of day and
night, we know, holds true of all the bodies of the solar system except
the sun itself; but we know this only because we are acquainted with the
causes: if we were not, we could not extend the proposition beyond the
orbits of the earth and moon, at both extremities of which we have the
evidence of observation for its truth. With respect to the probability
of counteracting causes, it has been seen that this calls for a greater
abatement of confidence, in proportion to our ignorance of the causes on
which the phenomena depend. On both accounts, therefore, a derivative
law which we know how to resolve, is susceptible of a greater extension
to cases adjacent in place, than a merely empirical law.



§ 1. The word Analogy, as the name of a mode of reasoning, is generally
taken for some kind of argument supposed to be of an inductive nature,
but not amounting to a complete induction. There is no word, however,
which is used more loosely, or in a greater variety of senses, than
Analogy. It sometimes stands for arguments which may be examples of the
most rigorous Induction. Archbishop Whately, for instance, following
Ferguson and other writers, defines Analogy conformably to its primitive
acceptation, that which was given to it by mathematicians, Resemblance
of Relations. In this sense, when a country which has sent out colonies
is termed the mother country, the expression is analogical, signifying
that the colonies of a country stand in the same _relation_ to her in
which children stand to their parents. And if any inference be drawn
from this resemblance of relations, as, for instance, that obedience or
affection is due from colonies to the mother country, this is called
reasoning by analogy. Or if it be argued that a nation is most
beneficially governed by an assembly elected by the people, from the
admitted fact that other associations for a common purpose, such as
joint-stock companies, are best managed by a committee chosen by the
parties interested; this, too, is an argument from analogy in the
preceding sense, because its foundation is, not that a nation is like a
joint stock company, or Parliament like a board of directors, but that
Parliament stands in the same _relation_ to the nation in which a board
of directors stands to a joint stock company. Now, in an argument of
this nature, there is no inherent inferiority of conclusiveness. Like
other arguments from resemblance, it may amount to nothing, or it may be
a perfect and conclusive induction. The circumstance in which the two
cases resemble, may be capable of being shown to be the _material_
circumstance; to be that on which all the consequences, necessary to be
taken into account in the particular discussion, depend. In the example
last given, the resemblance is one of relation; the _fundamentum
relationis_ being the management by a few persons, of affairs in which a
much greater number are interested along with them. Now, some may
contend that this circumstance which is common to the two cases, and the
various consequences which follow from it, have the chief share in
determining all the effects which make up what we term good or bad
administration. If they can establish this, their argument has the force
of a rigorous induction; if they cannot, they are said to have failed in
proving the analogy between the two cases; a mode of speech which
implies that when the analogy can be proved, the argument founded on it
cannot be resisted.

§ 2. It is on the whole more usual, however, to extend the name of
analogical evidence to arguments from any sort of resemblance, provided
they do not amount to a complete induction: without peculiarly
distinguishing resemblance of relations. Analogical reasoning, in this
sense, may be reduced to the following formula:--Two things resemble
each other in one or more respects; a certain proposition is true of the
one; therefore it is true of the other. But we have nothing here by
which to discriminate analogy from induction, since this type will serve
for all reasoning from experience. In the strictest induction, equally
with the faintest analogy, we conclude because A resembles B in one or
more properties, that it does so in a certain other property. The
difference is, that in the case of a complete induction it has been
previously shown, by due comparison of instances, that there is an
invariable conjunction between the former property or properties and the
latter property; but in what is called analogical reasoning, no such
conjunction has been made out. There have been no opportunities of
putting in practice the Method of Difference, or even the Method of
Agreement; but we conclude (and that is all which the argument of
analogy amounts to) that a fact _m_, known to be true of A, is more
likely to be true of B if B agrees with A in some of its properties
(even though no connexion is known to exist between _m_ and those
properties), than if no resemblance at all could be traced between B and
any other thing known to possess the attribute _m_.

To this argument it is of course requisite, that the properties common
to A with B shall be merely not known to be connected with _m_; they
must not be properties known to be unconnected with it. If, either by
processes of elimination, or by deduction from previous knowledge of the
laws of the properties in question, it can be concluded that they have
nothing to do with _m_, the argument of analogy is put out of court. The
supposition must be that _m_ is an effect really dependent on some
property of A, but we know not on which. We cannot point out any of the
properties of A, which is the cause of _m_, or united with it by any
law. After rejecting all which we know to have nothing to do with it,
there remain several between which we are unable to decide: of which
remaining properties, B possesses one or more. This accordingly, we
consider as affording grounds, of more or less strength, for concluding
by analogy that B possesses the attribute _m_.

There can be no doubt that every such resemblance which can be pointed
out between B and A, affords some degree of probability, beyond what
would otherwise exist, in favour of the conclusion drawn from it. If B
resembled A in all its ultimate properties, its possessing the attribute
_m_ would be a certainty, not a probability: and every resemblance which
can be shown to exist between them, places it by so much the nearer to
that point. If the resemblance be in an ultimate property, there will be
resemblance in all the derivative properties dependent on that ultimate
property, and of these _m_ may be one. If the resemblance be in a
derivative property, there is reason to expect resemblance in the
ultimate property on which it depends, and in the other derivative
properties dependent on the same ultimate property. Every resemblance
which can be shown to exist, affords ground for expecting an indefinite
number of other resemblances: the particular resemblance sought will,
therefore, be oftener found among things thus known to resemble, than
among things between which we know of no resemblance.[24]

For example, I might infer that there are probably inhabitants in the
moon, because there are inhabitants on the earth, in the sea, and in the
air: and this is the evidence of analogy. The circumstance of having
inhabitants is here assumed not to be an ultimate property, but (as is
reasonable to suppose) a consequence of other properties; and depending,
therefore, in the case of the earth, on some of its properties as a
portion of the universe, but on which of those properties we know not.
Now the moon resembles the earth in being a solid, opaque, nearly
spherical substance, appearing to contain, or to have contained, active
volcanoes; receiving heat and light from the sun, in about the same
quantity as our earth; revolving on its axis; composed of materials
which gravitate, and obeying all the various laws resulting from that
property. And I think no one will deny that if this were all that was
known of the moon, the existence of inhabitants in that luminary would
derive from these various resemblances to the earth, a greater degree of
probability than it would otherwise have: though the amount of the
augmentation it would be useless to attempt to estimate.

If, however, every resemblance proved between B and A, in any point not
known to be immaterial with respect to _m_, forms some additional
reason for presuming that B has the attribute _m_; it is clear, _è
contra_, that every dissimilarity which can be proved between them,
furnishes a counter-probability of the same nature on the other side. It
is not indeed unusual that different ultimate properties should, in some
particular instances, produce the same derivative property; but on the
whole it is certain that things which differ in their ultimate
properties, will differ at least as much in the aggregate of their
derivative properties, and that the differences which are unknown will
on the average of cases bear some proportion to those which are known.
There will, therefore, be a competition between the known points of
agreement and the known points of difference in A and B; and according
as the one or the other may be deemed to preponderate, the probability
derived from analogy will be for or against B's having the property _m_.
The moon, for instance, agrees with the earth in the circumstances
already mentioned; but differs in being smaller, in having its surface
more unequal, and apparently volcanic throughout, in having, at least on
the side next the earth, no atmosphere sufficient to refract light, no
clouds, and (it is therefore concluded) no water. These differences,
considered merely as such, might perhaps balance the resemblances, so
that analogy would afford no presumption either way. But considering
that some of the circumstances which are wanting on the moon are among
those which, on the earth, are found to be indispensable conditions of
animal life, we may conclude that if that phenomenon does exist in the
moon, (or at all events on the nearer side,) it must be as an effect of
causes totally different from those on which it depends here; as a
consequence, therefore, of the moon's differences from the earth, not of
the points of agreement. Viewed in this light, all the resemblances
which exist become presumptions against, not in favour of, the moon's
being inhabited. Since life cannot exist there in the manner in which it
exists here, the greater the resemblance of the lunar world to the
terrestrial in other respects, the less reason we have to believe that
it can contain life.

There are, however, other bodies in our system, between which and the
earth there is a much closer resemblance; which possess an atmosphere,
clouds, consequently water (or some fluid analogous to it), and even
give strong indications of snow in their polar regions; while the cold,
or heat, though differing greatly on the average from ours, is, in some
parts at least of those planets, possibly not more extreme than in some
regions of our own which are habitable. To balance these agreements, the
ascertained differences are chiefly in the average light and heat,
velocity of rotation, density of material, intensity of gravity, and
similar circumstances of a secondary kind. With regard to these planets,
therefore, the argument of analogy gives a decided preponderance in
favour of their resembling the earth in any of its derivative
properties, such as that of having inhabitants; though, when we consider
how immeasurably multitudinous are those of their properties which we
are entirely ignorant of, compared with the few which we know, we can
attach but trifling weight to any considerations of resemblance in which
the known elements bear so inconsiderable a proportion to the unknown.

Besides the competition between analogy and diversity, there may be a
competition of conflicting analogies. The new case may be similar in
some of its circumstances to cases in which the fact _m_ exists, but in
others to cases in which it is known not to exist. Amber has some
properties in common with vegetable, others with mineral products. A
painting of unknown origin, may resemble, in certain of its characters,
known works of a particular master, but in others it may as strikingly
resemble those of some other painter. A vase may bear some analogy to
works of Grecian, and some to those of Etruscan, or Egyptian art. We are
of course supposing that it does not possess any quality which has been
ascertained, by a sufficient induction, to be a conclusive mark either
of the one or of the other.

§ 3. Since the value of an analogical argument inferring one resemblance
from other resemblances without any antecedent evidence of a connexion
between them, depends on the extent of ascertained resemblance, compared
first with the amount of ascertained difference, and next with the
extent of the unexplored region of unascertained properties; it follows
that where the resemblance is very great, the ascertained difference
very small, and our knowledge of the subject-matter tolerably extensive,
the argument from analogy may approach in strength very near to a valid
induction. If, after much observation of B, we find that it agrees with
A in nine out of ten of its known properties, we may conclude with a
probability of nine to one, that it will possess any given derivative
property of A. If we discover, for example, an unknown animal or plant,
resembling closely some known one in the greater number of the
properties we observe in it, but differing in some few, we may
reasonably expect to find in the unobserved remainder of its properties,
a general agreement with those of the former; but also a difference
corresponding proportionately to the amount of observed diversity.

It thus appears that the conclusions derived from analogy are only of
any considerable value, when the case to which we reason is an adjacent
case; adjacent, not as before, in place or time, but in circumstances.
In the case of effects of which the causes are imperfectly or not at all
known, when consequently the observed order of their occurrence amounts
only to an empirical law, it often happens that the conditions which
have coexisted whenever the effect was observed, have been very
numerous. Now if a new case presents itself, in which all these
conditions do not exist, but the far greater part of them do, some one
or a few only being wanting, the inference that the effect will occur,
notwithstanding this deficiency of complete resemblance to the cases in
which it has been observed, may, though of the nature of analogy,
possess a high degree of probability. It is hardly necessary to add
that, however considerable this probability may be, no competent
inquirer into nature will rest satisfied with it when a complete
induction is attainable; but will consider the analogy as a mere
guide-post, pointing out the direction in which more rigorous
investigations should be prosecuted.

It is in this last respect that considerations of analogy have the
highest scientific value. The cases in which analogical evidence affords
in itself any very high degree of probability, are, as we have observed,
only those in which the resemblance is very close and extensive; but
there is no analogy, however faint, which may not be of the utmost value
in suggesting experiments or observations that may lead to more positive
conclusions. When the agents and their effects are out of the reach of
further observation and experiment, as in the speculations already
alluded to respecting the moon and planets, such slight probabilities
are no more than an interesting theme for the pleasant exercise of
imagination; but any suspicion, however slight, that sets an ingenious
person at work to contrive an experiment, or affords a reason for trying
one experiment rather than another, may be of the greatest benefit to

On this ground, though I cannot accept as positive doctrines any of
those scientific hypotheses which are unsusceptible of being ultimately
brought to the test of actual induction, such, for instance, as the two
theories of light, the emission theory of the last century, and the
undulatory theory which predominates in the present, I am yet unable to
agree with those who consider such hypotheses to be worthy of entire
disregard. As is well said by Hartley (and concurred in by a thinker in
general so diametrically opposed to Hartley's opinions as Dugald
Stewart), "any hypothesis which has so much plausibility as to explain a
considerable number of facts, helps us to digest these facts in proper
order, to bring new ones to light, and make _experimenta crucis_ for the
sake of future inquirers."[25] If an hypothesis both explains known
facts, and has led to the prediction of others previously unknown, and
since verified by experience, the laws of the phenomenon which is the
subject of inquiry must bear at least a great similarity to those of the
class of phenomena to which the hypothesis assimilates it; and since the
analogy which extends so far may probably extend farther, nothing is
more likely to suggest experiments tending to throw light upon the real
properties of the phenomenon, than the following out such an hypothesis.
But to this end it is by no means necessary that the hypothesis be
mistaken for a scientific truth. On the contrary, that illusion is in
this respect, as in every other, an impediment to the progress of real
knowledge, by leading inquirers to restrict themselves arbitrarily to
the particular hypothesis which is most accredited at the time, instead
of looking out for every class of phenomena between the laws of which
and those of the given phenomenon any analogy exists, and trying all
such experiments as may tend to the discovery of ulterior analogies
pointing in the same direction.



§ 1. We have now completed our review of the logical processes by which
the laws, or uniformities, of the sequence of phenomena, and those
uniformities in their coexistence which depend on the laws of their
sequence, are ascertained or tested. As we recognised in the
commencement, and have been enabled to see more clearly in the progress
of the investigation, the basis of all these logical operations is the
law of causation. The validity of all the Inductive Methods depends on
the assumption that every event, or the beginning of every phenomenon,
must have some cause; some antecedent, on the existence of which it is
invariably and unconditionally consequent. In the Method of Agreement
this is obvious; that method avowedly proceeding on the supposition that
we have found the true cause as soon as we have negatived every other.
The assertion is equally true of the Method of Difference. That method
authorizes us to infer a general law from two instances; one, in which A
exists together with a multitude of other circumstances, and B follows;
another, in which, A being removed, and all other circumstances
remaining the same, B is prevented. What, however, does this prove? It
proves that B, in the particular instance, cannot have had any other
cause than A; but to conclude from this that A was the cause, or that A
will on other occasions be followed by B, is only allowable on the
assumption that B must have some cause; that among its antecedents in
any single instance in which it occurs, there must be one which has the
capacity of producing it at other times. This being admitted, it is seen
that in the case in question that antecedent can be no other than A;
but, that if it be no other than A it must be A, is not proved, by these
instances at least, but taken for granted. There is no need to spend
time in proving that the same thing is true of the other Inductive
Methods. The universality of the law of causation is assumed in them

But is this assumption warranted? Doubtless (it may be said) _most_
phenomena are connected as effects with some antecedent or cause, that
is, are never produced unless some assignable fact has preceded them;
but the very circumstance that complicated processes of induction are
sometimes necessary, shows that cases exist in which this regular order
of succession is not apparent to our unaided apprehension. If, then, the
processes which bring these cases within the same category with the
rest, require that we should assume the universality of the very law
which they do not at first sight appear to exemplify, is not this a
_petitio principii_? Can we prove a proposition, by an argument which
takes it for granted? And if not so proved, on what evidence does it

For this difficulty, which I have purposely stated in the strongest
terms it will admit of, the school of metaphysicians who have long
predominated in this country find a ready salvo. They affirm, that the
universality of causation is a truth which we cannot help believing;
that the belief in it is an instinct, one of the laws of our believing
faculty. As the proof of this, they say, and they have nothing else to
say, that everybody does believe it; and they number it among the
propositions, rather numerous in their catalogue, which may be logically
argued against, and perhaps cannot be logically proved, but which are of
higher authority than logic, and so essentially inherent in the human
mind, that even he who denies them in speculation, shows by his habitual
practice that his arguments make no impression upon himself.

Into the merits of this question, considered as one of psychology, it
would be foreign to my purpose to enter here: but I must protest against
adducing, as evidence of the truth of a fact in external nature, the
disposition, however strong or however general, of the human mind to
believe it. Belief is not proof, and does not dispense with the
necessity of proof. I am aware, that to ask for evidence of a
proposition which we are supposed to believe instinctively, is to expose
oneself to the charge of rejecting the authority of the human faculties;
which of course no one can consistently do, since the human faculties
are all which any one has to judge by: and inasmuch as the meaning of
the word evidence is supposed to be, something which when laid before
the mind, induces it to believe; to demand evidence when the belief is
ensured by the mind's own laws, is supposed to be appealing to the
intellect against the intellect. But this, I apprehend, is a
misunderstanding of the nature of evidence. By evidence is not meant
anything and everything which produces belief. There are many things
which generate belief besides evidence. A mere strong association of
ideas often causes a belief so intense as to be unshakeable by
experience or argument. Evidence is not that which the mind does or must
yield to, but that which it ought to yield to, namely, that, by yielding
to which, its belief is kept conformable to fact. There is no appeal
from the human faculties generally, but there is an appeal from one
human faculty to another; from the judging faculty, to those which take
cognizance of fact, the faculties of sense and consciousness. The
legitimacy of this appeal is admitted whenever it is allowed that our
judgments ought to be conformable to fact. To say that belief suffices
for its own justification is making opinion the test of opinion; it is
denying the existence of any outward standard, the conformity of an
opinion to which constitutes its truth. We call one mode of forming
opinions right and another wrong, because the one does, and the other
does not, tend to make the opinion agree with the fact--to make people
believe what really is, and expect what really will be. Now a mere
disposition to believe, even if supposed instinctive, is no guarantee
for the truth of the thing believed. If, indeed, the belief ever
amounted to an irresistible necessity, there would then be no _use_ in
appealing from it, because there would be no possibility of altering it.
But even then the truth of the belief would not follow; it would only
follow that mankind were under a permanent necessity of believing what
might possibly not be true; in other words, that a case might occur in
which our senses or consciousness, if they could be appealed to, might
testify one thing, and our reason believe another. But in fact there is
no such permanent necessity. There is no proposition of which it can be
asserted that every human mind must eternally and irrevocably believe
it. Many of the propositions of which this is most confidently stated,
great numbers of human beings have disbelieved. The things which it has
been supposed that nobody could possibly help believing, are
innumerable; but no two generations would make out the same catalogue of
them. One age or nation believes implicitly what to another seems
incredible and inconceivable; one individual has not a vestige of a
belief which another deems to be absolutely inherent in humanity. There
is not one of these supposed instinctive beliefs which is really
inevitable. It is in the power of every one to cultivate habits of
thought which make him independent of them. The habit of philosophical
analysis, (of which it is the surest effect to enable the mind to
command, instead of being commanded by, the laws of the merely passive
part of its own nature,) by showing to us that things are not
necessarily connected in fact because their ideas are connected in our
minds, is able to loosen innumerable associations which reign
despotically over the undisciplined or early-prejudiced mind. And this
habit is not without power even over those associations which the school
of which I have been speaking regard as connate and instinctive. I am
convinced that any one accustomed to abstraction and analysis, who will
fairly exert his faculties for the purpose, will, when his imagination
has once learnt to entertain the notion, find no difficulty in
conceiving that in some one for instance of the many firmaments into
which sidereal astronomy now divides the universe, events may succeed
one another at random, without any fixed law; nor can anything in our
experience, or in our mental nature, constitute a sufficient, or indeed
any, reason for believing that this is nowhere the case.

Were we to suppose (what it is perfectly possible to imagine) that the
present order of the universe were brought to an end, and that a chaos
succeeded in which there was no fixed succession of events, and the past
gave no assurance of the future; if a human being were miraculously kept
alive to witness this change, he surely would soon cease to believe in
any uniformity, the uniformity itself no longer existing. If this be
admitted, the belief in uniformity either is not an instinct, or it is
an instinct conquerable, like all other instincts, by acquired

But there is no need to speculate on what might be, when we have
positive and certain knowledge of what has been. It is not true as a
matter of fact, that mankind have always believed that all the
successions of events were uniform and according to fixed laws. The
Greek philosophers, not even excepting Aristotle, recognised Chance and
Spontaneity (_τύχη_ and _τὸ αὐτομάτον_) as among the agents in nature;
in other words, they believed that to that extent there was no guarantee
that the past had been similar to itself, or that the future would
resemble the past. Even now a full half of the philosophical world,
including the very same metaphysicians who contend most for the
instinctive character of the belief in uniformity, consider one
important class of phenomena, volitions, to be an exception to the
uniformity, and not governed by a fixed law.[26]

§ 2. As was observed in a former place,[27] the belief we entertain in
the universality, throughout nature, of the law of cause and effect, is
itself an instance of induction; and by no means one of the earliest
which any of us, or which mankind in general, can have made. We arrive
at this universal law, by generalization from many laws of inferior
generality. We should never have had the notion of causation (in the
philosophical meaning of the term) as a condition of all phenomena,
unless many cases of causation, or in other words, many partial
uniformities of sequence, had previously become familiar. The more
obvious of the particular uniformities suggest, and give evidence of,
the general uniformity, and the general uniformity, once established,
enables us to prove the remainder of the particular uniformities of
which it is made up. As, however, all rigorous processes of induction
presuppose the general uniformity, our knowledge of the particular
uniformities from which it was first inferred was not, of course,
derived from rigorous induction, but from the loose and uncertain mode
of induction _per enumerationem simplicem_: and the law of universal
causation, being collected from results so obtained, cannot itself rest
on any better foundation.

It would seem, therefore, that induction _per enumerationem simplicem_
not only is not necessarily an illicit logical process, but is in
reality the only kind of induction possible; since the more elaborate
process depends for its validity on a law, itself obtained in that
inartificial mode. Is there not then an inconsistency in contrasting the
looseness of one method with the rigidity of another, when that other is
indebted to the looser method for its own foundation?

The inconsistency, however, is only apparent. Assuredly, if induction by
simple enumeration were an invalid process, no process grounded on it
could be valid; just as no reliance could be placed on telescopes, if we
could not trust our eyes. But though a valid process, it is a fallible
one, and fallible in very different degrees: if therefore we can
substitute for the more fallible forms of the process, an operation
grounded on the same process in a less fallible form, we shall have
effected a very material improvement. And this is what scientific
induction does.

A mode of concluding from experience must be pronounced untrustworthy,
when subsequent experience refuses to confirm it. According to this
criterion, induction by simple enumeration--in other words,
generalization of an observed fact from the mere absence of any known
instance to the contrary--affords in general a precarious and unsafe
ground of assurance; for such generalizations are incessantly
discovered, on further experience, to be false. Still, however, it
affords some assurance, sufficient, in many cases, for the ordinary
guidance of conduct. It would be absurd to say, that the generalizations
arrived at by mankind in the outset of their experience, such as these,
Food nourishes, Fire burns, Water drowns, were unworthy of reliance.[28]
There is a scale of trustworthiness in the results of the original
unscientific Induction; and on this diversity (as observed in the fourth
chapter of the present book) depend the rules for the improvement of the
process. The improvement consists in correcting one of these
inartificial generalizations by means of another. As has been already
pointed out, this is all that art can do. To test a generalization, by
showing that it either follows from, or conflicts with, some stronger
induction, some generalization resting on a broader foundation of
experience, is the beginning and end of the logic of Induction.

§ 3. Now the precariousness of the method of simple enumeration is in an
inverse ratio to the largeness of the generalization. The process is
delusive and insufficient, exactly in proportion as the subject-matter
of the observation is special and limited in extent. As the sphere
widens, this unscientific method becomes less and less liable to
mislead; and the most universal class of truths, the law of causation
for instance, and the principles of number and of geometry, are duly and
satisfactorily proved by that method alone, nor are they susceptible of
any other proof.

With respect to the whole class of generalizations of which we have
recently treated, the uniformities which depend on causation, the truth
of the remark just made follows by obvious inference from the principles
laid down in the preceding chapters. When a fact has been observed a
certain number of times to be true, and is not in any instance known to
be false; if we at once affirm that fact as an universal truth or law of
nature, without testing it by any of the four methods of induction, nor
deducing it from other known laws, we shall in general err grossly: but
we are perfectly justified in affirming it as an empirical law, true
within certain limits of time, place, and circumstance, provided the
number of coincidences be greater than can with any probability be
ascribed to chance. The reason for not extending it beyond those limits
is, that the fact of its holding true within them may be a consequence
of collocations, which cannot be concluded to exist in one place because
they exist in another; or may be dependent on the accidental absence of
counteracting agencies, which any variation of time, or the smallest
change of circumstances, may possibly bring into play. If we suppose,
then, the subject-matter of any generalization to be so widely diffused
that there is no time, no place, and no combination of circumstances,
but must afford an example either of its truth or of its falsity, and if
it be never found otherwise than true, its truth cannot depend on any
collocations, unless such as exist at all times and places; nor can it
be frustrated by any counteracting agencies, unless by such as never
actually occur. It is, therefore, an empirical law coextensive with all
human experience; at which point the distinction between empirical laws
and laws of nature vanishes, and the proposition takes its place among
the most firmly established as well as largest truths accessible to

Now, the most extensive in its subject-matter of all generalizations
which experience warrants, respecting the sequences and coexistences of
phenomena, is the law of causation. It stands at the head of all
observed uniformities, in point of universality, and therefore (if the
preceding observations are correct) in point of certainty. And if we
consider, not what mankind would have been justified in believing in the
infancy of their knowledge, but what may rationally be believed in its
present more advanced state, we shall find ourselves warranted in
considering this fundamental law, though itself obtained by induction
from particular laws of causation, as not less certain, but on the
contrary, more so, than any of those from which it was drawn. It adds
to them as much proof as it receives from them. For there is probably no
one even of the best established laws of causation which is not
sometimes counteracted, and to which, therefore, apparent exceptions do
not present themselves, which would have necessarily and justly shaken
the confidence of mankind in the universality of those laws, if
inductive processes founded on the universal law had not enabled us to
refer those exceptions to the agency of counteracting causes, and
thereby reconcile them with the law with which they apparently conflict.
Errors, moreover, may have slipped into the statement of any one of the
special laws, through inattention to some material circumstance: and
instead of the true proposition, another may have been enunciated, false
as an universal law, though leading, in all cases hitherto observed, to
the same result. To the law of causation, on the contrary, we not only
do not know of any exception, but the exceptions which limit or
apparently invalidate the special laws, are so far from contradicting
the universal one, that they confirm it; since in all cases which are
sufficiently open to our observation, we are able to trace the
difference of result, either to the absence of a cause which had been
present in ordinary cases, or to the presence of one which had been

The law of cause and effect, being thus certain, is capable of imparting
its certainty to all other inductive propositions which can be deduced
from it; and the narrower inductions may be regarded as receiving their
ultimate sanction from that law, since there is no one of them which is
not rendered more certain than it was before, when we are able to
connect it with that larger induction, and to show that it cannot be
denied, consistently with the law that everything which begins to exist
has a cause. And hence we are justified in the seeming inconsistency, of
holding induction by simple enumeration to be good for proving this
general truth, the foundation of scientific induction, and yet refusing
to rely on it for any of the narrower inductions. I fully admit that if
the law of causation were unknown, generalization in the more obvious
cases of uniformity in phenomena would nevertheless be possible, and
though in all cases more or less precarious, and in some extremely so,
would suffice to constitute a certain measure of probability: but what
the amount of this probability might be, we are dispensed from
estimating, since it never could amount to the degree of assurance which
the proposition acquires, when, by the application to it of the Four
Methods, the supposition of its falsity is shown to be inconsistent with
the Law of Causation. We are therefore logically entitled, and, by the
necessities of scientific Induction, required, to disregard the
probabilities derived from the early rude method of generalizing, and to
consider no minor generalization as proved except so far as the law of
causation confirms it, nor probable except so far as it may reasonably
be expected to be so confirmed.

§ 4. The assertion, that our inductive processes assume the law of
causation, while the law of causation is itself a case of induction, is
a paradox, only on the old theory of reasoning, which supposes the
universal truth, or major premise, in a ratiocination, to be the real
proof of the particular truths which are ostensibly inferred from it.
According to the doctrine maintained in the present treatise,[29] the
major premise is not the proof of the conclusion, but is itself proved,
along with the conclusion from the same evidence. "All men are mortal"
is not the proof that Lord Palmerston is mortal; but our past experience
of mortality authorizes us to infer _both_ the general truth and the
particular fact, and the one with exactly the same degree of assurance
as the other. The mortality of Lord Palmerston is not an inference from
the mortality of all men, but from the experience which proves the
mortality of all men; and is a correct inference from experience, if
that general truth is so too. This relation between our general beliefs
and their particular applications holds equally true in the more
comprehensive case which we are now discussing. Any new fact of
causation inferred by induction, is rightly inferred, if no other
objection can be made to the inference than can be made to the general
truth that every event has a cause. The utmost certainty which can be
given to a conclusion arrived at in the way of inference, stops at this
point. When we have ascertained that the particular conclusion must
stand or fall with the general uniformity of the laws of nature--that it
is liable to no doubt except the doubt whether every event has a
cause--we have done all that can be done for it. The strongest assurance
we can obtain of any theory respecting the cause of a given phenomenon,
is that the phenomenon has either that cause or none.

The latter supposition might have been an admissible one in a very early
period of our study of nature. But we have been able to perceive that in
the stage which mankind have now reached, the generalization which gives
the Law of Universal Causation has grown into a stronger and better
induction, one deserving of greater reliance, than any of the
subordinate generalizations. We may even, I think, go a step further
than this, and regard the certainty of that great induction as not
merely comparative, but, for all practical purposes, absolute.

The considerations which, as I apprehend, give, at the present day, to
the proof of the law of uniformity of succession as true of all
phenomena without exception, this character of completeness and
conclusiveness, are the following:--First, that we now know it directly
to be true of far the greatest number of phenomena; that there are none
of which we know it not to be true, the utmost that can be said being,
that of some we cannot positively from direct evidence affirm its truth;
while phenomenon after phenomenon, as they become better known to us,
are constantly passing from the latter class into the former; and in all
cases in which that transition has not yet taken place, the absence of
direct proof is accounted for by the rarity or the obscurity of the
phenomena, our deficient means of observing them, or the logical
difficulties arising from the complication of the circumstances in which
they occur; insomuch that, notwithstanding as rigid a dependence on
given conditions as exists in the case of any other phenomenon, it was
not likely that we should be better acquainted with those conditions
than we are. Besides this first class of considerations, there is a
second, which still further corroborates the conclusion. Although there
are phenomena the production and changes of which elude all our attempts
to reduce them universally to any ascertained law; yet in every such
case, the phenomenon, or the objects concerned in it, are found in some
instances to obey the known laws of nature. The wind, for example, is
the type of uncertainty and caprice, yet we find it in some cases
obeying with as much constancy as any phenomenon in nature the law of
the tendency of fluids to distribute themselves so as to equalize the
pressure on every side of each of their particles; as in the case of the
trade winds, and the monsoons. Lightning might once have been supposed
to obey no laws; but since it has been ascertained to be identical with
electricity, we know that the very same phenomenon in some of its
manifestations is implicitly obedient to the action of fixed causes. I
do not believe that there is now one object or event in all our
experience of nature, within the bounds of the solar system at least,
which has not either been ascertained by direct observation to follow
laws of its own, or been proved to be closely similar to objects and
events which, in more familiar manifestations, or on a more limited
scale, follow strict laws: our inability to trace the same laws on a
larger scale and in the more recondite instances, being accounted for by
the number and complication of the modifying causes, or by their
inaccessibility to observation.

The progress of experience, therefore, has dissipated the doubt which
must have rested on the universality of the law of causation while there
were phenomena which seemed to be _sui generis_, not subject to the same
laws with any other class of phenomena, and not as yet ascertained to
have peculiar laws of their own. This great generalization, however,
might reasonably have been, as it in fact was, acted on as a probability
of the highest order, before there were sufficient grounds for receiving
it as a certainty. For, whatever has been found true in innumerable
instances, and never found to be false after due examination in any, we
are safe in acting on as universal provisionally, until an undoubted
exception appears; provided the nature of the case be such that a real
exception could scarcely have escaped our notice. When every phenomenon
that we ever knew sufficiently well to be able to answer the question,
had a cause on which it was invariably consequent, it was more rational
to suppose that our inability to assign the causes of other phenomena
arose from our ignorance, than that there were phenomena which were
uncaused, and which happened to be exactly those which we had hitherto
had no sufficient opportunity of studying.

It must, at the same time, be remarked, that the reasons for this
reliance do not hold in circumstances unknown to us, and beyond the
possible range of our experience. In distant parts of the stellar
regions, where the phenomena may be entirely unlike those with which we
are acquainted, it would be folly to affirm confidently that this
general law prevails, any more than those special ones which we have
found to hold universally on our own planet. The uniformity in the
succession of events, otherwise called the law of causation, must be
received not as a law of the universe, but of that portion of it only
which is within the range of our means of sure observation, with a
reasonable degree of extension to adjacent cases. To extend it further
is to make a supposition without evidence, and to which, in the absence
of any ground from experience for estimating its degree of probability,
it would be idle to attempt to assign any.[30]



§ 1. The order of the occurrence of phenomena in time, is either
successive or simultaneous; the uniformities, therefore, which obtain in
their occurrence, are either uniformities of succession or of
coexistence. Uniformities of succession are all comprehended under the
law of causation and its consequences. Every phenomenon has a cause,
which it invariably follows; and from this are derived other invariable
sequences among the successive stages of the same effect, as well as
between the effects resulting from causes which invariably succeed one

In the same manner with these derivative uniformities of succession, a
great variety of uniformities of coexistence also take their rise.
Coordinate effects of the same cause naturally coexist with one another.
High water at any point on the earth's surface, and high water at the
point diametrically opposite to it, are effects uniformly simultaneous,
resulting from the direction in which the combined attractions of the
sun and moon act upon the waters of the ocean. An eclipse of the sun to
us, and an eclipse of the earth to a spectator situated in the moon, are
in like manner phenomena invariably coexistent; and their coexistence
can equally be deduced from the laws of their production.

It is an obvious question, therefore, whether all the uniformities of
coexistence among phenomena may not be accounted for in this manner. And
it cannot be doubted that between phenomena which are themselves
effects, the coexistences must necessarily depend on the causes of those
phenomena. If they are effects immediately or remotely of the same
cause, they cannot coexist except by virtue of some laws or properties
of that cause: if they are effects of different causes, they cannot
coexist unless it be because their causes coexist; and the uniformity of
coexistence, if such there be, between the effects, proves that those
particular causes, within the limits of our observation, have uniformly
been coexistent.

§ 2. But these same considerations compel us to recognise that there
must be one class of coexistences which cannot depend on causation; the
coexistences between the ultimate properties of things--those properties
which are the causes of all phenomena, but are not themselves caused by
any phenomenon, and a cause for which could only be sought by ascending
to the origin of all things. Yet among these ultimate properties there
are not only coexistences, but uniformities of coexistence. General
propositions may be, and are, formed, which assert that whenever certain
properties are found, certain others are found along with them. We
perceive an object; say, for instance, water. We recognise it to be
water, of course by certain of its properties. Having recognised it, we
are able to affirm of it innumerable other properties; which we could
not do unless it were a general truth, a law or uniformity in nature,
that the set of properties by which we identify the substance as water,
always have those other properties conjoined with them.

In a former place,[31] it has been explained in some detail what is
meant by the Kinds of objects; those classes which differ from one
another not by a limited and definite, but by an indefinite and unknown,
number of distinctions. To this we have now to add, that every
proposition by which anything is asserted of a Kind, affirms an
uniformity of coexistence. Since we know nothing of Kinds but their
properties, the Kind, to us, _is_ the set of properties by which it is
identified, and which must of course be sufficient to distinguish it
from every other kind.[32] In affirming anything, therefore, of a Kind,
we are affirming something to be uniformly coexistent with the
properties by which the kind is recognised; and that is the sole meaning
of the assertion.

Among the uniformities of coexistence which exist in nature, may hence
be numbered all the properties of Kinds. The whole of these, however,
are not independent of causation, but only a portion of them. Some are
ultimate properties, others derivative; of some, no cause can be
assigned, but others are manifestly dependent on causes. Thus, pure
atmospheric air is a Kind, and one of its most unequivocal properties is
its gaseous form: this property, however, has for its cause the presence
of a certain quantity of latent heat; and if that heat could be taken
away (as has been done from so many gases in Faraday's experiments), the
gaseous form would doubtless disappear, together with numerous other
properties which depend on, or are caused by, that property.

In regard to all substances which are chemical compounds, and which
therefore may be regarded as products of the juxtaposition of substances
different in Kind from themselves, there is considerable reason to
presume that the specific properties of the compound are consequent, as
effects, on some of the properties of the elements, though little
progress has yet been made in tracing any invariable relation between
the latter and the former. Still more strongly will a similar
presumption exist, when the object itself, as in the case of organized
beings, is no primeval agent, but an effect, which depends on a cause or
causes for its very existence. The Kinds therefore which are called in
chemistry simple substances, or elementary natural agents, are the only
ones, any of whose properties can with certainty be considered
ultimate; and of these the ultimate properties are probably much more
numerous that we at present recognise, since every successful instance
of the resolution of the properties of their compounds into simpler
laws, generally leads to the recognition of properties in the elements
distinct from any previously known. The resolution of the laws of the
heavenly motions, established the previously unknown ultimate property
of a mutual attraction between all bodies: the resolution, so far as it
has yet proceeded, of the laws of crystallization, of chemical
composition, electricity, magnetism, &c., points to various polarities,
ultimately inherent in the particles of which bodies are composed; the
comparative atomic weights of different kinds of bodies were ascertained
by resolving, into more general laws, the uniformities observed in the
proportions in which substances combine with one another; and so forth.
Thus although every resolution of a complex uniformity into simpler and
more elementary laws has an apparent tendency to diminish the number of
the ultimate properties, and really does remove many properties from the
list; yet, (since the result of this simplifying process is to trace up
an ever greater variety of different effects to the same agents,) the
further we advance in this direction, the greater number of distinct
properties we are forced to recognise in one and the same object: the
coexistences of which properties must accordingly be ranked among the
ultimate generalities of nature.

§ 3. There are, therefore, only two kinds of propositions which assert
uniformity of coexistence between properties. Either the properties
depend on causes, or they do not. If they do, the proposition which
affirms them to be coexistent is a derivative law of coexistence between
effects, and until resolved into the laws of causation on which it
depends, is an empirical law, and to be tried by the principles of
induction to which such laws are amenable. If, on the other hand, the
properties do not depend on causes, but are ultimate properties; then if
it be true that they invariably coexist, they must all be ultimate
properties of one and the same Kind; and it is of these only that the
coexistences can be classed as a peculiar sort of laws of nature.

When we affirm that all crows are black, or that all negroes have woolly
hair, we assert an uniformity of coexistence. We assert that the
property of blackness, or of having woolly hair, invariably coexists
with the properties which, in common language, or in the scientific
classification that we adopt, are taken to constitute the class crow, or
the class negro. Now, supposing blackness to be an ultimate property of
black objects, or woolly hair an ultimate property of the animals which
possess it; supposing that these properties are not results of
causation, are not connected with antecedent phenomena by any law; then
if all crows are black, and all negroes have woolly hair, these must be
ultimate properties of the Kind _crow_, or _negro_, or of some Kind
which includes them. If, on the contrary, blackness or woolly hair be an
effect depending on causes, these general propositions are manifestly
empirical laws; and all that has already been said respecting that class
of generalizations may be applied without modification to these.

Now, we have seen that in the case of all compounds--of all things, in
short, except the elementary substances and primary powers of
nature--the presumption is, that the properties do really depend upon
causes; and it is impossible in any case whatever to be certain that
they do not. We therefore should not be safe in claiming for any
generalization respecting the coexistence of properties, a degree of
certainty to which, if the properties should happen to be the result of
causes, it would have no claim. A generalization respecting coexistence,
or in other words respecting the properties of Kinds, may be an ultimate
truth, but it may, also, be merely a derivative one; and since, if so,
it is one of those derivative laws which are neither laws of causation,
nor have been resolved into the laws of causation on which they depend,
it can possess no higher degree of evidence than belongs to an empirical

§ 4. This conclusion will be confirmed by the consideration of one
great deficiency, which precludes the application to the ultimate
uniformities of coexistence, of a system of rigorous scientific
induction, such as the uniformities in the succession of phenomena have
been found to admit of. The basis of such a system is wanting: there is
no general axiom, standing in the same relation to the uniformities of
coexistence as the law of causation does to those of succession. The
Methods of Induction applicable to the ascertainment of causes and
effects, are grounded on the principle that everything which has a
beginning must have some cause or other; that among the circumstances
which actually existed at the time of its commencement, there is
certainly some one combination, on which the effect in question is
unconditionally consequent, and on the repetition of which it would
certainly again recur. But in an inquiry whether some kind (as crow)
universally possesses a certain property (as blackness), there is no
room for any assumption analogous to this. We have no previous certainty
that the property must have something which constantly coexists with it;
must have an invariable coexistent, in the same manner as an event must
have an invariable antecedent. When we feel pain, we must be in some
circumstances under which if exactly repeated we should always feel
pain. But when we are conscious of blackness, it does not follow that
there is something else present of which blackness is a constant
accompaniment. There is, therefore, no room for elimination; no Method
of Agreement or Difference, or of Concomitant Variations (which is but a
modification either of the Method of Agreement or of the Method of
Difference). We cannot conclude that the blackness we see in crows must
be an invariable property of crows, merely because there is nothing else
present of which it can be an invariable property. We therefore inquire
into the truth of a proposition like "All crows are black," under the
same disadvantage as if, in our inquiries into causation, we were
compelled to let in, as one of the possibilities, that the effect may in
that particular instance have arisen without any cause at all.

To overlook this grand distinction was, as it seems to me, the capital
error in Bacon's view of inductive philosophy. The principle of
elimination, that great logical instrument which he had the immense
merit of first bringing into general use, he deemed applicable in the
same sense, and in as unqualified a manner, to the investigation of the
coexistences, as to that of the successions of phenomena. He seems to
have thought that as every event has a cause, or invariable antecedent,
so every property of an object has an invariable coexistent, which he
called its Form: and the examples he chiefly selected for the
application and illustration of his method, were inquiries into such
Forms; attempts to determine in what else all those objects resembled,
which agreed in some one general property, as hardness or softness,
dryness or moistness, heat or coldness. Such inquiries could lead to no
result. The objects seldom have any such circumstances in common. They
usually agree in the one point inquired into, and in nothing else. A
great proportion of the properties which, so far as we can conjecture,
are the likeliest to be really ultimate, would seem to be inherently
properties of many different Kinds of things, not allied in any other
respect. And as for the properties which, being effects of causes, we
are able to give some account of, they have generally nothing to do with
the ultimate resemblances or diversities in the objects themselves, but
depend on some outward circumstances, under the influence of which any
objects whatever are capable of manifesting those properties; as is
emphatically the case with those favourite subjects of Bacon's
scientific inquiries, hotness and coldness; as well as with hardness and
softness, solidity and fluidity, and many other conspicuous qualities.

In the absence, then, of any universal law of coexistence, similar to
the universal law of causation which regulates sequence, we are thrown
back upon the unscientific induction of the ancients, _per enumerationem
simplicem, ubi non reperitur instantia contradictoria_. The reason we
have for believing that all crows are black, is simply that we have seen
and heard of many black crows, and never one of any other colour. It
remains to be considered how far this evidence can reach, and how we are
to measure its strength in any given case.

§ 5. It sometimes happens that a mere change in the mode of verbally
enunciating a question, though nothing is really added to the meaning
expressed, is of itself a considerable step towards its solution. This,
I think, happens in the present instance. The degree of certainty of any
generalization which rests on no other evidence than the agreement, so
far as it goes, of all past observation, is but another phrase for the
degree of improbability that an exception, if any existed, could have
hitherto remained unobserved. The reason for believing that all crows
are black, is measured by the improbability that crows of any other
colour should have existed to the present time without our being aware
of it. Let us state the question in this last mode, and consider what is
implied in the supposition that there may be crows which are not black,
and under what conditions we can be justified in regarding this as

If there really exist crows which are not black, one of two things must
be the fact. Either the circumstance of blackness, in all crows hitherto
observed, must be, as it were, an accident, not connected with any
distinction of Kind; or if it be a property of Kind, the crows which are
not black must be a new Kind, a Kind hitherto overlooked, though coming
under the same general description by which crows have hitherto been
characterized. The first supposition would be proved true if we were to
discover casually a white crow among black ones, or if it were found
that black crows sometimes turn white. The second would be shown to be
the fact if in Australia or Central Africa a species or a race of white
or grey crows were found to exist.

§ 6. The former of these suppositions necessarily implies that the
colour is an effect of causation. If blackness, in the crows in which it
has been observed, be not a property of Kind, but can be present or
absent without any difference generally in the properties of the object;
then it is not an ultimate fact in the individuals themselves, but is
certainly dependent on a cause. There are, no doubt, many properties
which vary from individual to individual of the same Kind, even the
same _infima species_, or lowest Kind. Some flowers may be either white
or red, without differing in any other respect. But these properties are
not ultimate; they depend on causes. So far as the properties of a thing
belong to its own nature, and do not arise from some cause extrinsic to
it, they are always the same in the same Kind. Take, for instance, all
simple substances and elementary powers; the only things of which we are
certain that some at least of their properties are really ultimate.
Colour is generally esteemed the most variable of all properties: yet we
do not find that sulphur is sometimes yellow and sometimes white, or
that it varies in colour at all, except so far as colour is the effect
of some extrinsic cause, as of the sort of light thrown upon it, the
mechanical arrangement of the particles, (as after fusion) &c. We do not
find that iron is sometimes fluid and sometimes solid at the same
temperature; gold sometimes malleable and sometimes brittle; that
hydrogen will sometimes combine with oxygen and sometimes not; or the
like. If from simple substances we pass to any of their definite
compounds, as water, lime, or sulphuric acid, there is the same
constancy in their properties. When properties vary from individual to
individual, it is either in the case of miscellaneous aggregations, such
as atmospheric air or rock, composed of heterogeneous substances, and
not constituting or belonging to any real Kind,[33] or it is in the case
of organic beings. In them, indeed, there is variability in a high
degree. Animals of the same species and race, human beings of the same
age, sex, and country, will be most different, for example, in face and
figure. But organized beings (from the extreme complication of the laws
by which they are regulated) being more eminently modifiable, that is,
liable to be influenced by a greater number and variety of causes, than
any other phenomena whatever; having also themselves had a beginning,
and therefore a cause; there is reason to believe that none of their
properties are ultimate, but all of them derivative, and produced by
causation. And the presumption is confirmed, by the fact that the
properties which vary from one individual to another, also generally
vary more or less at different times in the same individual; which
variation, like any other event, supposes a cause, and implies,
consequently, that the properties are not independent of causation.

If, therefore, blackness be merely accidental in crows, and capable of
varying while the Kind remains the same, its presence or absence is
doubtless no ultimate fact, but the effect of some unknown cause: and in
that case the universality of the experience that all crows are black is
sufficient proof of a common cause, and establishes the generalization
as an empirical law. Since there are innumerable instances in the
affirmative, and hitherto none at all in the negative, the causes on
which the property depends must exist everywhere in the limits of the
observations which have been made; and the proposition may be received
as universal within those limits, and with the allowable degree of
extension to adjacent cases.

§ 7. If, in the second place, the property, in the instances in which it
has been observed, is not an effect of causation, it is a property of
Kind; and in that case the generalization can only be set aside by the
discovery of a new Kind of crow. That, however, a peculiar Kind, not
hitherto discovered, should exist in nature, is a supposition so often
realized, that it cannot be considered at all improbable. We have
nothing to authorize us in attempting to limit the Kinds of things which
exist in nature. The only unlikelihood would be that a new Kind should
be discovered in localities which there was previously reason to believe
had been thoroughly explored; and even this improbability depends on the
degree of conspicuousness of the difference between the newly-discovered
Kind and all others, since new Kinds of minerals, plants, and even
animals, previously overlooked or confounded with known species, are
still continually detected in the most frequented situations. On this
second ground, therefore, as well as on the first, the observed
uniformity of coexistence can only hold good as an empirical law, within
the limits not only of actual observation, but of an observation as
accurate as the nature of the case required. And hence it is that (as
remarked in an early chapter of the present Book) we so often give up
generalizations of this class at the first summons. If any credible
witness stated that he had seen a white crow, under circumstances which
made it not incredible that it should have escaped notice previously, we
should give full credence to the statement.

It appears, then, that the uniformities which obtain in the coexistence
of phenomena,--those which we have reason to consider as ultimate, no
less than those which arise from the laws of causes yet undetected--are
entitled to reception only as empirical laws; are not to be presumed
true except within the limits of time, place, and circumstance, in which
the observations were made, or except in cases strictly adjacent.

§ 8. We have seen in the last chapter that there is a point of
generality at which empirical laws become as certain as laws of nature,
or rather, at which there is no longer any distinction between empirical
laws and laws of nature. As empirical laws approach this point, in other
words, as they rise in their degree of generality, they become more
certain; their universality may be more strongly relied on. For, in the
first place, if they are results of causation (which, even in the class
of uniformities treated of in the present chapter, we never can be
certain that they are not) the more general they are, the greater is
proved to be the space over which the necessary collocations prevail,
and within which no causes exist capable of counteracting the unknown
causes on which the empirical law depends. To say that anything is an
invariable property of some very limited class of objects, is to say
that it invariably accompanies some very numerous and complex group of
distinguishing properties; which, if causation be at all concerned in
the matter, argues a combination of many causes, and therefore a great
liability to counteraction; while the comparatively narrow range of the
observations renders it impossible to predict to what extent unknown
counteracting causes may be distributed throughout nature. But when a
generalization has been found to hold good of a very large proportion of
all things whatever, it is already proved that nearly all the causes
which exist in nature have no power over it; that very few changes in
the combination of causes can effect it; since the greater number of
possible combinations must have already existed in some one or other of
the instances in which it has been found true. If, therefore, any
empirical law is a result of causation, the more general it is, the more
it may be depended on. And even if it be no result of causation, but an
ultimate coexistence, the more general it is, the greater amount of
experience it is derived from, and the greater therefore is the
probability that if exceptions had existed, some would already have
presented themselves.

For these reasons, it requires much more evidence to establish an
exception to one of the more general empirical laws than to the more
special ones. We should not have any difficulty in believing that there
might be a new Kind of crow; or a new kind of bird resembling a crow in
the properties hitherto considered distinctive of that Kind. But it
would require stronger proof to convince us of the existence of a Kind
of crow having properties at variance with any generally recognised
universal property of birds; and a still higher degree if the properties
conflict with any recognised universal property of animals. And this is
conformable to the mode of judgment recommended by the common sense and
general practice of mankind, who are more incredulous as to any
novelties in nature, according to the degree of generality of the
experience which these novelties seem to contradict.

§ 9. Still, however, even these greater generalizations, which embrace
comprehensive Kinds, containing under them a great number and variety of
_infimæ species_, are only empirical laws, resting on induction by
simple enumeration merely, and not on any process of elimination, a
process wholly inapplicable to this sort of case. Such generalizations,
therefore, ought to be grounded on an examination of all the _infimæ
species_ comprehended in them, and not of a portion only. We cannot
conclude (where causation is not concerned), because a proposition is
true of a number of things resembling one another only in being animals,
that it is therefore true of all animals. If, indeed, anything be true
of species which differ more from one another than either differs from a
third, (especially if that third species occupies in most of its known
properties a position between the two former,) there is some probability
that the same thing will also be true of that intermediate species; for
it is often, though by no means universally, found, that there is a sort
of parallelism in the properties of different Kinds, and that their
degree of unlikeness in one respect bears some proportion to their
unlikeness in others. We see this parallelism in the properties of the
different metals; in those of sulphur, phosphorus, and carbon; of
chlorine, iodine, and bromine; in the natural orders of plants and
animals, &c. But there are innumerable anomalies and exceptions to this
sort of conformity; if indeed the conformity itself be anything but an
anomaly and an exception in nature.

Universal propositions, therefore, respecting the properties of superior
Kinds, unless grounded on proved or presumed connexion by causation,
ought not to be hazarded except after separately examining every known
sub-kind included in the larger Kind. And even then such generalizations
must be held in readiness to be given up on the occurrence of some new
anomaly, which, when the uniformity is not derived from causation, can
never, even in the case of the most general of these empirical laws, be
considered very improbable. Thus all the universal propositions which it
has been attempted to lay down respecting simple substances, or
concerning any of the classes which have been formed among simple
substances, (and the attempt has been often made,) have, with the
progress of experience, either faded into inanity, or been proved to be
erroneous; and each Kind of simple substance remains with its own
collection of properties apart from the rest, saving a certain
parallelism with a few other Kinds, the most similar to itself. In
organized beings, indeed, there are abundance of propositions
ascertained to be universally true of superior genera, to many of which
the discovery hereafter of any exceptions must be regarded as extremely
improbable. But these, as already observed, are, we have every reason to
believe, properties dependent on causation.

Uniformities of coexistence, then, not only when they are consequences
of laws of succession, but also when they are ultimate truths, must be
ranked, for the purpose of logic, among empirical laws; and are amenable
in every respect to the same rules with those unresolved uniformities
which are known to be dependent on causation.



§ 1. In our inquiries into the nature of the inductive process, we must
not confine our notice to such generalizations from experience as
profess to be universally true. There is a class of inductive truths
avowedly not universal; in which it is not pretended that the predicate
is always true of the subject; but the value of which, as
generalizations, is nevertheless extremely great. An important portion
of the field of inductive knowledge does not consist of universal
truths, but of approximations to such truths; and when a conclusion is
said to rest on probable evidence, the premises it is drawn from are
usually generalizations of this sort.

As every certain inference respecting a particular case, implies that
there is ground for a general proposition, of the form, Every A is B; so
does every probable inference suppose that there is ground for a
proposition of the form, Most A are B: and the degree of probability of
the inference in an average case, will depend on the proportion between
the number of instances existing in nature which accord with the
generalization, and the number of those which conflict with it.

§ 2. Propositions in the form, Most A are B, are of a very different
degree of importance in science, and in the practice of life. To the
scientific inquirer they are valuable chiefly as materials for, and
steps towards, universal truths. The discovery of these is the proper
end of science: its work is not done if it stops at the proposition that
a majority of A are B, without circumscribing that majority by some
common character, fitted to distinguish them from the minority.
Independently of the inferior precision of such imperfect
generalizations, and the inferior assurance with which they can be
applied to individual cases, it is plain that, compared with exact
generalizations, they are almost useless as means of discovering
ulterior truths by way of deduction. We may, it is true, by combining
the proposition Most A are B, with an universal proposition, Every B is
C, arrive at the conclusion that Most A are C. But when a second
proposition of the approximate kind is introduced,--or even when there
is but one, if that one be the major premise,--nothing can in general be
positively concluded. When the major is Most B are D, then, even if the
minor be Every A is B, we cannot infer that most A are D, or with any
certainty that even some A are D. Though the majority of the class B
have the attribute signified by D, the whole of the sub-class A may
belong to the minority.[34]

Though so little use can be made, in science, of approximate
generalizations, except as a stage on the road to something better, for
practical guidance they are often all we have to rely on. Even when
science has really determined the universal laws of any phenomenon, not
only are those laws generally too much encumbered with conditions to be
adapted for every-day use, but the cases which present themselves in
life are too complicated, and our decisions require to be taken too
rapidly, to admit of waiting till the existence of a phenomenon can be
proved by what have been scientifically ascertained to be universal
marks of it. To be indecisive and reluctant to act, because we have not
evidence of a perfectly conclusive character to act on, is a defect
sometimes incident to scientific minds, but which, wherever it exists,
renders them unfit for practical emergencies. If we would succeed in
action, we must judge by indications which, though they do not
generally mislead us, sometimes do; and must make up, as far as
possible, for the incomplete conclusiveness of any one indication, by
obtaining others to corroborate it. The principles of induction
applicable to approximate generalization are therefore a not less
important subject of inquiry, than the rules for the investigation of
universal truths; and might reasonably be expected to detain us almost
as long, were it not that these principles are mere corollaries from
those which have been already treated of.

§ 3. There are two sorts of cases in which we are forced to guide
ourselves by generalizations of the imperfect form, Most A are B. The
first is, when we have no others; when we have not been able to carry
our investigation of the laws of the phenomena any farther; as in the
following propositions: Most dark-eyed persons have dark hair; Most
springs contain mineral substances; Most stratified formations contain
fossils. The importance of this class of generalizations is not very
great; for, though it frequently happens that we see no reason why that
which is true of most individuals of a class is not true of the
remainder, nor are able to bring the former under any general
description which can distinguish them from the latter, yet if we are
willing to be satisfied with propositions of a less degree of
generality, and to break down the class A into subclasses, we may
generally obtain a collection of propositions exactly true. We do not
know why most wood is lighter than water, nor can we point out any
general property which discriminates wood that is lighter than water
from that which is heavier. But we know exactly what species are the one
and what the other. And if we meet with a specimen not conformable to
any known species (the only case in which our previous knowledge affords
no other guidance than the approximate generalization), we can generally
make a specific experiment, which is a surer resource.

It often happens, however, that the proposition, Most A are B, is not
the ultimatum of our scientific progress, though the knowledge we
possess beyond it cannot conveniently be brought to bear upon the
particular instance. In such a case we know well enough what
circumstances distinguish the portion of A which has the attribute B
from the portion which has it not, but have no means, or have not time,
to examine whether those characteristic circumstances exist or not in
the individual case. This is the situation we are generally in when the
inquiry is of the kind called moral, that is, of the kind which has in
view to predict human actions. To enable us to affirm anything
universally concerning the actions of classes of human beings, the
classification must be grounded on the circumstances of their mental
culture and habits, which in an individual case are seldom exactly
known; and classes grounded on these distinctions would never precisely
accord with those into which mankind are divided for social purposes.
All propositions which can be framed respecting the actions of human
beings as ordinarily classified, or as classified according to any kind
of outward indications, are merely approximate. We can only say, Most
persons of a particular age, profession, country, or rank in society,
have such and such qualities; or, Most persons when placed in certain
circumstances act in such and such a way. Not that we do not often know
well enough on what causes the qualities depend, or what sort of persons
they are who act in that particular way; but we have seldom the means of
knowing whether any individual person has been under the influence of
those causes, or is a person of that particular sort. We could replace
the approximate generalizations by propositions universally true; but
these would hardly ever be capable of being applied to practice. We
should be sure of our majors, but we should not be able to get minors to
fit: we are forced, therefore, to draw our conclusions from coarser and
more fallible indications.

§ 4. Proceeding now to consider, what is to be regarded as sufficient
evidence of an approximate generalization; we can have no difficulty in
at once recognising that when admissible at all, it is admissible only
as an empirical law. Propositions of the form, Every A is B, are not
necessarily laws of causation, or ultimate uniformities of coexistence;
propositions like Most A are B _cannot_ be so. Propositions hitherto
found true in every observed instance, may yet be no necessary
consequence of laws of causation, or of ultimate uniformities, and
unless they are so, may, for aught we know, be false beyond the limits
of actual observation: still more evidently must this be the case with
propositions which are only true in a mere majority of the observed

There is some difference, however, in the degree of certainty of the
proposition, Most A are B, according as that approximate generalization
composes the whole of our knowledge of the subject, or not. Suppose,
first, that the former is the case. We know only that most A are B, not
why they are so, nor in what respect those which are, differ from those
which are not. How then did we learn that most A are B? Precisely in the
manner in which we should have learnt, had such happened to be the fact,
that all A are B. We collected a number of instances sufficient to
eliminate chance, and having done so, compared the number of instances
in the affirmative with the number in the negative. The result, like
other unresolved derivative laws, can be relied on solely within the
limits not only of place and time, but also of circumstance, under which
its truth has been actually observed; for as we are supposed to be
ignorant of the causes which make the proposition true, we cannot tell
in what manner any new circumstance might perhaps affect it. The
proposition, Most judges are inaccessible to bribes, would be found true
of Englishmen, Frenchmen, Germans, North Americans, and so forth; but if
on this evidence alone we extended the assertion to Orientals, we should
step beyond the limits, not only of place but of circumstance, within
which the fact had been observed, and should let in possibilities of the
absence of the determining causes, or the presence of counteracting
ones, which might be fatal to the approximate generalization.

In the case where the approximate proposition is not the ultimatum of
our scientific knowledge, but only the most available form of it for
practical guidance; where we know, not only that most A have the
attribute B, but also the causes of B, or some properties by which the
portion of A which has that attribute is distinguished from the portion
which has it not; we are rather more favourably situated than in the
preceding case. For we have now a double mode of ascertaining whether it
be true that most A are B; the direct mode, as before, and an indirect
one, that of examining whether the proposition admits of being deduced
from the known cause, or from any known criterion, of B. Let the
question, for example, be whether most Scotchmen can read? We may not
have observed, or received the testimony of others respecting, a
sufficient number and variety of Scotchmen to ascertain this fact; but
when we consider that the cause of being able to read is the having been
taught it, another mode of determining the question presents itself,
namely, by inquiring whether most Scotchmen have been sent to schools
where reading is effectually taught. Of these two modes, sometimes one
and sometimes the other is the more available. In some cases, the
frequency of the effect is the more accessible to that extensive and
varied observation which is indispensable to the establishment of an
empirical law; at other times, the frequency of the causes, or of some
collateral indications. It commonly happens that neither is susceptible
of so satisfactory an induction as could be desired, and that the
grounds on which the conclusion is received are compounded of both. Thus
a person may believe that most Scotchmen can read, because, so far as
his information extends, most Scotchmen have been sent to school, and
most Scotch schools teach reading effectually; and also because most of
the Scotchmen whom he has known or heard of, could read; though neither
of these two sets of observations may by itself fulfil the necessary
conditions of extent and variety.

Although the approximate generalization may in most cases be
indispensable for our guidance, even when we know the cause, or some
certain mark, of the attribute predicated; it needs hardly be observed
that we may always replace the uncertain indication by a certain one, in
any case in which we can actually recognise the existence of the cause
or mark. For example, an assertion is made by a witness, and the
question is, whether to believe it. If we do not look to any of the
individual circumstances of the case, we have nothing to direct us but
the approximate generalization, that truth is more common than
falsehood, or, in other words, that most persons, on most occasions,
speak truth. But if we consider in what circumstances the cases where
truth is spoken differ from those in which it is not, we find, for
instance, the following: the witness's being an honest person or not;
his being an accurate observer or not; his having an interest to serve
in the matter or not. Now, not only may we be able to obtain other
approximate generalizations respecting the degree of frequency of these
various possibilities, but we may know which of them is positively
realized in the individual case. That the witness has or has not an
interest to serve, we perhaps know directly; and the other two points
indirectly, by means of marks; as, for example, from his conduct on some
former occasion; or from his reputation, which, though a very uncertain
mark, affords an approximate generalization (as, for instance, Most
persons who are believed to be honest by those with whom they have had
frequent dealings, are really so) which approaches nearer to an
universal truth than the approximate general proposition with which we
set out, viz. Most persons on most occasions speak truth.

As it seems unnecessary to dwell further on the question of the evidence
of approximate generalizations, we shall proceed to a not less important
topic, that of the cautions to be observed in arguing from these
incompletely universal propositions to particular cases.

§ 5. So far as regards the direct application of an approximate
generalization to an individual instance, this question presents no
difficulty. If the proposition, Most A are B, has been established, by a
sufficient induction, as an empirical law, we may conclude that any
particular A is B with a probability proportioned to the preponderance
of the number of affirmative instances over the number of exceptions. If
it has been found practicable to attain numerical precision in the data,
a corresponding degree of precision may be given to the evaluation of
the chances of error in the conclusion. If it can be established as an
empirical law that nine out of every ten A are B, there will be one
chance in ten of error in assuming that any A, not individually known to
us, is a B: but this of course holds only within the limits of time,
place, and circumstance, embraced in the observations, and therefore
cannot be counted on for any sub-class or variety of A (or for A in any
set of external circumstances) which were not included in the average.
It must be added, that we can guide ourselves by the proposition, Nine
out of every ten A are B, only in cases of which we know nothing except
that they fall within the class A. For if we know, of any particular
instance _i_, not only that it falls under A, but to what species or
variety of A it belongs, we shall generally err in applying to _i_ the
average struck for the whole genus, from which the average corresponding
to that species alone would, in all probability, materially differ. And
so if _i_, instead of being a particular sort of instance, is an
instance known to be under the influence of a particular set of
circumstances. The presumption drawn from the numerical proportions in
the whole genus would probably, in such a case, only mislead. A general
average should only be applied to cases which are neither known, nor can
be presumed, to be other than average cases. Such averages, therefore,
are commonly of little use for the practical guidance of any affairs but
those which concern large numbers. Tables of the chances of life are
useful to insurance offices, but they go a very little way towards
informing any one of the chances of his own life, or any other life in
which he is interested, since almost every life is either better or
worse than the average. Such averages can only be considered as
supplying the first term in a series of approximations; the subsequent
terms proceeding on an appreciation of the circumstances belonging to
the particular case.

§ 6. From the application of a single approximate generalization to
individual cases, we proceed to the application of two or more of them
together to the same case.

When a judgment applied to an individual instance is grounded on two
approximate generalizations taken in conjunction, the propositions may
co-operate towards the result in two different ways. In the one, each
proposition is separately applicable to the case in hand, and our object
in combining them is to give to the conclusion in that particular case
the double probability arising from the two propositions separately.
This may be called joining two probabilities by way of Addition; and the
result is a probability greater than either. The other mode is, when
only one of the propositions is directly applicable to the case, the
second being only applicable to it by virtue of the application of the
first. This is joining two probabilities by way of Ratiocination or
Deduction; the result of which is a less probability than either. The
type of the first argument is, Most A are B; most C are B; this thing is
both an A and a C; therefore it is probably a B. The type of the second
is, Most A are B; most C are A; this is a C; therefore it is probably an
A, therefore it is probably a B. The first is exemplified when we prove
a fact by the testimony of two unconnected witnesses; the second, when
we adduce only the testimony of one witness that he has heard the thing
asserted by another. Or again, in the first mode it may be argued that
the accused committed the crime, because he concealed himself, and
because his clothes were stained with blood; in the second, that he
committed it because he washed or destroyed his clothes, which is
supposed to render it probable that they were stained with blood.
Instead of only two links, as in these instances, we may suppose chains
of any length. A chain of the former kind was termed by Bentham[35] a
self-corroborative chain of evidence; the second, a self-infirmative

When approximate generalizations are joined by way of addition, we may
deduce from the theory of probabilities laid down in a former chapter,
in what manner each of them adds to the probability of a conclusion
which has the warrant of them all.

In the early editions of this treatise, the joint probability arising
from the sum of two independent probabilities was estimated in the
following manner. If, on an average, two of every three As are Bs, and
three of every four Cs are Bs, the probability that something which is
both an A and a C is a B, will be more than two in three, or than three
in four. Of every twelve things which are As, all except four are Bs by
the supposition; and if the whole twelve, and consequently those four,
have the characters of C likewise, three of these will be Bs on that
ground. Therefore, out of twelve which are both As and Cs, eleven are
Bs. To state the argument in another way; a thing which is both an A and
a C, but which is not a B, is found in only one of three sections of the
class A, and in only one of four sections of the class C; but this
fourth of C being spread over the whole of A indiscriminately, only
one-third part of it (or one-twelfth of the whole number) belongs to the
third section of A; therefore a thing which is not a B occurs only once,
among twelve things which are both As and Cs. The argument would in the
language of the doctrine of chances, be thus expressed: the chance that
an A is not a B is 1/3, the chance that a C is not a B is 1/4; hence if
the thing be both an A and a C, the chance is 1/3 of 1/4 = 1/12.

It has, however, been pointed out to me by a mathematical friend, that
in this statement the evaluation of the chances is erroneous. The
correct mode of setting out the possibilities is as follows. If the
thing (let us call it T) which is both an A and a C, is a B, something
is true which is only true twice in every thrice, and something else
which is only true thrice in every four times. The first fact being true
eight times in twelve, and the second being true six times in every
eight, and consequently six times in those eight; both facts will be
true only six times in twelve. On the other hand if T, although it is
both an A and a C, is not a B, something is true which is only true once
in every thrice, and something else which is only true once in every
four times. The former being true four times out of twelve, and the
latter once in every four, and therefore once in those four; both are
only true in one case out of twelve. So that T is a B six times in
twelve, and T is not a B, only once: making the comparative
probabilities, not eleven to one, as I had previously made them, but six
to one.

It may be asked, what happens in the remaining cases? since in this
calculation seven out of twelve cases seem to have exhausted the
possibilities. If T is a B in only six cases of every twelve, and a
not-B in only one, what is it in the other five? The only supposition
remaining for those cases is that it is neither a B nor not a B, which
is impossible. But this impossibility merely proves that the state of
things supposed in the hypothesis does not exist in those cases. They
are cases that do not furnish anything which is both an A and a C.

To make this intelligible, we will substitute for our symbols a concrete
case. Let there be two witnesses, M and N, whose probabilities of
veracity correspond with the ratios of the preceding example: M speaks
truth twice in every thrice, N thrice in every four times. The question
is, what is the probability that a statement, in which they both concur,
will be true. The cases may be classed as follows. Both the witnesses
will speak truly six in every twelve times; both falsely once in twelve
times. Therefore, if they both agree in an assertion, it will be true
six times, for once that it will be false. What happens in the remaining
cases is here evident; there will be five cases in every twelve in which
the witnesses will not agree. M will speak truth and N falsehood in two
cases of every twelve; N will speak truth and M falsehood in three
cases, making in all five. In these cases, however, the witnesses will
not agree in their testimony. But disagreement between them is excluded
by the supposition. There are, therefore, only seven cases which are
within the conditions of the hypothesis; of which seven, veracity exists
in six, and falsehood in one. Resuming our former symbols, in five cases
out of twelve T is not both an A and a C, but an A only, or a C only.
The cases in which it is both are only seven, in six of which it is a B,
in one not a B, making the chance six to one, or 6/7 and 1/7

In this correct, as in the former incorrect computation, it is of course
presupposed that the probabilities arising from A and C are independent
of each other. There must not be any such connexion between A and C,
that when a thing belongs to the one class it will therefore belong to
the other, or even have a greater chance of doing so. Otherwise the
not-Bs which are Cs may be, most or even all of them, identical with the
not-Bs which are As; in which last case the probability arising from A
and C together will be no greater than that arising from A alone.

When approximate generalizations are joined together in the other mode,
that of deduction, the degree of probability of the inference, instead
of increasing, diminishes at each step. From two such premises as Most A
are B, Most B are C, we cannot with certainty conclude that even a
single A is C; for the whole of the portion of A which in any way falls
under B, may perhaps be comprised in the exceptional part of it. Still,
the two propositions in question afford an appreciable probability that
any given A is C, provided the average on which the second proposition
is grounded, was taken fairly with reference to the first; provided the
proposition, Most B are C, was arrived at in a manner leaving no
suspicion that the probability arising from it is otherwise than fairly
distributed over the section of B which belongs to A. For though the
instances which are A _may_ be all in the minority, they may, also, be
all in the majority; and the one possibility is to be set against the
other. On the whole, the probability arising from the two propositions
taken together, will be correctly measured by the probability arising
from the one, abated in the ratio of that arising from the other. If
nine out of ten Swedes have light hair, and eight out of nine
inhabitants of Stockholm are Swedes, the probability arising from these
two propositions, that any given inhabitant of Stockholm is
light-haired, will amount to eight in ten; though it is rigorously
possible that the whole Swedish population of Stockholm might belong to
that tenth section of the people of Sweden who are an exception to the

If the premises are known to be true not of a bare majority, but of
nearly the whole, of their respective subjects, we may go on joining one
such proposition to another for several steps, before we reach a
conclusion not presumably true even of a majority. The error of the
conclusion will amount to the aggregate of the errors of all the
premises. Let the proposition, Most A are B, be true of nine in ten;
Most B are C, of eight in nine: then not only will one A in ten not be
C, because not B, but even of the nine-tenths which are B, only
eight-ninths will be C: that is, the cases of A which are C will be only
8/9 of 9/10, or four-fifths. Let us now add Most C are D, and suppose
this to be true of seven cases out of eight; the proportion of A which
is D will be only 7/8 of 8/9 of 9/10, or 7/10. Thus the probability
progressively dwindles. The experience, however, on which our
approximate generalizations are grounded, has so rarely been subjected
to, or admits of, accurate numerical estimation, that we cannot in
general apply any measurement to the diminution of probability which
takes place at each illation; but must be content with remembering that
it does diminish at every step, and that unless the premises approach
very nearly indeed to being universally true, the conclusion after a
very few steps is worth nothing. A hearsay of a hearsay, or an argument
from presumptive evidence depending not on immediate marks but on marks
of marks, is worthless at a very few removes from the first stage.

§ 7. There are, however, two cases in which reasonings depending on
approximate generalizations may be carried to any length we please with
as much assurance, and are as strictly scientific, as if they were
composed of universal laws of nature. But these cases are exceptions of
the sort which are currently said to prove the rule. The approximate
generalizations are as suitable, in the cases in question, for purposes
of ratiocination, as if they were complete generalizations, because they
are capable of being transformed into complete generalizations exactly

First: If the approximate generalization is of the class in which our
reason for stopping at the approximation is not the impossibility, but
only the inconvenience, of going further; if we are cognizant of the
character which distinguishes the cases that accord with the
generalization from those which are exceptions to it; we may then
substitute for the approximate proposition, an universal proposition
with a proviso. The proposition, Most persons who have uncontrolled
power employ it ill, is a generalization of this class, and may be
transformed into the following:--All persons who have uncontrolled power
employ it ill, provided they are not persons of unusual strength of
judgment and rectitude of purpose. The proposition, carrying the
hypothesis or proviso with it, may then be dealt with no longer as an
approximate, but as an universal proposition; and to whatever number of
steps the reasoning may reach, the hypothesis, being carried forward to
the conclusion, will exactly indicate how far that conclusion is from
being applicable universally. If in the course of the argument other
approximate generalizations are introduced, each of them being in like
manner expressed as an universal proposition with a condition annexed,
the sum of all the conditions will appear at the end as the sum of all
the errors which affect the conclusion. Thus, to the proposition last
cited, let us add the following:--All absolute monarchs have
uncontrolled power, unless their position is such that they need the
active support of their subjects (as was the case with Queen Elizabeth,
Frederick of Prussia, and others). Combining these two propositions, we
can deduce from them an universal conclusion, which will be subject to
both the hypotheses in the premises; All absolute monarchs employ their
power ill, unless their position makes them need the active support of
their subjects, or unless they are persons of unusual strength of
judgment and rectitude of purpose. It is of no consequence how rapidly
the errors in our premises accumulate, if we are able in this manner to
record each error, and keep an account of the aggregate as it swells up.

Secondly: there is a case in which approximate propositions, even
without our taking note of the conditions under which they are not true
of individual cases, are yet, for the purposes of science, universal
ones; namely, in the inquiries which relate to the properties not of
individuals, but of multitudes. The principal of these is the science of
politics, or of human society. This science is principally concerned
with the actions not of solitary individuals, but of masses; with the
fortunes not of single persons, but of communities.

For the statesman, therefore, it is generally enough to know that
_most_ persons act or are acted upon in a particular way; since his
speculations and his practical arrangements refer almost exclusively to
cases in which the whole community, or some large portion of it, is
acted upon at once, and in which, therefore, what is done or felt by
_most_ persons determines the result produced by or upon the body at
large. He can get on well enough with approximate generalizations on
human nature, since what is true approximately of all individuals is
true absolutely of all masses. And even when the operations of
individual men have a part to play in his deductions, as when he is
reasoning of kings, or other single rulers, still, as he is providing
for indefinite duration, involving an indefinite succession of such
individuals, he must in general both reason and act as if what is true
of most persons were true of all.

The two kinds of considerations above adduced are a sufficient
refutation of the popular error, that speculations on society and
government, as resting on merely probable evidence, must be inferior in
certainty and scientific accuracy to the conclusions of what are called
the exact sciences, and less to be relied on in practice. There are
reasons enough why the moral sciences must remain inferior to at least
the more perfect of the physical: why the laws of their more complicated
phenomena cannot be so completely deciphered, nor the phenomena
predicted with the same degree of assurance. But though we cannot attain
to so many truths, there is no reason that those we can attain should
deserve less reliance, or have less of a scientific character. Of this
topic, however, I shall treat more systematically in the concluding
Book, to which place any further consideration of it must be deferred.



§ 1. In the First Book, we found that all the assertions which can be
conveyed by language, express some one or more of five different things:
Existence; Order in Place; Order in Time; Causation; and
Resemblance.[36] Of these, Causation, in our view of the subject, not
being fundamentally different from Order in Time, the five species of
possible assertions are reduced to four. The propositions which affirm
Order in Time, in either of its two modes, Coexistence and Succession,
have formed, thus far, the subject of the present Book. And we have now
concluded the exposition, so far as it falls within the limits assigned
to this work, of the nature of the evidence on which these propositions
rest, and the processes of investigation by which they are ascertained
and proved. There remain three classes of facts: Existence, Order in
Place, and Resemblance; in regard to which the same questions are now to
be resolved.

Regarding the first of these, very little needs be said. Existence in
general, is a subject not for our science, but for metaphysics. To
determine what things can be recognised as really existing,
independently of our own sensible or other impressions, and in what
meaning the term is, in that case, predicated of them, belongs to the
consideration of "Things in themselves," from which, throughout this
work, we have as much as possible kept aloof. Existence, so far as Logic
is concerned about it, has reference only to phenomena; to actual, or
possible, states of external or internal consciousness, in ourselves or
others. Feelings of sensitive beings, or possibilities of having such
feelings, are the only things the existence of which can be a subject
of logical induction, because the only things of which the existence in
individual cases can be a subject of experience.

It is true that a thing is said by us to exist, even when it is absent,
and therefore is not and cannot be perceived. But even then, its
existence is to us only another word for our conviction that we should
perceive it on a certain supposition; namely, if we were in the needful
circumstances of time and place, and endowed with the needful perfection
of organs. My belief that the Emperor of China exists, is simply my
belief that if I were transported to the imperial palace or some other
locality in Pekin, I should see him. My belief that Julius Cæsar
existed, is my belief that I should have seen him if I had been present
in the field of Pharsalia, or in the senate-house at Rome. When I
believe that stars exist beyond the utmost range of my vision, though
assisted by the most powerful telescopes yet invented, my belief,
philosophically expressed, is, that with still better telescopes, if
such existed, I could see them, or that they may be perceived by beings
less remote from them in space, or whose capacities of perception are
superior to mine.

The existence, therefore, of a phenomenon, is but another word for its
being perceived, or for the inferred possibility of perceiving it. When
the phenomenon is within the range of present observation, by present
observation we assure ourselves of its existence; when it is beyond that
range, and is therefore said to be absent, we infer its existence from
marks or evidences. But what can these evidences be? Other phenomena;
ascertained by induction to be connected with the given phenomenon,
either in the way of succession or of coexistence. The simple existence,
therefore, of an individual phenomenon, when not directly perceived, is
inferred from some inductive law of succession or coexistence: and is
consequently not amenable to any peculiar inductive principles. We prove
the existence of a thing, by proving that it is connected by succession
or coexistence with some known thing.

With respect to _general_ propositions of this class, that is, which
affirm the bare fact of existence, they have a peculiarity which renders
the logical treatment of them a very easy matter; they are
generalizations which are sufficiently proved by a single instance. That
ghosts, or unicorns, or sea-serpents exist, would be fully established
if it could be ascertained positively that such things had been even
once seen. Whatever has once happened, is capable of happening again;
the only question relates to the conditions under which it happens.

So far, therefore, as relates to simple existence, the Inductive Logic
has no knots to untie. And we may proceed to the remaining two of the
great classes into which facts have been divided; Resemblance, and Order
in Space.

§ 2. Resemblance and its opposite, except in the case in which they
assume the names of Equality and Inequality, are seldom regarded as
subjects of science; they are supposed to be perceived by simple
apprehension; by merely applying our senses or directing our attention
to the two objects at once, or in immediate succession. And this
simultaneous, or virtually simultaneous, application of our faculties to
the two things which are to be compared, does necessarily constitute the
ultimate appeal, wherever such application is practicable. But, in most
cases, it is not practicable: the objects cannot be brought so close
together that the feeling of their resemblance (at least a complete
feeling of it) directly arises in the mind. We can only compare each of
them with some third object, capable of being transported from one to
the other. And besides, even when the objects can be brought into
immediate juxtaposition, their resemblance or difference is but
imperfectly known to us, unless we have compared them minutely, part by
part. Until this has been done, things in reality very dissimilar often
appear undistinguishably alike. Two lines of very unequal length will
appear about equal when lying in different directions; but place them
parallel, with their farther extremities even, and if we look at the
nearer extremities, their inequality becomes a matter of direct

To ascertain whether, and in what, two phenomena resemble or differ, is
not always, therefore, so easy a thing as it might at first appear. When
the two cannot be brought into juxtaposition, or not so that the
observer is able to compare their several parts in detail, he must
employ the indirect means of reasoning and general propositions. When we
cannot bring two straight lines together, to determine whether they are
equal, we do it by the physical aid of a foot rule applied first to one
and then to the other, and the logical aid of the general proposition or
formula, "Things which are equal to the same thing are equal to one
another." The comparison of two things through the intervention of a
third thing, when their direct comparison is impossible, is the
appropriate scientific process for ascertaining resemblances and
dissimilarities, and is the sum total of what Logic has to teach on the

An undue extension of this remark induced Locke to consider reasoning
itself as nothing but the comparison of two ideas through the medium of
a third, and knowledge as the perception of the agreement or
disagreement of two ideas: doctrines which the Condillac school blindly
adopted, without the qualifications and distinctions with which they
were studiously guarded by their illustrious author. Where, indeed, the
agreement or disagreement (otherwise called resemblance or
dissimilarity) of any two things is the very matter to be determined, as
is the case particularly in the sciences of quantity and extension;
there, the process by which a solution, if not attainable by direct
perception, must be indirectly sought, consists in comparing these two
things through the medium of a third. But this is far from being true of
all inquiries. The knowledge that bodies fall to the ground is not a
perception of agreement or disagreement, but of a series of physical
occurrences, a succession of sensations. Locke's definitions of
knowledge and of reasoning required to be limited to our knowledge of,
and reasoning about, resemblances. Nor, even when thus restricted, are
the propositions strictly correct; since the comparison is not made, as
he represents, between the ideas of the two phenomena, but between the
phenomena themselves. This mistake has been pointed out in an earlier
part of our inquiry,[37] and we traced it to an imperfect conception of
what takes place in mathematics, where very often the comparison is
really made between the ideas, without any appeal to the outward senses;
only, however, because in mathematics a comparison of the ideas is
strictly equivalent to a comparison of the phenomena themselves. Where,
as in the case of numbers, lines, and figures, our idea of an object is
a complete picture of the object, so far as respects the matter in hand;
we can, of course, learn from the picture, whatever could be learnt from
the object itself by mere contemplation of it as it exists at the
particular instant when the picture is taken. No mere contemplation of
gunpowder would ever teach us that a spark would make it explode, nor,
consequently, would the contemplation of the idea of gunpowder do so:
but the mere contemplation of a straight line shows that it cannot
inclose a space: accordingly the contemplation of the idea of it will
show the same. What takes place in mathematics is thus no argument that
the comparison is between the ideas only. It is always, either
indirectly or directly, a comparison of the phenomena.

In cases in which we cannot bring the phenomena to the test of direct
inspection at all, or not in a manner sufficiently precise, but must
judge of their resemblance by inference from other resemblances or
dissimilarities more accessible to observation, we of course require, as
in all cases of ratiocination, generalizations or formulæ applicable to
the subject. We must reason from laws of nature; from the uniformities
which are observable in the fact of likeness or unlikeness.

§ 3. Of these laws or uniformities, the most comprehensive are those
supplied by mathematics; the axioms relating to equality, inequality,
and proportionality, and the various theorems thereon founded. And these
are the only Laws of Resemblance which require to be, or which can be,
treated apart. It is true there are innumerable other theorems which
affirm resemblances among phenomena; as that the angle of the reflection
of light is _equal_ to its angle of incidence (equality being merely
exact resemblance in magnitude). Again, that the heavenly bodies
describe _equal_ areas in equal times; and that their periods of
revolution are _proportional_ (another species of resemblance) to the
sesquiplicate powers of their distances from the centre of force. These
and similar propositions affirm resemblances, of the same nature with
those asserted in the theorems of mathematics; but the distinction is,
that the propositions of mathematics are true of all phenomena whatever,
or at least without distinction of origin; while the truths in question
are affirmed only of special phenomena, which originate in a certain
way; and the equalities, proportionalities, or other resemblances, which
exist between such phenomena, must necessarily be either derived from,
or identical with, the law of their origin--the law of causation on
which they depend. The equality of the areas described in equal times by
the planets, is _derived_ from the laws of the causes; and, until its
derivation was shown, it was an empirical law. The equality of the
angles of reflexion and incidence is _identical_ with the law of the
cause; for the cause is the incidence of a ray of light upon a
reflecting surface, and the equality in question is the very law
according to which that cause produces its effects. This class,
therefore, of the uniformities of resemblance between phenomena, are
inseparable, in fact and in thought, from the laws of the production of
those phenomena: and the principles of induction applicable to them are
no other than those of which we have treated in the preceding chapters
of this Book.

It is otherwise with the truths of mathematics. The laws of equality and
inequality between spaces, or between numbers, have no connexion with
laws of causation. That the angle of reflexion is equal to the angle of
incidence, is a statement of the mode of action of a particular cause;
but that when two straight lines intersect each other the opposite
angles are equal, is true of all such lines and angles, by whatever
cause produced. That the squares of the periodic times of the planets
are proportional to the cubes of their distances from the sun, is an
uniformity derived from the laws of the causes (or forces) which produce
the planetary motions; but that the square of any number is four times
the square of half the number, is true independently of any cause. The
only laws of resemblance, therefore, which we are called upon to
consider independently of causation, belong to the province of

§ 4. The same thing is evident with respect to the only one remaining of
our five categories, Order in Place. The order in place, of the effects
of a cause, is (like everything else belonging to the effects) a
consequence of the laws of that cause. The order in place, or, as we
have termed it, the collocation, of the primeval causes, is (as well as
their resemblance) in each instance an ultimate fact, in which no laws
or uniformities are traceable. The only remaining general propositions
respecting order in place, and the only ones which have nothing to do
with causation, are some of the truths of geometry; laws through which
we are able, from the order in place of certain points, lines, or
spaces, to infer the order in place of others which are connected with
the former in some known mode; quite independently of the particular
nature of those points, lines, or spaces, in any other respect than
position or magnitude, as well as independently of the physical cause
from which in any particular case they happen to derive their origin.

It thus appears that mathematics is the only department of science into
the methods of which it still remains to inquire. And there is the less
necessity that this inquiry should occupy us long, as we have already,
in the Second Book, made considerable progress in it. We there remarked,
that the directly inductive truths of mathematics are few in number;
consisting of the axioms, together with certain propositions concerning
existence, tacitly involved in most of the so-called definitions. And we
gave what appeared conclusive reasons for affirming that these original
premises, from which the remaining truths of the science are deduced,
are, notwithstanding all appearances to the contrary, results of
observation and experience; founded, in short, on the evidence of the
senses. That things equal to the same thing are equal to one another,
and that two straight lines which have once intersected one another
continue to diverge, are inductive truths; resting, indeed, like the law
of universal causation, only on induction _per enumerationem simplicem_;
on the fact that they have been perpetually perceived to be true, and
never once found to be false. But, as we have seen in a recent chapter
that this evidence, in the case of a law so completely universal as the
law of causation, amounts to the fullest proof, so is this even more
evidently true of the general propositions to which we are now
adverting; because, as a perception of their truth in any individual
case whatever, requires only the simple act of looking at the objects in
a proper position, there never could have been in their case (what, for
a long period, there were in the case of the law of causation) instances
which were apparently, though not really, exceptions to them. Their
infallible truth was recognised from the very dawn of speculation; and
as their extreme familiarity made it impossible for the mind to conceive
the objects under any other law, they were, and still are, generally
considered as truths recognised by their own evidence, or by instinct.

§ 5. There is something which seems to require explanation, in the fact
that the immense multitude of truths (a multitude still as far from
being exhausted as ever) comprised in the mathematical sciences, can be
elicited from so small a number of elementary laws. One sees not, at
first, how it is that there can be room for such an infinite variety of
true propositions, on subjects apparently so limited.

To begin with the science of number. The elementary or ultimate truths
of this science are the common axioms concerning equality, namely,
"Things which are equal to the same thing are equal to one another," and
"Equals added to equals make equal sums," (no other axioms are
required,[38]) together with the definitions of the various numbers.
Like other so-called definitions, these are composed of two things, the
explanation of a name, and the assertion of a fact: of which the latter
alone can form a first principle or premise of a science. The fact
asserted in the definition of a number is a physical fact. Each of the
numbers two, three, four, &c., denotes physical phenomena, and connotes
a physical property of those phenomena. Two, for instance, denotes all
pairs of things, and twelve all dozens of things, connoting what makes
them pairs, or dozens; and that which makes them so is something
physical; since it cannot be denied that two apples are physically
distinguishable from three apples, two horses from one horse, and so
forth: that they are a different visible and tangible phenomenon. I am
not undertaking to say what the difference is; it is enough that there
is a difference of which the senses can take cognizance. And although a
hundred and two horses are not so easily distinguished from a hundred
and three, as two horses are from three--though in most positions the
senses do not perceive any difference--yet they may be so placed that a
difference will be perceptible, or else we should never have
distinguished them, and given them different names. Weight is
confessedly a physical property of things; yet small differences between
great weights are as imperceptible to the senses in most situations, as
small differences between great numbers; and are only put in evidence by
placing the two objects in a peculiar position--namely, in the opposite
scales of a delicate balance.

What, then, is that which is connoted by a name of number? Of course
some property belonging to the agglomeration of things which we call by
the name; and that property is, the characteristic manner in which the
agglomeration is made up of, and may be separated into, parts. I will
endeavour to make this more intelligible by a few explanations.

When we call a collection of objects _two_, _three_, or _four_, they are
not two, three, or four in the abstract; they are two, three, or four
things of some particular kind; pebbles, horses, inches, pounds weight.
What the name of number connotes is, the manner in which single objects
of the given kind must be put together, in order to produce that
particular aggregate. If the aggregate be of pebbles, and we call it
_two_, the name implies that, to compose the aggregate, one pebble must
be joined to one pebble. If we call it _three_, one and one and one
pebble must be brought together to produce it, or else one pebble must
be joined to an aggregate of the kind called _two_, already existing.
The aggregate which we call _four_, has a still greater number of
characteristic modes of formation. One and one and one and one pebble
may be brought together; or two aggregates of the kind called _two_ may
be united; or one pebble may be added to an aggregate of the kind called
_three_. Every succeeding number in the ascending series, may be formed
by the junction of smaller numbers in a progressively greater variety of
ways. Even limiting the parts to two, the number may be formed, and
consequently may be divided, in as many different ways as there are
numbers smaller than itself; and, if we admit of threes, fours, &c., in
a still greater variety. Other modes of arriving at the same aggregate
present themselves, not by the union of smaller, but by the
dismemberment of larger aggregates. Thus, _three pebbles_ may be formed
by taking away one pebble from an aggregate of four; _two pebbles_, by
an equal division of a similar aggregate; and so on.

Every arithmetical proposition; every statement of the result of an
arithmetical operation; is a statement of one of the modes of formation
of a given number. It affirms that a certain aggregate might have been
formed by putting together certain other aggregates, or by withdrawing
certain portions of some aggregate; and that, by consequence, we might
reproduce those aggregates from it, by reversing the process.

Thus, when we say that the cube of 12 is 1728, what we affirm is this:
that if, having a sufficient number of pebbles or of any other objects,
we put them together into the particular sort of parcels or aggregates
called twelves; and put together these twelves again into similar
collections; and, finally, make up twelve of these largest parcels; the
aggregate thus formed will be such a one as we call 1728; namely, that
which (to take the most familiar of its modes of formation) may be made
by joining the parcel called a thousand pebbles, the parcel called seven
hundred pebbles, the parcel called twenty pebbles, and the parcel called
eight pebbles.

The converse proposition, that the cube root of 1728 is 12, asserts that
this large aggregate may again be decomposed into the twelve twelves of
twelves of pebbles which it consists of.

The modes of formation of any number are innumerable; but when we know
one mode of formation of each, all the rest may be determined
deductively. If we know that _a_ is formed from _b_ and _c_, _b_ from
_a_ and _e_, _c_ from _d_ and _f_, and so forth, until we have included
all the numbers of any scale we choose to select, (taking care that for
each number the mode of formation be really a distinct one, not bringing
us round again to the former numbers, but introducing a new number,) we
have a set of propositions from which we may reason to all the other
modes of formation of those numbers from one another. Having established
a chain of inductive truths connecting together all the numbers of the
scale, we can ascertain the formation of any one of those numbers from
any other by merely travelling from one to the other along the chain.
Suppose that we know only the following modes of formation: 6 = 4 + 2, 4
= 7 - 3, 7 = 5 + 2, 5 = 9 - 4. We could determine how 6 may be formed
from 9. For 6 = 4 + 2 = 7 - 3 + 2 = 5 + 2 - 3 + 2 = 9 - 4 + 2 - 3 + 2.
It may therefore be formed by taking away 4 and 3, and adding 2 and 2.
If we know besides that 2 + 2 = 4, we obtain 6 from 9 in a simpler mode,
by merely taking away 3.

It is sufficient, therefore, to select one of the various modes of
formation of each number, as a means of ascertaining all the rest. And
since things which are uniform, and therefore simple, are most easily
received and retained by the understanding, there is an obvious
advantage in selecting a mode of formation which shall be alike for all;
in fixing the connotation of names of number on one uniform principle.
The mode in which our existing numerical nomenclature is contrived
possesses this advantage, with the additional one, that it happily
conveys to the mind two of the modes of formation of every number. Each
number is considered as formed by the addition of an unit to the number
next below it in magnitude, and this mode of formation is conveyed by
the place which it occupies in the series. And each is also considered
as formed by the addition of a number of units less than ten, and a
number of aggregates each equal to one of the successive powers of ten;
and this mode of its formation is expressed by its spoken name, and by
its numerical character.

What renders arithmetic the type of a deductive science, is the
fortunate applicability to it of a law so comprehensive as "The sums of
equals are equals:" or (to express the same principle in less familiar
but more characteristic language), Whatever is made up of parts, is made
up of the parts of those parts. This truth, obvious to the senses in all
cases which can be fairly referred to their decision, and so general as
to be coextensive with nature itself, being true of all sorts of
phenomena, (for all admit of being numbered,) must be considered an
inductive truth, or law of nature, of the highest order. And every
arithmetical operation is an application of this law, or of other laws
capable of being deduced from it. This is our warrant for all
calculations. We believe that five and two are equal to seven, on the
evidence of this inductive law, combined with the definitions of those
numbers. We arrive at that conclusion (as all know who remember how they
first learned it) by adding a single unit at a time: 5 + 1 = 6,
therefore 5 + 1 + 1 = 6 + 1 = 7: and again 2 = 1 + 1, therefore 5 + 2 =
5 + 1 + 1 = 7.

§ 6. Innumerable as are the true propositions which can be formed
concerning particular numbers, no adequate conception could be gained,
from these alone, of the extent of the truths composing the science of
number. Such propositions as we have spoken of are the least general of
all numerical truths. It is true that even these are coextensive with
all nature: the properties of the number four are true of all objects
that are divisible into four equal parts, and all objects are either
actually or ideally so divisible. But the propositions which compose the
science of algebra are true, not of a particular number, but of all
numbers; not of all things under the condition of being divided in a
particular way, but of all things under the condition of being divided
in any way--of being designated by a number at all.

Since it is impossible for different numbers to have any of their modes
of formation completely in common, it is a kind of paradox to say, that
all propositions which can be made concerning numbers relate to their
modes of formation from other numbers, and yet that there are
propositions which are true of all numbers. But this very paradox leads
to the real principle of generalization concerning the properties of
numbers. Two different numbers cannot be formed in the same manner from
the same numbers; but they may be formed in the same manner from
different numbers; as nine is formed from three by multiplying it into
itself, and sixteen is formed from four by the same process. Thus there
arises a classification of modes of formation, or in the language
commonly used by mathematicians, a classification of Functions. Any
number, considered as formed from any other number, is called a function
of it; and there are as many kinds of functions as there are modes of
formation. The simple functions are by no means numerous, most functions
being formed by the combination of several of the operations which form
simple functions, or by successive repetitions of some one of those
operations. The simple functions of any number _x_ are all reducible to
the following forms: _x + a_, _x - a_, _a x_, _x/a_, _x^a_, _a [root
of] x_, log. _x_ (to the base _a_), and the same expressions varied by
putting _x_ for _a_ and _a_ for _x_, wherever that substitution would
alter the value: to which perhaps ought to be added sin _x_, and arc
(sin = _x_). All other functions of _x_ are formed by putting some one
or more of the simple functions in the place of _x_ or _a_, and
subjecting them to the same elementary operations.

In order to carry on general reasonings on the subject of Functions, we
require a nomenclature enabling us to express any two numbers by names
which, without specifying what particular numbers they are, shall show
what function each is of the other; or, in other words, shall put in
evidence their mode of formation from one another. The system of general
language called algebraical notation does this. The expressions _a_ and
_a^2 + 3a_ denote, the one any number, the other the number formed
from it in a particular manner. The expressions _a_, _b_, _n_, and _(a +
b)^n_, denote any three numbers, and a fourth which is formed from
them in a certain mode.

The following may be stated as the general problem of the algebraical
calculus: F being a certain function of a given number, to find what
function F will be of any function of that number. For example, a
binomial _a_ + _b_ is a function of its two parts _a_ and _b_, and the
parts are, in their turn, functions of _a + b_: now _(a + b)^n_ is a
certain function of the binomial; what function will this be of _a_ and
_b_, the two parts? The answer to this question is the binomial theorem.
The formula _(a + b)^n = a^n + (n / 1) a^(n - 1) b + ((n·(n - 1)) /
(1·2)) a^(n - 2) b^2 + &c._, shows in what manner the number which is
formed by multiplying _a + b_ into itself _n_ times, might be formed
without that process, directly from _a_, _b_, and _n_. And of this
nature are all the theorems of the science of number. They assert the
identity of the result of different modes of formation. They affirm that
some mode of formation from _x_, and some mode of formation from a
certain function of _x_, produce the same number.

Besides these general theorems of formulæ, what remains in the
algebraical calculus is the resolution of equations. But the resolution
of an equation is also a theorem. If the equation be _x^2 + ax = b_,
the resolution of this equation, viz. _x = -(1/2) a ± [root of]((1/4)
a^2 + b)_, is a general proposition, which may be regarded as an
answer to the question, If _b_ is a certain function of _x_ and _a_
(namely _x^2 + ax_), what function is _x_ of _b_ and _a_? The
resolution of equations is, therefore, a mere variety of the general
problem as above stated. The problem is--Given a function, what function
is it of some other function? And in the resolution of an equation, the
question is, to find what function of one of its own functions the
number itself is.

Such as above described, is the aim and end of the calculus. As for its
processes, every one knows that they are simply deductive. In
demonstrating an algebraical theorem, or in resolving an equation, we
travel from the _datum_ to the _quæsitum_ by pure ratiocination; in
which the only premises introduced, besides the original hypotheses, are
the fundamental axioms already mentioned--that things equal to the same
thing are equal to one another, and that the sums of equal things are
equal. At each step in the demonstration or in the calculation, we apply
one or other of these truths, or truths deducible from them, as, that
the differences, products, &c., of equal numbers are equal.

It would be inconsistent with the scale of this work, and not necessary
to its design, to carry the analysis of the truths and processes of
algebra any farther; which is also the less needful, as the task has
been, to a very great extent, performed by other writers. Peacock's
Algebra, and Dr. Whewell's _Doctrine of Limits_, are full of instruction
on the subject. The profound treatises of a truly philosophical
mathematician, Professor De Morgan, should be studied by every one who
desires to comprehend the evidence of mathematical truths, and the
meaning of the obscurer processes of the calculus; and the speculations
of M. Comte, in his _Cours de Philosophie Positive_, on the philosophy
of the higher branches of mathematics, are among the many valuable gifts
for which philosophy is indebted to that eminent thinker.

§ 7. If the extreme generality, and remoteness not so much from sense as
from the visual and tactual imagination, of the laws of number, renders
it a somewhat difficult effort of abstraction to conceive those laws as
being in reality physical truths obtained by observation; the same
difficulty does not exist with regard to the laws of extension. The
facts of which those laws are expressions, are of a kind peculiarly
accessible to the senses, and suggesting eminently distinct images to
the fancy. That geometry is a strictly physical science would doubtless
have been recognised in all ages, had it not been for the illusions
produced by two circumstances. One of these is the characteristic
property, already noticed, of the facts of geometry, that they may be
collected from our ideas or mental pictures of objects as effectually as
from the objects themselves. The other is, the demonstrative character
of geometrical truths; which was at one time supposed to constitute a
radical distinction between them and physical truths, the latter, as
resting on merely probable evidence, being deemed essentially uncertain
and unprecise. The advance of knowledge has, however, made it manifest
that physical science, in its better understood branches, is quite as
demonstrative as geometry. The task of deducing its details from a few
comparatively simple principles is found to be anything but the
impossibility it was once supposed to be; and the notion of the superior
certainty of geometry is an illusion, arising from the ancient prejudice
which, in that science, mistakes the ideal data from which we reason,
for a peculiar class of realities, while the corresponding ideal data of
any deductive physical science are recognised as what they really are,
mere hypotheses.

Every theorem in geometry is a law of external nature, and might have
been ascertained by generalizing from observation and experiment, which
in this case resolve themselves into comparison and measurement. But it
was found practicable, and being practicable, was desirable, to deduce
these truths by ratiocination from a small number of general laws of
nature, the certainty and universality of which are obvious to the most
careless observer, and which compose the first principles and ultimate
premises of the science. Among these general laws must be included the
same two which we have noticed as ultimate principles of the Science of
Number also, and which are applicable to every description of quantity;
viz. The sums of equals are equal, and Things which are equal to the
same thing are equal to one another; the latter of which may be
expressed in a manner more suggestive of the inexhaustible multitude of
its consequences, by the following terms: Whatever is equal to any one
of a number of equal magnitudes, is equal to any other of them. To these
two must be added, in geometry, a third law of equality, namely, that
lines, surfaces, or solid spaces, which can be so applied to one another
as to coincide, are equal. Some writers have asserted that this law of
nature is a mere verbal definition; that the expression "equal
magnitudes" _means_ nothing but magnitudes which can be so applied to
one another as to coincide. But in this opinion I cannot agree. The
equality of two geometrical magnitudes cannot differ fundamentally in
its nature from the equality of two weights, two degrees of heat, or two
portions of duration, to none of which would this pretended definition
of equality be suitable. None of these things can be so applied to one
another as to coincide, yet we perfectly understand what we mean when we
call them equal. Things are equal in magnitude, as things are equal in
weight, when they are felt to be exactly similar in respect of the
attribute in which we compare them: and the application of the objects
to each other in the one case, like the balancing them with a pair of
scales in the other, is but a mode of bringing them into a position in
which our senses can recognise deficiencies of exact resemblance that
would otherwise escape our notice.

Along with these three general principles or axioms, the remainder of
the premises of geometry consists of the so-called definitions, that is
to say, propositions asserting the real existence of the various
objects therein designated, together with some one property of each. In
some cases more than one property is commonly assumed, but in no case is
more than one necessary. It is assumed that there are such things in
nature as straight lines, and that any two of them setting out from the
same point, diverge more and more without limit. This assumption, (which
includes and goes beyond Euclid's axiom that two straight lines cannot
inclose a space,) is as indispensable in geometry, and as evident,
resting on as simple, familiar, and universal observation, as any of the
other axioms. It is also assumed that straight lines diverge from one
another in different degrees; in other words, that there are such things
as angles, and that they are capable of being equal or unequal. It is
assumed that there is such a thing as a circle, and that all its radii
are equal; such things as ellipses, and that the sums of the focal
distances are equal for every point in an ellipse; such things as
parallel lines, and that those lines are everywhere equally distant.[39]

§ 8. It is a matter of more than curiosity to consider, to what
peculiarity of the physical truths which are the subject of geometry, it
is owing that they can all be deduced from so small a number of
original premises: why it is that we can set out from only one
characteristic property of each kind of phenomenon, and with that and
two or three general truths relating to equality, can travel from mark
to mark until we obtain a vast body of derivative truths, to all
appearance extremely unlike those elementary ones.

The explanation of this remarkable fact seems to lie in the following
circumstances. In the first place, all questions of position and figure
may be resolved into questions of magnitude. The position and figure of
any object are determined, by determining the position of a sufficient
number of points in it; and the position of any point may be determined
by the magnitude of three rectangular co-ordinates, that is, of the
perpendiculars drawn from the point to three planes at right angles to
one another, arbitrarily selected. By this transformation of all
questions of quality into questions only of quantity, geometry is
reduced to the single problem of the measurement of magnitudes, that is,
the ascertainment of the equalities which exist between them. Now when
we consider that by one of the general axioms, any equality, when
ascertained, is proof of as many other equalities as there are other
things equal to either of the two equals; and that by another of those
axioms, any ascertained equality is proof of the equality of as many
pairs of magnitudes as can be formed by the numerous operations which
resolve themselves into the addition of the equals to themselves or to
other equals; we cease to wonder that in proportion as a science is
conversant about equality, it should afford a more copious supply of
marks of marks; and that the sciences of number and extension, which are
conversant with little else than equality, should be the most deductive
of all the sciences.

There are also two or three of the principal laws of space or extension
which are unusually fitted for rendering one position or magnitude a
mark of another, and thereby contributing to render the science largely
deductive. First; the magnitudes of inclosed spaces, whether superficial
or solid, are completely determined by the magnitudes of the lines and
angles which bound them. Secondly, the length of any line, whether
straight or curve, is measured (certain other things being given) by the
angle which it subtends, and _vice versâ_. Lastly, the angle which any
two straight lines make with each other at an inaccessible point, is
measured by the angles they severally make with any third line we choose
to select. By means of these general laws, the measurement of all lines,
angles, and spaces whatsoever might be accomplished by measuring a
single straight line and a sufficient number of angles; which is the
plan actually pursued in the trigonometrical survey of a country; and
fortunate it is that this is practicable, the exact measurement of long
straight lines being always difficult, and often impossible, but that of
angles very easy. Three such generalizations as the foregoing afford
such facilities for the indirect measurement of magnitudes, (by
supplying us with known lines or angles which are marks of the magnitude
of unknown ones, and thereby of the spaces which they inclose,) that it
is easily intelligible how from a few data we can go on to ascertain the
magnitude of an indefinite multitude of lines, angles, and spaces, which
we could not easily, or could not at all, measure by any more direct

§ 9. Such are the few remarks which it seemed necessary to make in this
place, respecting the laws of nature which are the peculiar subject of
the sciences of number and extension. The immense part which those laws
take in giving a deductive character to the other departments of
physical science, is well known; and is not surprising, when we consider
that all causes operate according to mathematical laws. The effect is
always dependent on, or is a function of, the quantity of the agent; and
generally of its position also. We cannot, therefore, reason respecting
causation, without introducing considerations of quantity and extension
at every step; and if the nature of the phenomena admits of our
obtaining numerical data of sufficient accuracy, the laws of quantity
become the grand instrument for calculating forward to an effect, or
backward to a cause. That in all other sciences, as well as in
geometry, questions of quality are scarcely ever independent of
questions of quantity, may be seen from the most familiar phenomena.
Even when several colours are mixed on a painter's palette, the
comparative quantity of each entirely determines the colour of the

With this mere suggestion of the general causes which render
mathematical principles and processes so predominant in those deductive
sciences which afford precise numerical data, I must, on the present
occasion, content myself: referring the reader who desires a more
thorough acquaintance with the subject, to the first two volumes of M.
Comte's systematic work.

In the same work, and more particularly in the third volume, are also
fully discussed the limits of the applicability of mathematical
principles to the improvement of other sciences. Such principles are
manifestly inapplicable, where the causes on which any class of
phenomena depend are so imperfectly accessible to our observation, that
we cannot ascertain, by a proper induction, their numerical laws; or
where the causes are so numerous, and intermixed in so complex a manner
with one another, that even supposing their laws known, the computation
of the aggregate effect transcends the powers of the calculus as it is,
or is likely to be; or lastly, where the causes themselves are in a
state of perpetual fluctuation; as in physiology, and still more, if
possible, in the social science. The mathematical solutions of physical
questions become progressively more difficult and imperfect, in
proportion as the questions divest themselves of their abstract and
hypothetical character, and approach nearer to the degree of
complication actually existing in nature; insomuch that beyond the
limits of astronomical phenomena, and of those most nearly analogous to
them, mathematical accuracy is generally obtained "at the expense of the
reality of the inquiry:" while even in astronomical questions,
"notwithstanding the admirable simplicity of their mathematical
elements, our feeble intelligence becomes incapable of following out
effectually the logical combinations of the laws on which the phenomena
are dependent, as soon as we attempt to take into simultaneous
consideration more than two or three essential influences."[40] Of
this, the problem of the Three Bodies has already been cited, more than
once, as a remarkable instance; the complete solution of so
comparatively simple a question having vainly tried the skill of the
most profound mathematicians. We may conceive, then, how chimerical
would be the hope that mathematical principles could be advantageously
applied to phenomena dependent on the mutual action of the innumerable
minute particles of bodies, as those of chemistry, and still more, of
physiology; and for similar reasons those principles remain inapplicable
to the still more complex inquiries, the subjects of which are phenomena
of society and government.

The value of mathematical instruction as a preparation for those more
difficult investigations, consists in the applicability not of its
doctrines, but of its method. Mathematics will ever remain the most
perfect type of the Deductive Method in general; and the applications of
mathematics to the deductive branches of physics, furnish the only
school in which philosophers can effectually learn the most difficult
and important portion of their art, the employment of the laws of
simpler phenomena for explaining and predicting those of the more
complex. These grounds are quite sufficient for deeming mathematical
training an indispensable basis of real scientific education, and
regarding (according to the _dictum_ which an old but unauthentic
tradition ascribes to Plato) one who is _ἀγεωμέτρητος_, as wanting in
one of the most essential qualifications for the successful cultivation
of the higher branches of philosophy.



§ 1. The method of arriving at general truths, or general propositions
fit to be believed, and the nature of the evidence on which they are
grounded, have been discussed, as far as space and the writer's
faculties permitted, in the twenty-four preceding chapters. But the
result of the examination of evidence is not always belief, nor even
suspension of judgment; it is sometimes disbelief. The philosophy,
therefore, of induction and experimental inquiry is incomplete, unless
the grounds not only of belief, but of disbelief, are treated of; and to
this topic we shall devote one, and the final, chapter.

By disbelief is not here to be understood the mere absence of belief.
The ground for abstaining from belief is simply the absence or
insufficiency of proof; and in considering what is sufficient evidence
to support any given conclusion, we have already, by implication,
considered what evidence is not sufficient for the same purpose. By
disbelief is here meant, not the state of mind in which we form no
opinion concerning a subject, but that in which we are fully persuaded
that some opinion is not true; insomuch that if evidence, even of great
apparent strength, (whether grounded on the testimony of others or on
our own supposed perceptions,) were produced in favour of the opinion,
we should believe that the witnesses spoke falsely, or that they, or we
ourselves if we were the direct percipients, were mistaken.

That there are such cases, no one is likely to dispute. Assertions for
which there is abundant positive evidence are often disbelieved, on
account of what is called their improbability, or impossibility. And the
question for consideration is what, in the present case, these words
mean, and how far and in what circumstances the properties which they
express are sufficient grounds for disbelief.

§ 2. It is to be remarked in the first place, that the positive evidence
produced in support of an assertion which is nevertheless rejected on
the score of impossibility or improbability, is never such as amounts to
full proof. It is always grounded on some approximate generalization.
The fact may have been asserted by a hundred witnesses; but there are
many exceptions to the universality of the generalization that what a
hundred witnesses affirm is true. We may seem to ourselves to have
actually seen the fact: but, that we really see what we think we see, is
by no means an universal truth; our organs may have been in a morbid
state; or we may have inferred something, and imagined that we perceived
it. The evidence, then, in the affirmative being never more than an
approximate generalization, all will depend on what the evidence in the
negative is. If that also rests on an approximate generalization, it is
a case for comparison of probabilities. If the approximate
generalizations leading to the affirmative are, when added together,
less strong, or in other words, farther from being universal, than the
approximate generalizations which support the negative side of the
question, the proposition is said to be improbable, and is to be
disbelieved provisionally. If however an alleged fact be in
contradiction, not to any number of approximate generalizations, but to
a completed generalization grounded on a rigorous induction, it is said
to be impossible, and is to be disbelieved totally.

This last principle, simple and evident as it appears, is the doctrine
which, on the occasion of an attempt to apply it to the question of the
credibility of miracles, excited so violent a controversy. Hume's
celebrated doctrine, that nothing is credible which is contradictory to
experience, or at variance with laws of nature, is merely this very
plain and harmless proposition, that whatever is contradictory to a
complete induction is incredible. That such a maxim as this should
either be accounted a dangerous heresy, or mistaken for a great and
recondite truth, speaks ill for the state of philosophical speculation
on such subjects.

But does not (it may be asked) the very statement of the proposition
imply a contradiction? An alleged fact, according to this theory, is not
to be believed if it contradict a complete induction. But it is
essential to the completeness of an induction that it shall not
contradict any known fact. Is it not then a _petitio principii_ to say,
that the fact ought to be disbelieved because the induction opposed to
it is complete? How can we have a right to declare the induction
complete, while facts, supported by credible evidence, present
themselves in opposition to it?

I answer, we have that right whenever the scientific canons of induction
give it to us; that is, whenever the induction _can_ be complete. We
have it, for example, in a case of causation in which there has been an
_experimentum crucis_. If an antecedent A, superadded to a set of
antecedents in all other respects unaltered, is followed by an effect B
which did not exist before, A is, in that instance at least, the cause
of B, or an indispensable part of its cause; and if A be tried again
with many totally different sets of antecedents and B still follows,
then it is the whole cause. If these observations or experiments have
been repeated so often, and by so many persons, as to exclude all
supposition of error in the observer, a law of nature is established;
and so long as this law is received as such, the assertion that on any
particular occasion A took place, and yet B did not follow, _without any
counteracting cause_, must be disbelieved. Such an assertion is not to
be credited on any less evidence than what would suffice to overturn the
law. The general truths, that whatever has a beginning has a cause, and
that when none but the same causes exist, the same effects follow, rest
on the strongest inductive evidence possible; the proposition that
things affirmed by even a crowd of respectable witnesses are true, is
but an approximate generalization; and--even if we fancy we actually saw
or felt the fact which is in contradiction to the law--what a human
being can see is no more than a set of appearances; from which the real
nature of the phenomenon is merely an inference, and in this inference
approximate generalizations usually have a large share. If, therefore,
we make our election to hold by the law, no quantity of evidence
whatever ought to persuade us that there has occurred anything in
contradiction to it. If, indeed, the evidence produced is such that it
is more likely that the set of observations and experiments on which the
law rests should have been inaccurately performed or incorrectly
interpreted, than that the evidence in question should be false, we may
believe the evidence; but then we must abandon the law. And since the
law was received on what seemed a complete induction, it can only be
rejected on evidence equivalent; namely, as being inconsistent not with
any number of approximate generalizations, but with some other and
better established law of nature. This extreme case, of a conflict
between two supposed laws of nature, has probably never actually
occurred where, in the process of investigating both the laws, the true
canons of scientific induction had been kept in view; but if it did
occur, it must terminate in the total rejection of one of the supposed
laws. It would prove that there must be a flaw in the logical process by
which either one or the other was established: and if there be so, that
supposed general truth is no truth at all. We cannot admit a proposition
as a law of nature, and yet believe a fact in real contradiction to it.
We must disbelieve the alleged fact, or believe that we were mistaken in
admitting the supposed law.

But in order that any alleged fact should be contradictory to a law of
causation, the allegation must be, not simply that the cause existed
without being followed by the effect, for that would be no uncommon
occurrence; but that this happened in the absence of any adequate
counteracting cause. Now in the case of an alleged miracle, the
assertion is the exact opposite of this. It is, that the effect was
defeated, not in the absence, but in consequence of a counteracting
cause, namely, a direct interposition of an act of the will of some
being who has power over nature; and in particular of a Being, whose
will being assumed to have endowed all the causes with the powers by
which they produce their effects, may well be supposed able to
counteract them. A miracle (as was justly remarked by Brown[41]) is no
contradiction to the law of cause and effect; it is a new effect,
supposed to be produced by the introduction of a new cause. Of the
adequacy of that cause, if present, there can be no doubt; and the only
antecedent improbability which can be ascribed to the miracle, is the
improbability that any such cause existed.

All, therefore, which Hume has made out, and this he must be considered
to have made out, is, that (at least in the imperfect state of our
knowledge of natural agencies, which leaves it always possible that some
of the physical antecedents may have been hidden from us,) no evidence
can prove a miracle to any one who did not previously believe the
existence of a being or beings with supernatural power; or who believes
himself to have full proof that the character of the Being whom he
recognises, is inconsistent with his having seen fit to interfere on the
occasion in question.

If we do not already believe in supernatural agencies, no miracle can
prove to us their existence. The miracle itself, considered merely as an
extraordinary fact, may be satisfactorily certified by our senses or by
testimony; but nothing can ever prove that it is a miracle: there is
still another possible hypothesis, that of its being the result of some
unknown natural cause: and this possibility cannot be so completely shut
out, as to leave no alternative but that of admitting the existence and
intervention of a being superior to nature. Those, however, who already
believe in such a being, have two hypotheses to choose from, a
supernatural and an unknown natural agency; and they have to judge which
of the two is the most probable in the particular case. In forming this
judgment, an important element of the question will be the conformity of
the result to the laws of the supposed agent, that is, to the character
of the Deity as they conceive it. But, with the knowledge which we now
possess of the general uniformity of the course of nature, religion,
following in the wake of science, has been compelled to acknowledge the
government of the universe as being on the whole carried on by general
laws, and not by special interpositions. To whoever holds this belief,
there is a general presumption against any supposition of divine agency
not operating through general laws, or in other words, there is an
antecedent improbability in every miracle, which, in order to outweigh
it, requires an extraordinary strength of antecedent probability derived
from the special circumstances of the case.

§ 3. It appears from what has been said, that the assertion that a cause
has been defeated of an effect which is connected with it by a
completely ascertained law of causation, is to be disbelieved or not,
according to the probability or improbability that there existed in the
particular instance an adequate counteracting cause. To form an estimate
of this, is not more difficult than of other probabilities. With regard
to all _known_ causes capable of counteracting the given causes, we have
generally some previous knowledge of the frequency or rarity of their
occurrence, from which we may draw an inference as to the antecedent
improbability of their having been present in any particular case. And
neither in respect to known or unknown causes are we required to
pronounce on the probability of their existing in nature, but only of
their having existed at the time and place at which the transaction is
alleged to have happened. We are seldom, therefore, without the means
(when the circumstances of the case are at all known to us) of judging
how far it is likely that such a cause should have existed at that time
and place without manifesting its presence by some other marks, and (in
the case of an unknown cause) without having hitherto manifested its
existence in any other instance. According as this circumstance, or the
falsity of the testimony, appears more improbable, that is, conflicts
with an approximate generalization of a higher order, we believe the
testimony, or disbelieve it; with a stronger or a weaker degree of
conviction, according to the preponderance: at least until we have
sifted the matter further.

So much, then, for the case in which the alleged fact conflicts, or
appears to conflict, with a real law of causation. But a more common
case, perhaps, is that of its conflicting with uniformities of mere
coexistence, not proved to be dependent on causation: in other words,
with the properties of Kinds. It is with these uniformities principally,
that the marvellous stories related by travellers are apt to be at
variance: as of men with tails, or with wings, and (until confirmed by
experience) of flying fish; or of ice, in the celebrated anecdote of the
Dutch travellers and the King of Siam. Facts of this description, facts
previously unheard of but which could not from any known law of
causation be pronounced impossible, are what Hume characterizes as not
contrary to experience, but merely unconformable to it; and Bentham, in
his treatise on Evidence, denominates them facts disconformable _in
specie_, as distinguished from such as are disconformable _in toto_ or
in _degree_.

In a case of this description, the fact asserted is the existence of a
new Kind; which in itself is not in the slightest degree incredible, and
only to be rejected if the improbability that any variety of object
existing at the particular place and time should not have been
discovered sooner, be greater than that of error or mendacity in the
witnesses. Accordingly, such assertions, when made by credible persons,
and of unexplored places, are not disbelieved, but at most regarded as
requiring confirmation from subsequent observers; unless the alleged
properties of the supposed new Kind are at variance with known
properties of some larger kind which includes it; or in other words,
unless, in the new Kind which is asserted to exist, some properties are
said to have been found disjoined from others which have always been
known to accompany them; as in the case of Pliny's men, or any other
kind of animal of a structure different from that which has always been
found to coexist with animal life. On the mode of dealing with any such
case, little needs be added to what has been said on the same topic in
the twenty-second chapter.[42] When the uniformities of coexistence
which the alleged fact would violate, are such as to raise a strong
presumption of their being the result of causation, the fact which
conflicts with them is to be disbelieved; at least provisionally, and
subject to further investigation. When the presumption amounts to a
virtual certainty, as in the case of the general structure of organized
beings, the only question requiring consideration is whether, in
phenomena so little understood, there may not be liabilities to
counteraction from causes hitherto unknown; or whether the phenomena may
not be capable of originating in some other way, which would produce a
different set of derivative uniformities. Where (as in the case of the
flying fish, or the ornithorhynchus) the generalization to which the
alleged fact would be an exception is very special and of limited range,
neither of the above suppositions can be deemed very improbable; and it
is generally, in the case of such alleged anomalies, wise to suspend our
judgment, pending the subsequent inquiries which will not fail to
confirm the assertion if it be true. But when the generalization is very
comprehensive, embracing a vast number and variety of observations, and
covering a considerable province of the domain of nature; then, for
reasons which have been fully explained, such an empirical law comes
near to the certainty of an ascertained law of causation: and any
alleged exception to it cannot be admitted, unless on the evidence of
some law of causation proved by a still more complete induction.

Such uniformities in the course of nature as do not bear marks of being
the results of causation, are, as we have already seen, admissible as
universal truths with a degree of credence proportioned to their
generality. Those which are true of all things whatever, or at least
which are totally independent of the varieties of Kinds, namely, the
laws of number and extension, to which we may add the law of causation
itself, are probably the only ones, an exception to which is absolutely
and permanently incredible. Accordingly, it is to assertions supposed to
be contradictory to these laws, or to some others coming near to them in
generality, that the word impossibility (at least _total_ impossibility)
seems to be generally confined. Violations of other laws, of special
laws of causation for instance, are said, by persons studious of
accuracy in expression, to be impossible _in the circumstances of the
case_; or impossible unless some cause had existed which did not exist
in the particular case.[43] Of no assertion, not in contradiction to
some of these very general laws, will more than improbability be
asserted by any cautious person; and improbability not of the highest
degree, unless the time and place in which the fact is said to have
occurred, render it almost certain that the anomaly, if real, could not
have been overlooked by other observers. Suspension of judgment is in
all other cases the resource of the judicious inquirer; provided the
testimony in favour of the anomaly presents, when well sifted, no
suspicious circumstances.

But the testimony is scarcely ever found to stand that test, in cases in
which the anomaly is not real. In the instances on record in which a
great number of witnesses, of good reputation and scientific
acquirements, have testified to the truth of something which has turned
out untrue, there have almost always been circumstances which, to a keen
observer who had taken due pains to sift the matter, would have rendered
the testimony untrustworthy. There have generally been means of
accounting for the impression on the senses or minds of the alleged
percipients, by fallacious appearances; or some epidemic delusion,
propagated by the contagious influence of popular feeling, has been
concerned in the case; or some strong interest has been
implicated--religious zeal, party feeling, vanity, or at least the
passion for the marvellous, in persons strongly susceptible of it. When
none of these or similar circumstances exist to account for the apparent
strength of the testimony; and where the assertion is not in
contradiction either to those universal laws which know no counteraction
or anomaly, or to the generalizations next in comprehensiveness to them,
but would only amount, if admitted, to the existence of an unknown cause
or an anomalous Kind, in circumstances not so thoroughly explored but
that it is credible that things hitherto unknown may still come to
light; a cautious person will neither admit nor reject the testimony,
but will wait for confirmation at other times and from other unconnected
sources. Such ought to have been the conduct of the King of Siam when
the Dutch travellers affirmed to him the existence of ice. But an
ignorant person is as obstinate in his contemptuous incredulity as he is
unreasonably credulous. Anything unlike his own narrow experience he
disbelieves, if it flatters no propensity; any nursery tale is swallowed
implicitly by him if it does.

§ 4. I shall now advert to a very serious misapprehension of the
principles of the subject, which has been committed by some of the
writers against Hume's Essay on Miracles, and by Bishop Butler before
them, in their anxiety to destroy what appeared to them a formidable
weapon of assault against the Christian religion; and the effect of
which is entirely to confound the doctrine of the Grounds of Disbelief.
The mistake consists in overlooking the distinction between (what may be
called) improbability before the fact, and improbability after it; or
(since, as Mr. Venn remarks, the distinction of past and future is not
the material circumstance) between the improbability of a mere guess
being right, and the improbability of an alleged fact being true.

Many events are altogether improbable to us, before they have happened,
or before we are informed of their happening, which are not in the least
incredible when we are informed of them, because not contrary to any,
even approximate, induction. In the cast of a perfectly fair die, the
chances are five to one against throwing ace, that is, ace will be
thrown on an average only once in six throws. But this is no reason
against believing that ace was thrown on a given occasion, if any
credible witness asserts it; since though ace is only thrown once in six
times, _some_ number which is only thrown once in six times must have
been thrown if the die was thrown at all. The improbability, then, or in
other words, the unusualness, of any fact, is no reason for disbelieving
it, if the nature of the case renders it certain that either that or
something equally improbable, that is, equally unusual, did happen. Nor
is this all: for even if the other five sides of the die were all twos,
or all threes, yet as ace would still on the average come up once in
every six throws, its coming up in a given throw would be not in any way
contradictory to experience. If we disbelieved all facts which had the
chances against them beforehand, we should believe hardly anything. We
are told that A. B. died yesterday: the moment before we were so told,
the chances against his having died on that day may have been ten
thousand to one; but since he was certain to die at some time or other,
and when he died must necessarily die on some particular day, while the
preponderance of chances is very great against every day in particular,
experience affords no ground for discrediting any testimony which may be
produced to the event's having taken place on a given day.

Yet it has been considered, by Dr. Campbell and others, as a complete
answer to Hume's doctrine (that things are incredible which are
_contrary_ to the uniform course of experience), that we do not
disbelieve, merely because the chances were against them, things in
strict _conformity_ to the uniform course of experience; that we do not
disbelieve an alleged fact merely because the combination of causes on
which it depends occurs only once in a certain number of times. It is
evident that whatever is shown by observation, or can be proved from
laws of nature, to occur in a certain proportion (however small) of the
whole number of possible cases, is not contrary to experience; though we
are right in disbelieving it, if some other supposition respecting the
matter in question involves on the whole a less departure from the
ordinary course of events. Yet, on such grounds as this have able
writers been led to the extraordinary conclusion, that nothing supported
by credible testimony ought ever to be disbelieved.

§ 5. We have considered two species of events, commonly said to be
improbable; one kind which are in no way extraordinary, but which,
having an immense preponderance of chances against them, are improbable
until they are affirmed, but no longer; another kind which, being
contrary to some recognised law of nature, are incredible on any amount
of testimony except such as would be sufficient to shake our belief in
the law itself. But between these two classes of events, there is an
intermediate class, consisting of what are commonly termed Coincidences:
in other words, those combinations of chances which present some
peculiar and unexpected regularity, assimilating them, in so far, to the
results of law. As if, for example, in a lottery of a thousand tickets,
the numbers should be drawn in the exact order of what are called the
natural numbers, 1, 2, 3, &c. We have still to consider the principles
of evidence applicable to this case: whether there is any difference
between coincidences and ordinary events, in the amount of testimony or
other evidence necessary to render them credible.

It is certain, that on every rational principle of expectation, a
combination of this peculiar sort may be expected quite as often as any
other given series of a thousand numbers; that with perfectly fair dice,
sixes will be thrown twice, thrice, or any number of times in
succession, quite as often in a thousand or a million throws, as any
other succession of numbers fixed upon beforehand; and that no judicious
player would give greater odds against the one series than against the
other. Notwithstanding this, there is a general disposition to regard
the one as much more improbable than the other, and as requiring much
stronger evidence to make it credible. Such is the force of this
impression, that it has led some thinkers to the conclusion, that nature
has greater difficulty in producing regular combinations than irregular
ones; or in other words, that there is some general tendency of things,
some law, which prevents regular combinations from occurring, or at
least from occurring so often as others. Among these thinkers may be
numbered D'Alembert; who, in an Essay on Probabilities to be found in
the fifth volume of his _Mélanges_, contends that regular combinations,
though equally probable according to the mathematical theory with any
others, are physically less probable. He appeals to common sense, or in
other words, to common impressions; saying, if dice thrown repeatedly in
our presence gave sixes every time, should we not, before the number of
throws had reached ten, (not to speak of thousands of millions,) be
ready to affirm, with the most positive conviction, that the dice were

The common and natural impression is in favour of D'Alembert: the
regular series would be thought much more unlikely than an irregular.
But this common impression is, I apprehend, merely grounded on the fact,
that scarcely anybody remembers to have ever seen one of these peculiar
coincidences: the reason of which is simply that no one's experience
extends to anything like the number of trials, within which that or any
other given combination of events can be expected to happen. The chance
of sixes on a single throw of two dice being 1/36, the chance of sixes
ten times in succession is 1 divided by the tenth power of 36; in other
words, such a concurrence is only likely to happen once in
3,656,158,440,062,976 trials, a number which no dice-player's experience
comes up to a millionth part of. But if, instead of sixes ten times, any
other given succession of ten throws had been fixed upon, it would have
been exactly as unlikely that in any individual's experience that
particular succession had ever occurred; although this does not _seem_
equally improbable, because no one could possibly have remembered
whether it had occurred or not, and because the comparison is tacitly
made, not between sixes ten times and any one particular series of
throws, but between all regular and all irregular successions taken

That (as D'Alembert says) if the succession of sixes was actually thrown
before our eyes, we should ascribe it not to chance, but to unfairness
in the dice, is unquestionably true. But this arises from a totally
different principle. We should then be considering, not the probability
of the fact in itself, but the comparative probability with which, when
it is known to have happened, it may be referred to one or to another
cause. The regular series is not at all less likely than the irregular
one to be brought about by chance, but it is much more likely than the
irregular one to be produced by design; or by some general cause
operating through the structure of the dice. It is the nature of casual
combinations to produce a repetition of the same event, as often and no
oftener than any other series of events. But it is the nature of general
causes to reproduce, in the same circumstances, always the same event.
Common sense and science alike dictate that, all other things being the
same, we should rather attribute the effect to a cause which if real
would be very likely to produce it, than to a cause which would be very
unlikely to produce it. According to Laplace's sixth theorem, which we
demonstrated in a former chapter, the difference of probability arising
from the superior _efficacy_ of the constant cause, unfairness in the
dice, would after a very few throws far outweigh any antecedent
probability which there could be against its existence.

D'Alembert should have put the question in another manner. He should
have supposed that we had ourselves previously tried the dice, and knew
by ample experience that they were fair. Another person then tries them
in our absence, and assures us that he threw sixes ten times in
succession. Is the assertion credible or not? Here the effect to be
accounted for is not the occurrence itself, but the fact of the
witness's asserting it. This may arise either from its having really
happened, or from some other cause. What we have to estimate is the
comparative probability of these two suppositions.

If the witness affirmed that he had thrown any other series of numbers,
supposing him to be a person of veracity, and tolerable accuracy, and to
profess that he took particular notice, we should believe him. But the
ten sixes are exactly as likely to have been really thrown as the other
series. If, therefore, this assertion is less credible than the other,
the reason must be, not that it is less likely than the other to be made
truly, but that it is more likely than the other to be made falsely.

One reason obviously presents itself why what is called a coincidence,
should be oftener asserted falsely than an ordinary combination. It
excites wonder. It gratifies the love of the marvellous. The motives,
therefore, to falsehood, one of the most frequent of which is the desire
to astonish, operate more strongly in favour of this kind of assertion
than of the other kind. Thus far there is evidently more reason for
discrediting an alleged coincidence, than a statement in itself not more
probable, but which if made would not be thought remarkable. There are
cases, however, in which the presumption on this ground would be the
other way. There are some witnesses who, the more extraordinary an
occurrence might appear, would be the more anxious to verify it by the
utmost carefulness of observation before they would venture to believe
it, and still more before they would assert it to others.

§ 6. Independently, however, of any peculiar chances of mendacity
arising from the nature of the assertion, Laplace contends, that merely
on the general ground of the fallibility of testimony, a coincidence is
not credible on the same amount of testimony on which we should be
warranted in believing an ordinary combination of events. In order to do
justice to his argument, it is necessary to illustrate it by the example
chosen by himself.

If, says Laplace, there were one thousand tickets in a box, and one only
has been drawn out, then if an eye-witness affirms that the number drawn
was 79, this, though the chances were 999 in 1000 against it, is not on
that account the less credible; its credibility is equal to the
antecedent probability of the witness's veracity. But if there were in
the box 999 black balls and only one white, and the witness affirms that
the white ball was drawn, the case according to Laplace is very
different: the credibility of his assertion is but a small fraction of
what it was in the former case; the reason of the difference being as

The witnesses of whom we are speaking must, from the nature of the case,
be of a kind whose credibility falls materially short of certainty: let
us suppose, then, the credibility of the witness in the case in question
to be 9/10; that is, let us suppose that in every ten statements which
the witness makes, nine on an average are correct, and one incorrect.
Let us now suppose that there have taken place a sufficient number of
drawings to exhaust all the possible combinations, the witness deposing
in every one. In one case out of every ten in all these drawings he will
actually have made a false announcement. But in the case of the thousand
tickets these false announcements will have been distributed impartially
over all the numbers, and of the 999 cases in which No. 79 was not
drawn, there will have been only one case in which it was announced. On
the contrary, in the case of the thousand balls, (the announcement being
always either "black" or "white,") if white was not drawn, and there was
a false announcement, that false announcement _must_ have been white;
and since by the supposition there was a false announcement once in
every ten times, white will have been announced falsely in one tenth
part of all the cases in which it was not drawn, that is, in one tenth
part of 999 cases out of every thousand. White, then, is drawn, on an
average, exactly as often as No. 79, but it is announced, without having
been really drawn, 999 times as often as No. 79; the announcement
therefore requires a much greater amount of testimony to render it

To make this argument valid it must of course be supposed, that the
announcements made by the witness are average specimens of his general
veracity and accuracy; or, at least, that they are neither more nor less
so in the case of the black and white balls, than in the case of the
thousand tickets. This assumption, however, is not warranted. A person
is far less likely to mistake, who has only one form of error to guard
against, than if he had 999 different errors to avoid. For instance, in
the example chosen, a messenger who might make a mistake once in ten
times in reporting the number drawn in a lottery, might not err once in
a thousand times if sent simply to observe whether a ball was black or
white. Laplace's argument therefore is faulty even as applied to his own
case. Still less can that case be received as completely representing
all cases of coincidence. Laplace has so contrived his example, that
though black answers to 999 distinct possibilities, and white only to
one, the witness has nevertheless no bias which can make him prefer
black to white. The witness did not know that there were 999 black balls
in the box and only one white; or if he did, Laplace has taken care to
make all the 999 cases so undistinguishably alike, that there is hardly
a possibility of any cause of falsehood or error operating in favour of
any of them, which would not operate in the same manner if there were
only one. Alter this supposition, and the whole argument falls to the
ground. Let the balls, for instance, be numbered, and let the white ball
be No. 79. Considered in respect of their colour, there are but two
things which the witness can be interested in asserting, or can have
dreamt or hallucinated, or has to choose from if he answers at random,
viz. black and white: but considered in respect of the numbers attached
to them, there are a thousand: and if his interest or error happens to
be connected with the numbers, though the only assertion he makes is
about the colour, the case becomes precisely assimilated to that of the
thousand tickets. Or instead of the balls suppose a lottery, with 1000
tickets and but one prize, and that I hold No. 79, and being interested
only in that, ask the witness not what was the number drawn, but whether
it was 79 or some other. There are now only two cases, as in Laplace's
example; yet he surely would not say that if the witness answered 79,
the assertion would be in an enormous proportion less credible, than if
he made the same answer to the same question asked in the other way. If,
for instance, (to put a case supposed by Laplace himself,) he has staked
a large sum on one of the chances, and thinks that by announcing its
occurrence he shall increase his credit; he is equally likely to have
betted on any one of the 999 numbers which are attached to black balls,
and so far as the chances of mendacity from this cause are concerned,
there will be 999 times as many chances of his announcing black falsely,
as white.

Or suppose a regiment of 1000 men, 999 Englishmen and one Frenchman, and
that of these one man has been killed, and it is not known which. I ask
the question, and the witness answers, the Frenchman. This was not only
as improbable _à priori_, but is in itself as singular a circumstance,
as remarkable a coincidence, as the drawing of the white ball: yet we
should believe the statement as readily, as if the answer had been John
Thompson. Because though the 999 Englishmen were all alike in the point
in which they differed from the Frenchman, they were not, like the 999
black balls, undistinguishable in every other respect; but being all
different, they admitted as many chances of interest or error, as if
each man had been of a different nation; and if a lie was told or a
mistake made, the misstatement was as likely to fall on any Jones or
Thompson of the set, as on the Frenchman.

The example of a coincidence selected by D'Alembert, that of sixes
thrown on a pair of dice ten times in succession, belongs to this sort
of cases rather than to such as Laplace's. The coincidence is here far
more remarkable, because of far rarer occurrence, than the drawing of
the white ball. But though the improbability of its really occurring is
greater, the superior probability of its being announced falsely cannot
be established with the same evidence. The announcement "black"
represented 999 cases, but the witness may not have known this, and if
he did, the 999 cases are so exactly alike, that there is really only
one set of possible causes of mendacity corresponding to the whole. The
announcement "sixes _not_ drawn ten times," represents, and is known by
the witness to represent, a great multitude of contingencies, every one
of which being unlike every other, there may be a different and a fresh
set of causes of mendacity corresponding to each.

It appears to me, therefore, that Laplace's doctrine is not strictly
true of any coincidences, and is wholly inapplicable to most: and that
to know whether a coincidence does or does not require more evidence to
render it credible than an ordinary event, we must refer, in every
instance, to first principles, and estimate afresh what is the
probability that the given testimony would have been delivered in that
instance, supposing the fact which it asserts not to be true.

With these remarks we close the discussion of the Grounds of Disbelief;
and along with it, such exposition as space admits, and as the writer
has it in his power to furnish, of the Logic of Induction.


[1] _Cours de Philosophie Positive_, ii. 656.

[2] Vide supra, book iii. ch. xi.

[3] _Philosophy of Discovery_, pp. 185 et seqq.

[4] _Philosophie Positive_, ii. 434-437.

[5] As an example of legitimate hypothesis according to the test here
laid down, has been justly cited that of Broussais, who, proceeding on
the very rational principle that every disease must originate in some
definite part or other of the organism, boldly assumed that certain
fevers, which not being known to be local were called constitutional,
had their origin in the mucous membrane of the alimentary canal. The
supposition was indeed, as is now generally admitted, erroneous; but he
was justified in making it, since by deducing the consequences of the
supposition, and comparing them with the facts of those maladies, he
might be certain of disproving his hypothesis if it was ill founded, and
might expect that the comparison would materially aid him in framing
another more conformable to the phenomena.

The doctrine now universally received, that the earth is a natural
magnet, was originally an hypothesis of the celebrated Gilbert.

Another hypothesis, to the legitimacy of which no objection can lie, and
which is well calculated to light the path of scientific inquiry, is
that suggested by several recent writers, that the brain is a voltaic
pile, and that each of its pulsations is a discharge of electricity
through the system. It has been remarked that the sensation felt by the
hand from the beating of a brain, bears a strong resemblance to a
voltaic shock. And the hypothesis, if followed to its consequences,
might afford a plausible explanation of many physiological facts, while
there is nothing to discourage the hope that we may in time sufficiently
understand the conditions of voltaic phenomena to render the truth of
the hypothesis amenable to observation and experiment.

The attempt to localize, in different regions of the brain, the physical
organs of our different mental faculties and propensities, was, on the
part of its original author, a legitimate example of a scientific
hypothesis; and we ought not, therefore, to blame him for the extremely
slight grounds on which he often proceeded, in an operation which could
only be tentative, though we may regret that materials barely sufficient
for a first rude hypothesis should have been hastily worked up into the
vain semblance of a science. If there be really a connexion between the
scale of mental endowments and the various degrees of complication in
the cerebral system, the nature of that connexion was in no other way so
likely to be brought to light as by framing, in the first instance, an
hypothesis similar to that of Gall. But the verification of any such
hypothesis is attended, from the peculiar nature of the phenomena, with
difficulties which phrenologists have not shown themselves even
competent to appreciate, much less to overcome.

Mr. Darwin's remarkable speculation on the Origin of Species is another
unimpeachable example of a legitimate hypothesis. What he terms "natural
selection" is not only a _vera causa_, but one proved to be capable of
producing effects of the same kind with those which the hypothesis
ascribes to it: the question of possibility is entirely one of degree.
It is unreasonable to accuse Mr. Darwin (as has been done) of violating
the rules of Induction. The rules of Induction are concerned with the
conditions of Proof. Mr. Darwin has never pretended that his doctrine
was proved. He was not bound by the rules of Induction, but by those of
Hypothesis. And these last have seldom been more completely fulfilled.
He has opened a path of inquiry full of promise, the results of which
none can foresee. And is it not a wonderful feat of scientific knowledge
and ingenuity to have rendered so bold a suggestion, which the first
impulse of every one was to reject at once, admissible and discussable,
even as a conjecture?

[6] Whewell's _Phil. of Discovery_, pp. 275, 276.

[7] What has most contributed to accredit the hypothesis of a physical
medium for the conveyance of light, is the certain fact that light
_travels_, (which cannot be proved of gravitation,) that its
communication is not instantaneous, but requires time, and that it is
intercepted (which gravitation is not) by intervening objects. These are
analogies between its phenomena and those of the mechanical motion of a
solid or fluid substance. But we are not entitled to assume that
mechanical motion is the only power in nature capable of exhibiting
those attributes.

[8] _Phil. of Disc._ p. 274.

[9] P. 271.

[10] P. 251 and the whole of Appendix G.

[11] In Dr. Whewell's latest version of his theory (_Philosophy of
Discovery_, p. 331) he makes a concession respecting the medium of the
transmission of light, which, taken in conjunction with the rest of his
doctrine on the subject, is not, I confess, very intelligible to me, but
which goes far towards removing, if it does not actually remove, the
whole of the difference between us. He is contending, against Sir
William Hamilton, that all matter has weight. Sir William, in proof of
the contrary, cited the luminiferous ether, and the calorific and
electric fluids, "which," he said, "we can neither denude of their
character of substance, nor clothe with the attribute of weight." "To
which," continues Dr. Whewell, "my reply is, that precisely because I
cannot clothe these agents with the attribute of Weight, I _do_ denude
them of the character of Substance. They are not substances, but
agencies. These Imponderable Agents, are not properly called
Imponderable Fluids. This I conceive that I have proved." Nothing can be
more philosophical. But if the luminiferous ether is not matter, and
fluid matter too, what is the meaning of its undulations? Can an agency
undulate? Can there be alternate motion forward and backward of the
particles of an agency? And does not the whole mathematical theory of
the undulations imply them to be material? Is it not a series of
deductions from the known properties of elastic fluids? _This_ opinion
of Dr. Whewell reduces the undulations to a figure of speech, and the
undulatory theory to the proposition which all must admit, that the
transmission of light takes place according to laws which present a very
striking and remarkable agreement with those of undulations. If Dr.
Whewell is prepared to stand by this doctrine, I have no difference with
him on the subject.

Since this chapter was written, the hypothesis of the luminiferous ether
has acquired a great accession of apparent strength, by being adopted
into the new doctrine of the Conservation of Force, as affording a
mechanism by which to explain the mode of production not of light only,
but of heat, and probably of all the other so-called imponderable
agencies. In the present immature stage of the great speculation in
question, I would not undertake to define the ultimate relation of the
hypothetical fluid to it; but I must remark that the essential part of
the new theory, the reciprocal convertibility and interchangeability of
these great cosmic agencies, is quite independent of the molecular
motions which have been imagined as the immediate causes of those
different manifestations and of their substitutions for one another; and
the former doctrine by no means necessarily carries the latter with it.
I confess that the entire theory of the vibrations of the ether, and the
movements which these vibrations are supposed to communicate to the
particles of solid bodies, seems to me at present the weakest part of
the new system, tending rather to weigh down than to prop up those of
its doctrines which rest on real scientific induction.

[12] Thus, water, of which eight-ninths in weight are oxygen, dissolves
most bodies which contain a high proportion of oxygen, such as all the
nitrates, (which have more oxygen than any others of the common salts,)
most of the sulphates, many of the carbonates, &c. Again, bodies largely
composed of combustible elements, like hydrogen and carbon, are soluble
in bodies of similar composition; rosin, for instance, will dissolve in
alcohol, tar in oil of turpentine. This empirical generalization is far
from being universally true; no doubt because it is a remote, and
therefore easily defeated, result of general laws too deep for us at
present to penetrate; but it will probably in time suggest processes of
inquiry, leading to the discovery of those laws.

[13] Or (according to Laplace's theory) the sun and the sun's rotation.

[14] Supra, book iii. ch. v. § 7.

[15] Supra, book iii. ch. x. § 2.

[16] In the preceding discussion, the _mean_ is spoken of as if it were
exactly the same thing with the _average_. But the mean for purposes of
inductive inquiry, is not the average, or arithmetical mean, though in a
familiar illustration of the theory the difference may be disregarded.
If the deviations on one side of the average are much more numerous than
those on the other (these last being fewer but greater), the effect due
to the invariable cause, as distinct from the variable ones, will not
coincide with the average, but will be either below or above the
average, whichever be the side on which the greatest number of the
instances are found. This follows from a truth, ascertained both
inductively and deductively, that small deviations from the true central
point are greatly more frequent than large ones. The mathematical law
is, "that the most probable determination of one or more invariable
elements from observation is that in which _the sum of the squares_ of
the individual aberrations," or deviations, "_shall be the least
possible_." See this principle stated, and its grounds popularly
explained, by Sir John Herschel, in his review of Quetelet on
Probabilities, _Essays_, pp. 395 _et seq._

[17] _Essai Philosophique sur les Probabilités_, fifth Paris Edition, p.

[18] It even appears to me that the calculation of chances, where there
are no data grounded either on special experience or on special
inference, must, in an immense majority of cases, break down, from sheer
impossibility of assigning any principle by which to be guided in
setting out the list of possibilities. In the case of the coloured balls
we have no difficulty in making the enumeration, because we ourselves
determine what the possibilities shall be. But suppose a case more
analogous to those which occur in nature: instead of three colours, let
there be in the box all possible colours: we being supposed ignorant of
the comparative frequency with which different colours occur in nature,
or in the productions of art. How is the list of cases to be made out?
Is every distinct shade to count as a colour? If so, is the test to be a
common eye, or an educated eye, a painter's for instance? On the answer
to these questions would depend whether the chances against some
particular colour would be estimated at ten, twenty, or perhaps five
hundred to one. While if we knew from experience that the particular
colour occurs on an average a certain number of times in every hundred
or thousand, we should not require to know anything either of the
frequency or of the number of the other possibilities.

[19] _Prospective Review_ for February 1850.

[20] "If this be not so, why do we feel so much more probability added
by the first instance, than by any single subsequent instance? Why,
except that the first instance gives us its possibility (a cause
_adequate_ to it), while every other only gives us the frequency of its
conditions? If no reference to a cause be supposed, possibility would
have no meaning; yet it is clear, that, antecedent to its happening, we
might have supposed the event impossible, _i.e._, have believed that
there was no physical energy really existing in the world equal to
producing it.... After the first time of happening, which is, then, more
important to the whole probability than any other single instance
(because proving the possibility), the _number_ of times becomes
important as an index to the intensity or extent of the cause, and its
independence of any particular time. If we took the case of a tremendous
leap, for instance, and wished to form an estimate of the probability of
its succeeding a certain number of times; the first instance, by showing
its possibility (before doubtful) is of the most importance; but every
succeeding leap shows the power to be more perfectly under control,
greater and more invariable, and so increases the probability; and no
one would think of reasoning in this case straight from one instance to
the next, without referring to the physical energy which each leap
indicated. Is it not then clear that we do not ever" (let us rather say,
that we do not in an advanced state of our knowledge) "conclude directly
from the happening of an event to the probability of its happening
again; but that we refer to the cause, regarding the past cases as an
index to the cause, and the cause as our guide to the future?"--_Ibid._

[21] The writer last quoted says that the valuation of chances by
comparing the number of cases in which the event occurs with the number
in which it does not occur, "would generally be wholly erroneous," and
"is not the true theory of probability." It is at least that which forms
the foundation of insurance, and of all those calculations of chances in
the business of life which experience so abundantly verifies. The reason
which the reviewer gives for rejecting the theory, is that it "would
regard an event as certain which had hitherto never failed; which is
exceedingly far from the truth, even for a very large number of constant
successes." This is not a defect in a particular theory, but in any
theory of chances. No principle of evaluation can provide for such a
case as that which the reviewer supposes. If an event has never once
failed, in a number of trials sufficient to eliminate chance, it really
has all the certainty which can be given by an empirical law: it _is_
certain during the continuance of the same collocation of causes which
existed during the observations. If it ever fails, it is in consequence
of some change in that collocation. Now, no theory of chances will
enable us to infer the future probability of an event from the past, if
the causes in operation, capable of influencing the event, have
intermediately undergone a change.

[22] Pp. 18, 19. The theorem is not stated by Laplace in the exact terms
in which I have stated it; but the identity of import of the two modes
of expression is easily demonstrable.

[23] For a fuller treatment of the many interesting questions raised by
the theory of probabilities, I may now refer to a recent work by Mr.
Venn, Fellow of Caius College, Cambridge, "The Logic of Chance;" one of
the most thoughtful and philosophical treatises on any subject connected
with Logic and Evidence, which have been produced in this or any other
country for many years. Some criticisms contained in it have been very
useful to me in revising the corresponding chapters of the present work.
In several of Mr. Venn's opinions, however, I do not agree. What these
are will be obvious to any reader of Mr. Venn's work who is also a
reader of this.

[24] There was no greater foundation for this than for Newton's
celebrated conjecture that the diamond was combustible. He grounded his
guess on the very high refracting power of the diamond, comparatively to
its density; a peculiarity which had been observed to exist in
combustible substances; and on similar grounds he conjectured that
water, though not combustible, contained a combustible ingredient.
Experiment having subsequently shown that in both instances he guessed
right, the prophecy is considered to have done great honour to his
scientific sagacity; but it is to this day uncertain whether the guess
was, in truth, what there are so many examples of in the history of
science, a farsighted anticipation of a law afterwards to be discovered.
The progress of science has not hitherto shown ground for believing that
there is any real connexion between combustibility and a high refracting

[25] Hartley's _Observations on Man_, vol. i. p. 16. The passage is not
in Priestley's curtailed edition.

[26] I am happy to be able to quote the following excellent passage from
Mr. Baden Powell's _Essay on the Inductive Philosophy_, in confirmation,
both in regard to history and to doctrine, of the statement made in the
text. Speaking of the "conviction of the universal and permanent
uniformity of nature," Mr. Powell says (pp. 98-100),

"We may remark that this idea, in its proper extent, is by no means one
of popular acceptance or natural growth. Just so far as the daily
experience of every one goes, so far indeed he comes to embrace a
certain persuasion of this kind, but merely to this limited extent, that
what is going on around him at present, in his own narrow sphere of
observation, will go on in like manner in future. The peasant believes
that the sun which rose to-day will rise again to-morrow; that the seed
put into the ground will be followed in due time by the harvest this
year as it was last year, and the like; but has no notion of such
inferences in subjects beyond his immediate observation. And it should
be observed that each class of persons, in admitting this belief within
the limited range of his own experience, though he doubt or deny it in
everything beyond, is, in fact, bearing unconscious testimony to its
universal truth. Nor, again, is it only among the _most_ ignorant that
this limitation is put upon the truth. There is a very general
propensity to believe that everything beyond common experience, or
especially ascertained laws of nature, is left to the dominion of chance
or fate or arbitrary intervention; and even to object to any attempted
explanation by physical causes, if conjecturally thrown out for an
apparently unaccountable phenomenon.

"The precise doctrine of the _generalization_ of this idea of the
uniformity of nature, so far from being obvious, natural, or intuitive,
is utterly beyond the attainment of the many. In all the extent of its
universality it is characteristic of the philosopher. It is clearly the
result of philosophic cultivation and training, and by no means the
spontaneous offspring of any primary principle naturally inherent in the
mind, as some seem to believe. It is no mere vague persuasion taken up
without examination, as a common prepossession to which we are always
accustomed; on the contrary, all common prejudices and associations are
against it. It is pre-eminently _an acquired idea_. It is not attained
without deep study and reflection. The best informed philosopher is the
man who most firmly believes it, even in opposition to received notions;
its acceptance depends on the extent and profoundness of his inductive

[27] Supra, book iii. ch. iii. § 1.

[28] It deserves remark, that these early generalizations did not, like
scientific inductions, presuppose causation. What they did presuppose,
was _uniformity_ in physical facts. But the observers were as ready to
presume uniformity in the coexistences of facts as in the sequences. On
the other hand, they never thought of assuming that this uniformity was
a principle pervading all nature: their generalizations did not imply
that there was uniformity in everything, but only that as much
uniformity as existed within their observation, existed also beyond it.
The induction, Fire burns, does not require for its validity that all
nature should observe uniform laws, but only that there should be
uniformity in one particular class of natural phenomena: the effects of
fire on the senses and on combustible substances. And uniformity to this
extent was not assumed, anterior to the experience, but proved by the
experience. The same observed instances which proved the narrower truth,
proved as much of the wider one as corresponded to it. It is from losing
sight of this fact, and considering the law of causation in its full
extent as necessarily presupposed in the very earliest generalizations,
that persons have been led into the belief that the law of causation is
known _à priori_, and is not itself a conclusion from experience.

[29] Book ii. chap. iii.

[30] One of the most rising thinkers of the new generation in France, M.
Taine (who has given, in the Revue des Deux Mondes, the most masterly
analysis, at least in one point of view, ever made of the present work),
though he rejects, on this and similar points of psychology, the
intuition theory in its ordinary form, nevertheless assigns to the law
of causation, and to some other of the most universal laws, that
certainty beyond the bounds of human experience, which I have not been
able to accord to them. He does this on the faith of our faculty of
abstraction, in which he seems to recognise an independent source of
evidence, not indeed disclosing truths not contained in our experience,
but affording an assurance which experience cannot give, of the
universality of those which it does contain. By abstraction M. Taine
seems to think that we are able, not merely to analyse that part of
nature which we see, and exhibit apart the elements which pervade it,
but to distinguish such of them as are elements of the system of nature
considered as a whole, not incidents belonging to our limited
terrestrial experience. I am not sure that I fully enter into M. Taine's
meaning; but I confess I do not see how any mere abstract conception,
elicited by our minds from our experience, can be evidence of an
objective fact in universal Nature, beyond what the experience itself
bears witness of; or how, in the process of interpreting in general
language the testimony of experience, the limitations of the testimony
itself can be cast off.

[31] Book i. chap. vii.

[32] In some cases, a Kind is sufficiently identified by some one
remarkable property: but most commonly several are required; each
property considered singly, being a joint property of that and of other
Kinds. The colour and brightness of the diamond are common to it with
the paste from which false diamonds are made; its octohedral form is
common to it with alum, and magnetic iron ore; but the colour and
brightness and the form together, identify its Kind; that is, are a mark
to us that it is combustible; that when burnt it produces carbonic acid;
that it cannot be cut with any known substance; together with many other
ascertained properties, and the fact that there exist an indefinite
number still unascertained.

[33] This doctrine of course assumes that the allotropic forms of what
is chemically the same substance are so many different Kinds; and such,
in the sense in which the word Kind is used in this treatise, they
really are.

[34] Mr. De Morgan, in his _Formal Logic_, makes the just remark, that
from two such premises as Most A are B, and Most A are C, we may infer
with certainty that some B are C. But this is the utmost limit of the
conclusions which can be drawn from two approximate generalizations,
when the precise degree of their approximation to universality is
unknown or undefined.

[35] _Rationale of Judicial Evidence_, vol. iii. p. 224.

[36] Supra, vol. i. p. 115.

[37] Supra, book i. ch. v. § 1, and book ii. ch. v. § 5.

[38] The axiom, "Equals subtracted from equals leave equal differences,"
may be demonstrated from the two axioms in the text. If A = _a_ and B =
_b_, A - B = _a - b_. For if not, let A - B = _a - b + c_. Then since B
= _b_, adding equals to equals, A = _a + c_. But A = _a_. Therefore _a =
a + c_, which is impossible.

This proposition having been demonstrated, we may, by means of it,
demonstrate the following: "If equals be added to unequals, the sums are
unequal." If A = _a_ and B not = _b_, A + B is not = _a + b_. For
suppose it be so. Then, since A = _a_ and A + B = _a + b_, subtracting
equals from equals, B = _b_; which is contrary to the hypothesis.

So again, it may be proved that two things, one of which is equal and
the other unequal to a third thing, are unequal to one another. If A =
_a_ and A not = B, neither is _a_ = B. For suppose it to be equal. Then
since A = _a_ and _a_ = B, and since things equal to the same thing are
equal to one another, A = B: which is contrary to the hypothesis.

[39] Geometers have usually preferred to define parallel lines by the
property of being in the same plane and never meeting. This, however,
has rendered it necessary for them to assume, as an additional axiom,
some other property of parallel lines; and the unsatisfactory manner in
which properties for that purpose have been selected by Euclid and
others has always been deemed the opprobrium of elementary geometry.
Even as a verbal definition, equidistance is a fitter property to
characterize parallels by, since it is the attribute really involved in
the signification of the name. If to be in the same plane and never to
meet were all that is meant by being parallel, we should feel no
incongruity in speaking of a curve as parallel to its asymptote. The
meaning of parallel lines is, lines which pursue exactly the same
direction, and which, therefore, neither draw nearer nor go farther from
one another; a conception suggested at once by the contemplation of
nature. That the lines will never meet is of course included in the more
comprehensive proposition that they are everywhere equally distant. And
that any straight lines which are in the same plane and not equidistant
will certainly meet, may be demonstrated in the most rigorous manner
from the fundamental property of straight lines assumed in the text,
viz. that if they set out from the same point, they diverge more and
more without limit.

[40] _Philosophie Positive_, iii. 414-416.

[41] See the two remarkable notes (A) and (F), appended to his _Inquiry
into the Relation of Cause and Effect_.

[42] Supra, pp. 119, 120.

[43] A writer to whom I have several times referred, gives as the
definition of an impossibility, that which there exists in the world no
cause adequate to produce. This definition does not take in such
impossibilities as these--that two and two should make five; that two
straight lines should inclose a space; or that anything should begin to
exist without a cause. I can think of no definition of impossibility
comprehensive enough to include all its varieties, except the one which
I have given: viz. An impossibility is that, the truth of which would
conflict with a complete induction, that is, with the most conclusive
evidence which we possess of universal truth.

As to the reputed impossibilities which rest on no other grounds than
our ignorance of any cause capable of producing the supposed effects;
very few of them are certainly impossible, or permanently incredible.
The facts of travelling seventy miles an hour, painless surgical
operations, and conversing by instantaneous signals between London and
New York, held a high place, not many years ago, among such

[44] Not, however, as might at first sight appear, 999 times as much. A
complete analysis of the cases shows that (always assuming the veracity
of the witness to be 9/10) in 10,000 drawings, the drawing of No. 79
will occur nine times, and be announced incorrectly once; the
credibility therefore of the announcement of No. 79 is 9/10; while the
drawing of a white ball will occur nine times, and be announced
incorrectly 999 times. The credibility therefore of the announcement of
white is 9/1008, and the ratio of the two 1008:10; the one announcement
being thus only about a hundred times more credible than the other,
instead of 999 times.



"Clear and distinct ideas are terms which, though familiar and frequent
in men's mouths, I have reason to think every one who uses does not
perfectly understand. And possibly it is but here and there one who
gives himself the trouble to consider them so far as to know what he
himself or others precisely mean by them; I have, therefore, in most
places, chose to put determinate or determined, instead of clear and
distinct, as more likely to direct men's thoughts to my meaning in this
matter."--LOCKE'S _Essay on the Human Understanding_; Epistle to the

"Il ne peut y avoir qu'une méthode parfaite, qui est la _méthode
naturelle_; on nomme ainsi un arrangement dans lequel les êtres du même
genre seraient plus voisins entre eux que ceux de tous les autres
genres; les genres du même ordre, plus que ceux de tous les autres
ordres; et ainsi de suite. Cette méthode est l'idéal auquel l'histoire
naturelle doit tendre; car il est évident que si l'on y parvenait, l'on
aurait l'expression exacte et complète de la nature entière."--CUVIER,
_Règne Animal_, Introduction.

"Deux grandes notions philosophiques dominent la théorie fondamentale de
la méthode naturelle proprement dite, savoir la formation des groupes
naturels, et ensuite leur succession hiérarchique."--COMTE, _Cours de
Philosophie Positive_, 42me leçon.



§ 1. The inquiry which occupied us in the two preceding books, has
conducted us to what appears a satisfactory solution of the principal
problem of Logic, according to the conception I have formed of the
science. We have found, that the mental process with which Logic is
conversant, the operation of ascertaining truths by means of evidence,
is always, even when appearances point to a different theory of it, a
process of induction. And we have particularized the various modes of
induction, and obtained a clear view of the principles to which it must
conform, in order to lead to results which can be relied on.

The consideration of Induction, however, does not end with the direct
rules for its performance. Something must be said of those other
operations of the mind, which are either necessarily presupposed in all
induction, or are instrumental to the more difficult and complicated
inductive processes. The present book will be devoted to the
consideration of these subsidiary operations: among which our attention
must first be given to those, which are indispensable preliminaries to
all induction whatsoever.

Induction being merely the extension to a class of cases, of something
which has been observed to be true in certain individual instances of
the class; the first place among the operations subsidiary to induction,
is claimed by Observation. This is not, however, the place to lay down
rules for making good observers; nor is it within the competence of
Logic to do so, but of the art of intellectual Education. Our business
with observation is only in its connexion with the appropriate problem
of logic, the estimation of evidence. We have to consider, not how or
what to observe, but under what conditions observation is to be relied
on; what is needful, in order that the fact, supposed to be observed,
may safely be received as true.

§ 2. The answer to this question is very simple, at least in its first
aspect. The sole condition is, that what is supposed to have been
observed shall really have been observed; that it be an observation, not
an inference. For in almost every act of our perceiving faculties,
observation and inference are intimately blended. What we are said to
observe is usually a compound result, of which one-tenth may be
observation, and the remaining nine-tenths inference.

I affirm, for example, that I hear a man's voice. This would pass, in
common language, for a direct perception. All, however, which is really
perception, is that I hear a sound. That the sound is a voice, and that
voice the voice of a man, are not perceptions but inferences. I affirm,
again, that I saw my brother at a certain hour this morning. If any
proposition concerning a matter of fact would commonly be said to be
known by the direct testimony of the senses, this surely would be so.
The truth, however, is far otherwise. I only saw a certain coloured
surface; or rather I had the kind of visual sensations which are usually
produced by a coloured surface; and from these as marks, known to be
such by previous experience, I concluded that I saw my brother. I might
have had sensations precisely similar, when my brother was not there. I
might have seen some other person so nearly resembling him in
appearance, as, at the distance, and with the degree of attention which
I bestowed, to be mistaken for him. I might have been asleep, and have
dreamed that I saw him; or in a state of nervous disorder, which brought
his image before me in a waking hallucination. In all these modes, many
have been led to believe that they saw persons well known to them, who
were dead or far distant. If any of these suppositions had been true,
the affirmation that I saw my brother would have been erroneous; but
whatever was matter of direct perception, namely the visual sensations,
would have been real. The inference only would have been ill grounded;
I should have ascribed those sensations to a wrong cause.

Innumerable instances might be given, and analysed in the same manner,
of what are vulgarly called errors of sense. There are none of them
properly errors of sense; they are erroneous inferences from sense. When
I look at a candle through a multiplying glass, I see what seems a dozen
candles instead of one: and if the real circumstances of the case were
skilfully disguised, I might suppose that there were really that number;
there would be what is called an optical deception. In the kaleidoscope
there really is that deception: when I look through the instrument,
instead of what is actually there, namely a casual arrangement of
coloured fragments, the appearance presented is that of the same
combination several times repeated in symmetrical arrangement round a
point. The delusion is of course effected by giving me the same
sensations which I should have had if such a symmetrical combination had
really been presented to me. If I cross two of my fingers, and bring any
small object, a marble for instance, into contact with both, at points
not usually touched simultaneously by one object, I can hardly, if my
eyes are shut, help believing that there are two marbles instead of one.
But it is not my touch in this case, nor my sight in the other, which is
deceived; the deception, whether durable or only momentary, is in my
judgment. From my senses I have only the sensations, and those are
genuine. Being accustomed to have those or similar sensations when, and
only when, a certain arrangement of outward objects is present to my
organs, I have the habit of instantly, when I experience the sensations,
inferring the existence of that state of outward things. This habit has
become so powerful, that the inference, performed with the speed and
certainty of an instinct, is confounded with intuitive perceptions. When
it is correct, I am unconscious that it ever needed proof; even when I
know it to be incorrect, I cannot without considerable effort abstain
from making it. In order to be aware that it is not made by instinct but
by an acquired habit, I am obliged to reflect on the slow process
through which I learnt to judge by the eye of many things which I now
appear to perceive directly by sight; and on the reverse operation
performed by persons learning to draw, who with difficulty and labour
divest themselves of their acquired perceptions, and learn afresh to see
things as they appear to the eye.

It would be easy to prolong these illustrations, were there any need to
expatiate on a topic so copiously exemplified in various popular works.
From the examples already given, it is seen sufficiently, that the
individual facts from which we collect our inductive generalizations are
scarcely ever obtained by observation alone. Observation extends only to
the sensations by which we recognise objects; but the propositions which
we make use of, either in science or in common life, relate mostly to
the objects themselves. In every act of what is called observation,
there is at least one inference--from the sensations to the presence of
the object; from the marks or diagnostics, to the entire phenomenon. And
hence, among other consequences, follows the seeming paradox, that a
general proposition collected from particulars is often more certainly
true than any one of the particular propositions from which, by an act
of induction, it was inferred. For, each of those particular (or rather
singular) propositions involved an inference, from the impression on the
senses to the fact which caused that impression: and this inference may
have been erroneous in any one of the instances, but cannot well have
been erroneous in all of them, provided their number was sufficient to
eliminate chance. The conclusion, therefore, that is, the general
proposition, may deserve more complete reliance than it would be safe to
repose in any one of the inductive premises.

The logic of observation, then, consists solely in a correct
discrimination between that, in a result of observation, which has
really been perceived, and that which is an inference from the
perception. Whatever portion is inference, is amenable to the rules of
induction already treated of, and requires no further notice here: the
question for us in this place is, when all which is inference is taken
away, what remains. There remains, in the first place, the mind's own
feelings or states of consciousness, namely, its outward feelings or
sensations, and its inward feelings--its thoughts, emotions, and
volitions. Whether anything else remains, or all else is inference from
this; whether the mind is capable of directly perceiving or apprehending
anything except states of its own consciousness--is a problem of
metaphysics not to be discussed in this place. But after excluding all
questions on which metaphysicians differ, it remains true, that for most
purposes the discrimination we are called upon practically to exercise
is that between sensations or other feelings, of our own or of other
people, and inferences drawn from them. And on the theory of Observation
this is all which seems necessary to be said for the purposes of the
present work.

§ 3. If, in the simplest observation, or in what passes for such, there
is a large part which is not observation but something else; so in the
simplest description of an observation, there is, and must always be,
much more asserted than is contained in the perception itself. We cannot
describe a fact, without implying more than the fact. The perception is
only of one individual thing; but to describe it is to affirm a
connexion between it and every other thing which is either denoted or
connoted by any of the terms used. To begin with an example, than which
none can be conceived more elementary: I have a sensation of sight, and
I endeavour to describe it by saying that I see something white. In
saying this, I do not solely affirm my sensation; I also class it. I
assert a resemblance between the thing I see, and all things which I and
others are accustomed to call white. I assert that it resembles them in
the circumstance in which they all resemble one another, in that which
is the ground of their being called by the name. This is not merely one
way of describing an observation, but the only way. If I would either
register my observation for my own future use, or make it known for the
benefit of others, I must assert a resemblance between the fact which I
have observed and something else. It is inherent in a description, to be
the statement of a resemblance, or resemblances.

We thus see that it is impossible to express in words any result of
observation, without performing an act possessing what Dr. Whewell
considers to be characteristic of Induction. There is always something
introduced which was not included in the observation itself; some
conception common to the phenomenon with other phenomena to which it is
compared. An observation cannot be spoken of in language at all without
declaring more than that one observation; without assimilating it to
other phenomena already observed and classified. But this identification
of an object--this recognition of it as possessing certain known
characteristics--has never been confounded with Induction. It is an
operation which precedes all induction, and supplies it with its
materials. It is a perception of resemblances, obtained by comparison.

These resemblances are not always apprehended directly, by merely
comparing the object observed with some other present object, or with
our recollection of an object which is absent. They are often
ascertained through intermediate marks, that is, deductively. In
describing some new kind of animal, suppose me to say that it measures
ten feet in length, from the forehead to the extremity of the tail. I
did not ascertain this by the unassisted eye. I had a two-foot rule
which I applied to the object, and, as we commonly say, measured it; an
operation which was not wholly manual, but partly also mathematical,
involving the two propositions, Five times two is ten, and Things which
are equal to the same thing are equal to one another. Hence, the fact
that the animal is ten feet long is not an immediate perception, but a
conclusion from reasoning; the minor premises alone being furnished by
observation of the object. Nevertheless, this is called an observation
or a description of the animal, not an induction respecting it.

To pass at once from a very simple to a very complex example: I affirm
that the earth is globular. The assertion is not grounded on direct
perception; for the figure of the earth cannot, by us, be directly
perceived, though the assertion would not be true unless circumstances
could be supposed under which its truth could be so perceived. That the
form of the earth is globular is inferred from certain marks, as for
instance from this, that its shadow thrown upon the moon is circular; or
this, that on the sea, or any extensive plain, our horizon is always a
circle; either of which marks is incompatible with any other than a
globular form. I assert further, that the earth is that particular kind
of globe which is termed an oblate spheroid; because it is found by
measurement in the direction of the meridian, that the length on the
surface of the earth which subtends a given angle at its centre,
diminishes as we recede from the equator and approach the poles. But
these propositions, that the earth is globular, and that it is an oblate
spheroid, assert, each of them, an individual fact; in its own nature
capable of being perceived by the senses when the requisite organs and
the necessary position are supposed, and only not actually perceived
because those organs and that position are wanting. This identification
of the earth, first as a globe, and next as an oblate spheroid, which,
if the fact could have been seen, would have been called a description
of the figure of the earth, may without impropriety be so called when,
instead of being seen, it is inferred. But we could not without
impropriety call either of these assertions an induction from facts
respecting the earth. They are not general propositions collected from
particular facts, but particular facts deduced from general
propositions. They are conclusions obtained deductively, from premises
originating in induction: but of these premises some were not obtained
by observation of the earth, nor had any peculiar reference to it.

If, then, the truth respecting the figure of the earth is not an
induction, why should the truth respecting the figure of the earth's
orbit be so? The two cases only differ in this, that the form of the
orbit was not, like the form of the earth itself, deduced by
ratiocination from facts which were marks of ellipticity, but was got at
by boldly guessing that the path was an ellipse, and finding afterwards,
on examination, that the observations were in harmony with the
hypothesis. According to Dr. Whewell, however, this process of guessing
and verifying our guesses is not only induction, but the whole of
induction: no other exposition can be given of that logical operation.
That he is wrong in the latter assertion, the whole of the preceding
book has, I hope, sufficiently proved; and that the process by which the
ellipticity of the planetary orbits was ascertained, is not induction at
all, was attempted to be shown in the second chapter of the same
book.[1] We are now, however, prepared to go more into the heart of the
matter than at that earlier period of our inquiry, and to show, not
merely what the operation in question is not, but what it is.

§ 4. We observed, in the second chapter, that the proposition "the earth
moves in an ellipse," so far as it only serves for the colligation or
connecting together of actual observations, (that is, as it only affirms
that the observed positions of the earth may be correctly represented by
as many points in the circumference of an imaginary ellipse,) is not an
induction, but a description: it is an induction, only when it affirms
that the intermediate positions, of which there has been no direct
observation, would be found to correspond to the remaining points of the
same elliptic circumference. Now, though this real induction is one
thing, and the description another, we are in a very different condition
for making the induction before we have obtained the description, and
after it. For inasmuch as the description, like all other descriptions,
contains the assertion of a resemblance between the phenomenon described
and something else; in pointing out something which the series of
observed places of a planet resembles, it points out something in which
the several places themselves agree. If the series of places correspond
to as many points of an ellipse, the places themselves agree in being
situated in that ellipse. We have, therefore, by the same process which
gave us the description, obtained the requisites for an induction by the
Method of Agreement. The successive observed places of the earth being
considered as effects, and its motion as the cause which produces them,
we find that those effects, that is, those places, agree in the
circumstance of being in an ellipse. We conclude that the remaining
effects, the places which have not been observed, agree in the same
circumstance, and that the _law_ of the motion of the earth is motion in
an ellipse.

The Colligation of Facts, therefore, by means of hypotheses, or, as Dr.
Whewell prefers to say, by means of Conceptions, instead of being, as he
supposes, Induction itself, takes its proper place among operations
subsidiary to Induction. All Induction supposes that we have previously
compared the requisite number of individual instances, and ascertained
in what circumstances they agree. The Colligation of Facts is no other
than this preliminary operation. When Kepler, after vainly endeavouring
to connect the observed places of a planet by various hypotheses of
circular motion, at last tried the hypothesis of an ellipse and found it
answer to the phenomena; what he really attempted, first unsuccessfully
and at last successfully, was to discover the circumstance in which all
the observed positions of the planet agreed. And when he in like manner
connected another set of observed facts, the periodic times of the
different planets, by the proposition that the squares of the times are
proportional to the cubes of the distances, what he did was simply to
ascertain the property in which the periodic times of all the different
planets agreed.

Since, therefore, all that is true and to the purpose in Dr. Whewell's
doctrine of Conceptions might be fully expressed by the more familiar
term Hypothesis; and since his Colligation of Facts by means of
appropriate Conceptions, is but the ordinary process of finding by a
comparison of phenomena, in what consists their agreement or
resemblance; I would willingly have confined myself to those better
understood expressions, and persevered to the end in the same abstinence
which I have hitherto observed from ideological discussions; considering
the mechanism of our thoughts to be a topic distinct from and irrelevant
to the principles and rules by which the trustworthiness of the results
of thinking is to be estimated. Since, however, a work of such high
pretensions, and, it must also be said, of so much real merit, has
rested the whole theory of Induction upon such ideological
considerations, it seems necessary for others who follow, to claim for
themselves and their doctrines whatever position may properly belong to
them on the same metaphysical ground. And this is the object of the
succeeding chapter.



§ 1. The metaphysical inquiry into the nature and composition of what
have been called Abstract Ideas, or in other words, of the notions which
answer in the mind to classes and to general names, belongs not to
Logic, but to a different science, and our purpose does not require that
we should enter upon it here. We are only concerned with the universally
acknowledged fact, that such notions or conceptions do exist. The mind
can conceive a multitude of individual things as one assemblage or
class; and general names do really suggest to us certain ideas or mental
representations, otherwise we could not use the names with consciousness
of a meaning. Whether the idea called up by a general name is composed
of the various circumstances in which all the individuals denoted by the
name agree, and of no others, (which is the doctrine of Locke, Brown,
and the Conceptualists;) or whether it be the idea of some one of those
individuals, clothed in its individualizing peculiarities, but with the
accompanying knowledge that those peculiarities are not properties of
the class, (which is the doctrine of Berkeley, Mr. Bailey,[2] and the
modern Nominalists;) or whether (as held by Mr. James Mill) the idea of
the class is that of a miscellaneous assemblage of individuals belonging
to the class; or whether, finally, (what appears to be the truest
opinion,) it be any one or any other of all these, according to the
accidental circumstances of the case; certain it is, that _some_ idea or
mental conception is suggested by a general name, whenever we either
hear it or employ it with consciousness of a meaning. And this, which we
may call if we please a general idea, _represents_ in our minds the
whole class of things to which the name is applied. Whenever we think or
reason concerning the class, we do so by means of this idea. And the
voluntary power which the mind has, of attending to one part of what is
present to it at any moment, and neglecting another part, enables us to
keep our reasonings and conclusions respecting the class unaffected by
anything in the idea or mental image which is not really, or at least
which we do not really believe to be, common to the whole class.[3]

There are, then, such things as general conceptions, or conceptions by
means of which we can think generally: and when we form a set of
phenomena into a class, that is, when we compare them with one another
to ascertain in what they agree, some general conception is implied in
this mental operation. And inasmuch as such a comparison is a necessary
preliminary to Induction, it is most true that Induction could not go on
without general conceptions.

§ 2. But it does not therefore follow that these general conceptions
must have existed in the mind previously to the comparison. It is not a
law of our intellect, that in comparing things with each other and
taking note of their agreement we merely recognise as realized in the
outward world something that we already had in our minds. The conception
originally found its way to us as the _result_ of such a comparison. It
was obtained (in metaphysical phrase) by _abstraction_ from individual
things. These things may be things which we perceived or thought of on
former occasions, but they may also be the things which we are
perceiving or thinking of on the very occasion. When Kepler compared the
observed places of the planet Mars, and found that they agreed in being
points of an elliptic circumference, he applied a general conception
which was already in his mind, having been derived from his former
experience. But this is by no means universally the case. When we
compare several objects and find them to agree in being white, or when
we compare the various species of ruminating animals and find them to
agree in being cloven-footed, we have just as much a general conception
in our minds as Kepler had in his: we have the conception of "a white
thing," or the conception of "a cloven-footed animal." But no one
supposes that we necessarily bring these conceptions with us, and
_superinduce_ them (to adopt Dr. Whewell's expression) upon the facts:
because in these simple cases everybody sees that the very act of
comparison which ends in our connecting the facts by means of the
conception, may be the source from which we derive the conception
itself. If we had never seen any white object or had never seen any
cloven-footed animal before, we should at the same time and by the same
mental act acquire the idea, and employ it for the colligation of the
observed phenomena. Kepler, on the contrary, really had to bring the
idea with him, and superinduce it upon the facts; he could not evolve it
out of them: if he had not already had the idea, he would not have been
able to acquire it by a comparison of the planet's positions. But this
inability was a mere accident: the idea of an ellipse could have been
acquired from the paths of the planets as effectually as from anything
else, if the paths had not happened to be invisible. If the planet had
left a visible track, and we had been so placed that we could see it at
the proper angle, we might have abstracted our original idea of an
ellipse from the planetary orbit. Indeed, every conception which can be
made the instrument for connecting a set of facts, might have been
originally evolved from those very facts. The conception is a conception
_of_ something; and that which it is a conception of, is really _in_ the
facts, and might, under some supposable circumstances, or by some
supposable extension of the faculties which we actually possess, have
been detected in them. And not only is this always in itself possible,
but it actually happens, in almost all cases in which the obtaining of
the right conception is a matter of any considerable difficulty. For if
there be no new conception required; if one of those already familiar to
mankind will serve the purpose, the accident of being the first to whom
the right one occurs, may happen to almost anybody; at least in the case
of a set of phenomena which the whole scientific world are engaged in
attempting to connect. The honour, in Kepler's case, was that of the
accurate, patient, and toilsome calculations by which he compared the
results that followed from his different guesses, with the observations
of Tycho Brahe; but the merit was very small of guessing an ellipse; the
only wonder is that men had not guessed it before, nor could they have
failed to do so if there had not existed an obstinate _à priori_
prejudice that the heavenly bodies must move, if not in a circle, in
some combination of circles.

The really difficult cases are those in which the conception destined to
create light and order out of darkness and confusion, has to be sought
for among the very phenomena which it afterwards serves to arrange. Why,
according to Dr. Whewell himself, did the ancients fail in discovering
the laws of mechanics, that is, of equilibrium and of the communication
of motion? Because they had not, or at least had not clearly, the ideas
or conceptions of pressure and resistance, momentum, and uniform and
accelerating force. And whence could they have obtained these ideas,
except from the very facts of equilibrium and motion? The tardy
development of several of the physical sciences, for example of optics,
electricity, magnetism, and the higher generalizations of chemistry, he
ascribes to the fact that mankind had not yet possessed themselves of
the Idea of Polarity, that is, the idea of opposite properties in
opposite directions. But what was there to suggest such an idea, until,
by a separate examination of several of these different branches of
knowledge, it was shown that the facts of each of them did present, in
some instances at least, the curious phenomenon of opposite properties
in opposite directions? The thing was superficially manifest only in two
cases, those of the magnet, and of electrified bodies; and there the
conception was encumbered with the circumstance of material poles, or
fixed points in the body itself, in which points this opposition of
properties seemed to be inherent. The first comparison and abstraction
had led only to this conception of poles; and if anything corresponding
to that conception had existed in the phenomena of chemistry or optics,
the difficulty now justly considered so great, would have been extremely
small. The obscurity rose from the fact, that the polarities in
chemistry and optics were distinct species, though of the same genus,
with the polarities in electricity and magnetism: and that in order to
assimilate the phenomena to one another, it was necessary to compare a
polarity without poles, such for instance as is exemplified in the
polarization of light, and the polarity with (apparent) poles, which we
see in the magnet; and to recognise that these polarities, while
different in many other respects, agree in the one character which is
expressed by the phrase, opposite properties in opposite directions.
From the result of such a comparison it was that the minds of scientific
men formed this new general conception: between which, and the first
confused feeling of an analogy between some of the phenomena of light
and those of electricity and magnetism, there is a long interval, filled
up by the labours and more or less sagacious suggestions of many
superior minds.

The conceptions, then, which we employ for the colligation and
methodization of facts, do not develop themselves from within, but are
impressed upon the mind from without; they are never obtained otherwise
than by way of comparison and abstraction, and, in the most important
and the most numerous cases, are evolved by abstraction from the very
phenomena which it is their office to colligate. I am far, however, from
wishing to imply that it is not often a very difficult thing to perform
this process of abstraction well, or that the success of an inductive
operation does not, in many cases, principally depend on the skill with
which we perform it. Bacon was quite justified in designating as one of
the principal obstacles to good induction, general conceptions wrongly
formed, "notiones temerè à rebus abstractæ:" to which Dr. Whewell adds,
that not only does bad abstraction make bad induction, but that in order
to perform induction well, we must have abstracted well; our general
conceptions must be "clear" and "appropriate" to the matter in hand.

§ 3. In attempting to show what the difficulty in this matter really is,
and how it is surmounted, I must beg the reader, once for all, to bear
this in mind; that although in discussing the opinions of a different
school of philosophy, I am willing to adopt their language, and to
speak, therefore, of connecting facts through the instrumentality of a
conception, this technical phraseology means neither more nor less than
what is commonly called comparing the facts with one another and
determining in what they agree. Nor has the technical expression even
the advantage of being metaphysically correct. The facts are not
_connected_, except in a merely metaphorical acceptation of the term.
The _ideas_ of the facts may become connected, that is, we may be led to
think of them together; but this consequence is no more than what may be
produced by any casual association. What really takes place, is, I
conceive, more philosophically expressed by the common word Comparison,
than by the phrases "to connect" or "to superinduce." For, as the
general conception is itself obtained by a comparison of particular
phenomena, so, when obtained, the mode in which we apply it to other
phenomena is again by comparison. We compare phenomena with each other
to get the conception, and we then compare those and other phenomena
_with_ the conception. We get the conception of an animal (for instance)
by comparing different animals, and when we afterwards see a creature
resembling an animal, we compare it with our general conception of an
animal; and if it agrees with that general conception, we include it in
the class. The conception becomes the type of comparison.

And we need only consider what comparison is, to see that where the
objects are more than two, and still more when they are an indefinite
number, a type of some sort is an indispensable condition of the
comparison. When we have to arrange and classify a great number of
objects according to their agreements and differences, we do not make a
confused attempt to compare all with all. We know that two things are as
much as the mind can easily attend to at a time, and we therefore fix
upon one of the objects, either at hazard or because it offers in a
peculiarly striking manner some important character, and, taking this as
our standard, compare it with one object after another. If we find a
second object which presents a remarkable agreement with the first,
inducing us to class them together, the question instantly arises, in
what particular circumstances do they agree? and to take notice of these
circumstances is already a first stage of abstraction, giving rise to a
general conception. Having advanced thus far, when we now take in hand a
third object we naturally ask ourselves the question, not merely whether
this third object agrees with the first, but whether it agrees with it
in the same circumstances in which the second did? in other words,
whether it agrees with the general conception which has been obtained by
abstraction from the first and second? Thus we see the tendency of
general conceptions, as soon as formed, to substitute themselves as
types, for whatever individual objects previously answered that purpose
in our comparisons. We may, perhaps, find that no considerable number of
other objects agree with this first general conception; and that we must
drop the conception, and beginning again with a different individual
case, proceed by fresh comparisons to a different general conception.
Sometimes, again, we find that the same conception will serve, by merely
leaving out some of its circumstances; and by this higher effort of
abstraction, we obtain a still more general conception; as in the case
formerly referred to, the scientific world rose from the conception of
poles to the general conception of opposite properties in opposite
directions; or as those South-Sea islanders, whose conception of a
quadruped had been abstracted from hogs (the only animals of that
description which they had seen), when they afterwards compared that
conception with other quadrupeds, dropped some of the circumstances,
and arrived at the more general conception which Europeans associate
with the term.

These brief remarks contain, I believe, all that is well-grounded in the
doctrine, that the conception by which the mind arranges and gives unity
to phenomena must be furnished by the mind itself, and that we find the
right conception by a tentative process, trying first one and then
another until we hit the mark. The conception is not furnished _by_ the
mind until it has been furnished _to_ the mind; and the facts which
supply it are sometimes extraneous facts, but more often the very facts
which we are attempting to arrange by it. It is quite true, however,
that in endeavouring to arrange the facts, at whatever point we begin,
we never advance three steps without forming a general conception, more
or less distinct and precise; and that this general conception becomes
the clue which we instantly endeavour to trace through the rest of the
facts, or rather, becomes the standard with which we thenceforth compare
them. If we are not satisfied with the agreements which we discover
among the phenomena by comparing them with this type, or with some still
more general conception which by an additional stage of abstraction we
can form from the type; we change our path, and look out for other
agreements: we recommence the comparison from a different
starting-point, and so generate a different set of general conceptions.
This is the tentative process which Dr. Whewell speaks of; and which has
not unnaturally suggested the theory, that the conception is supplied by
the mind itself: since the different conceptions which the mind
successively tries, it either already possessed from its previous
experience, or they were supplied to it in the first stage of the
corresponding act of comparison; so that, in the subsequent part of the
process, the conception manifested itself as something compared with the
phenomena, not evolved from them.

§ 4. If this be a correct account of the instrumentality of general
conceptions in the comparison which necessarily precedes Induction, we
shall easily be able to translate into our own language what Dr. Whewell
means by saying that conceptions, to be subservient to Induction, must
be "clear" and "appropriate."

If the conception corresponds to a real agreement among the phenomena;
if the comparison which we have made of a set of objects has led us to
class them according to real resemblances and differences; the
conception which does this cannot fail to be appropriate, for some
purpose or other. The question of appropriateness is relative to the
particular object we have in view. As soon as, by our comparison, we
have ascertained some agreement, something which can be predicated in
common of a number of objects; we have obtained a basis on which an
inductive process is capable of being founded. But the agreements, or
the ulterior consequences to which those agreements lead, may be of very
different degrees of importance. If, for instance, we only compare
animals according to their colour, and class those together which are
coloured alike, we form the general conceptions of a white animal, a
black animal, &c., which are conceptions legitimately formed; and if an
induction were to be attempted concerning the causes of the colours of
animals, this comparison would be the proper and necessary preparation
for such an induction, but would not help us towards a knowledge of the
laws of any other of the properties of animals: while if, with Cuvier,
we compare and class them according to the structure of the skeleton,
or, with Blainville, according to the nature of their outward
integuments, the agreements and differences which are observable in
these respects are not only of much greater importance in themselves,
but are marks of agreements and differences in many other important
particulars of the structure and mode of life of the animals. If,
therefore, the study of their structure and habits be our object, the
conceptions generated by these last comparisons are far more
"appropriate" than those generated by the former. Nothing, other than
this, can be meant by the appropriateness of a conception.

When Dr. Whewell says that the ancients, or the schoolmen, or any modern
inquirers, missed discovering the real law of a phenomenon because they
applied to it an inappropriate instead of an appropriate conception; he
can only mean that in comparing various instances of the phenomenon, to
ascertain in what those instances agreed, they missed the important
points of agreement; and fastened upon such as were either imaginary,
and not agreements at all, or if real agreements, were comparatively
trifling, and had no connexion with the phenomenon, the law of which was

Aristotle, philosophizing on the subject of motion, remarked that
certain motions apparently take place spontaneously; bodies fall to the
ground, flame ascends, bubbles of air rise in water, &c.: and these he
called natural motions; while others not only never take place without
external incitement, but even when such incitement is applied, tend
spontaneously to cease; which, to distinguish them from the former, he
called violent motions. Now, in comparing the so-called natural motions
with one another, it appeared to Aristotle that they agreed in one
circumstance, namely, that the body which moved (or seemed to move)
spontaneously, was moving _towards its own place_; meaning thereby the
place from whence it originally came, or the place where a great
quantity of matter similar to itself was assembled. In the other class
of motions, as when bodies are thrown up in the air, they are, on the
contrary, moving _from_ their own place. Now, this conception of a body
moving towards its own place may justly be considered inappropriate;
because, though it expresses a circumstance really found in some of the
most familiar instances of motion apparently spontaneous, yet, first,
there are many other cases of such motion, in which that circumstance is
absent: the motion, for instance, of the earth and planets. Secondly,
even when it is present, the motion, on closer examination, would often
be seen not to be spontaneous: as, when air rises in water, it does not
rise by its own nature, but is pushed up by the superior weight of the
water which presses upon it. Finally, there are many cases in which the
spontaneous motion takes place in the contrary direction to what the
theory considers as the body's own place; for instance, when a fog rises
from a lake, or when water dries up. The agreement, therefore, which
Aristotle selected as his principle of classification, did not extend to
all cases of the phenomenon he wanted to study, spontaneous motion;
while it did include cases of the absence of the phenomenon, cases of
motion not spontaneous. The conception was hence "inappropriate." We may
add that, in the case in question, no conception would be appropriate;
there is no agreement which runs through all the cases of spontaneous or
apparently spontaneous motion and no others: they cannot be brought
under one law: it is a case of Plurality of Causes.[4]

§ 5. So much for the first of Dr. Whewell's conditions, that conceptions
must be appropriate. The second is, that they shall be "clear:" and let
us consider what this implies. Unless the conception corresponds to a
real agreement, it has a worse defect than that of not being clear; it
is not applicable to the case at all. Among the phenomena, therefore,
which we are attempting to connect by means of the conception, we must
suppose that there really is an agreement, and that the conception is a
conception of that agreement. In order, then, that it may be clear, the
only requisite is, that we shall know exactly in what the agreement
consists; that it shall have been carefully observed, and accurately
remembered. We are said not to have a clear conception of the
resemblance among a set of objects, when we have only a general feeling
that they resemble, without having analysed their resemblance, or
perceived in what points it consists, and fixed in our memory an exact
recollection of those points. This want of clearness, or, as it may be
otherwise called, this vagueness, in the general conception, may be
owing either to our having no accurate knowledge of the objects
themselves, or merely to our not having carefully compared them. Thus a
person may have no clear idea of a ship because he has never seen one,
or because he remembers but little, and that faintly, of what he has
seen. Or he may have a perfect knowledge and remembrance of many ships
of various kinds, frigates among the rest, but he may have no clear but
only a confused idea of a frigate, because he has never been told, and
has not compared them sufficiently to have remarked and remembered, in
what particular points a frigate differs from some other kind of ship.

It is not, however, necessary, in order to have clear ideas, that we
should know all the common properties of the things which we class
together. That would be to have our conception of the class complete as
well as clear. It is sufficient if we never class things together
without knowing exactly why we do so,--without having ascertained
exactly what agreements we are about to include in our conception; and
if, after having thus fixed our conception, we never vary from it, never
include in the class anything which has not those common properties, nor
exclude from it anything which has. A clear conception means a
determinate conception; one which does not fluctuate, which is not one
thing to-day and another to-morrow, but remains fixed and invariable,
except when, from the progress of our knowledge, or the correction of
some error, we consciously add to it or alter it. A person of clear
ideas, is a person who always knows in virtue of what properties his
classes are constituted; what attributes are connoted by his general

The principal requisites, therefore, of clear conceptions, are habits of
attentive observation, an extensive experience, and a memory which
receives and retains an exact image of what is observed. And in
proportion as any one has the habit of observing minutely and comparing
carefully a particular class of phenomena, and an accurate memory for
the results of the observation and comparison, so will his conceptions
of that class of phenomena be clear; provided he has the indispensable
habit, (naturally, however, resulting from those other endowments,) of
never using general names without a precise connotation.

As the clearness of our conceptions chiefly depends on the _carefulness_
and _accuracy_ of our observing and comparing faculties, so their
appropriateness, or rather the chance we have of hitting upon the
appropriate conception in any case, mainly depends on the _activity_ of
the same faculties. He who by habit, grounded on sufficient natural
aptitude, has acquired a readiness in accurately observing and comparing
phenomena, will perceive so many more agreements and will perceive them
so much more rapidly than other people, that the chances are much
greater of his perceiving, in any instance, the agreement on which the
important consequences depend.

§ 6. It is of so much importance that the part of the process of
investigating truth, discussed in this chapter, should be rightly
understood, that I think it is desirable to restate the results we have
arrived at, in a somewhat different mode of expression.

We cannot ascertain general truths, that is, truths applicable to
classes, unless we have formed the classes in such a manner that general
truths can be affirmed of them. In the formation of any class, there is
involved a conception of it as a class, that is, a conception of certain
circumstances as being those which characterize the class, and
distinguish the objects composing it from all other things. When we know
exactly what these circumstances are, we have a clear idea (or
conception) of the class, and of the meaning of the general name which
designates it. The primary condition implied in having this clear idea,
is that the class be really a class; that it correspond to a real
distinction; that the things it includes really do agree with one
another in certain particulars, and differ, in those same particulars,
from all other things. A person without clear ideas, is one who
habitually classes together, under the same general names, things which
have no common properties, or none which are not possessed also by other
things; or who, if the usage of other people prevents him from actually
misclassing things, is unable to state to himself the common properties
in virtue of which he classes them rightly.

But it is not the sole requisite of classification that the classes
should be real classes, framed by a legitimate mental process. Some
modes of classing things are more valuable than others for human uses,
whether of speculation or of practice; and our classifications are not
well made, unless the things which they bring together not only agree
with each other in something which distinguishes them from all other
things, but agree with each other and differ from other things in the
very circumstances which are of primary importance for the purpose
(theoretical or practical) which we have in view, and which constitutes
the problem before us. In other words, our conceptions, though they may
be clear, are not _appropriate_ for our purpose, unless the properties
we comprise in them are those which will help us towards what we wish to
understand--_i. e._, either those which go deepest into the nature of
the things, if our object be to understand that, or those which are most
closely connected with the particular property which we are endeavouring
to investigate.

We cannot, therefore, frame good general conceptions beforehand. That
the conception we have obtained is the one we want, can only be known
when we have done the work for the sake of which we wanted it; when we
completely understand the general character of the phenomena, or the
conditions of the particular property with which we concern ourselves.
General conceptions formed without this thorough knowledge, are Bacon's
"notiones temerè à rebus abstractæ." Yet such premature conceptions we
must be continually making up, in our progress to something better. They
are an impediment to the progress of knowledge, only when they are
permanently acquiesced in. When it has become our habit to group things
in wrong classes--in groups which either are not really classes, having
no distinctive points of agreement (absence of _clear_ ideas), or which
are not classes of which anything important to our purpose can be
predicated (absence of _appropriate_ ideas); and when, in the belief
that these badly made classes are those sanctioned by Nature, we refuse
to exchange them for others, and cannot or will not make up our general
conceptions from any other elements; in that case all the evils which
Bacon ascribes to his "notiones temerè abstractæ" really occur. This was
what the ancients did in physics, and what the world in general does in
morals and politics to the present day.

It would thus, in my view of the matter, be an inaccurate mode of
expression to say, that obtaining appropriate conceptions is a condition
precedent to generalization. Throughout the whole process of comparing
phenomena with one another for the purpose of generalization, the mind
is trying to make up a conception; but the conception which it is trying
to make up is that of the really important point of agreement in the
phenomena. As we obtain more knowledge of the phenomena themselves, and
of the conditions on which their important properties depend, our views
on this subject naturally alter; and thus we advance from a less to a
more "appropriate" general conception, in the progress of our

We ought not, at the same time, to forget that the really important
agreement cannot always be discovered by mere comparison of the very
phenomena in question, without the aid of a conception acquired
elsewhere; as in the case, so often referred to, of the planetary

The search for the agreement of a set of phenomena is in truth very
similar to the search for a lost or hidden object. At first we place
ourselves in a sufficiently commanding position, and cast our eyes round
us, and if we can see the object it is well; if not, we ask ourselves
mentally what are the places in which it may be hid, in order that we
may there search for it: and so on, until we imagine the place where it
really is. And here too we require to have had a previous conception, or
knowledge, of those different places. As in this familiar process, so in
the philosophical operation which it illustrates, we first endeavour to
find the lost object or recognise the common attribute, without
conjecturally invoking the aid of any previously acquired conception, or
in other words, of any hypothesis. Having failed in this, we call upon
our imagination for some hypothesis of a possible place, or a possible
point of resemblance, and then look, to see whether the facts agree with
the conjecture.

For such cases something more is required than a mind accustomed to
accurate observation and comparison. It must be a mind stored with
general conceptions, previously acquired, of the sorts which bear
affinity to the subject of the particular inquiry. And much will also
depend on the natural strength and acquired culture of what has been
termed the scientific imagination; on the faculty possessed of mentally
arranging known elements into new combinations, such as have not yet
been observed in nature, though not contradictory to any known laws.

But the variety of intellectual habits, the purposes which they serve,
and the modes in which they may be fostered and cultivated, are
considerations belonging to the Art of Education: a subject far wider
than Logic, and which this treatise does not profess to discuss. Here,
therefore, the present chapter may properly close.



§ 1. It does not belong to the present undertaking to dwell on the
importance of language as a medium of human intercourse, whether for
purposes of sympathy or of information. Nor does our design admit of
more than a passing allusion to that great property of names, on which
their functions as an intellectual instrument are, in reality,
ultimately dependent; their potency as a means of forming, and of
riveting, associations among our other ideas: a subject on which an able
thinker[5] has thus written:--

"Names are impressions of sense, and as such take the strongest hold on
the mind, and of all other impressions can be most easily recalled and
retained in view. They therefore serve to give a point of attachment to
all the more volatile objects of thought and feeling. Impressions that
when passed might be dissipated for ever, are, by their connexion with
language, always within reach. Thoughts, of themselves, are perpetually
slipping out of the field of immediate mental vision; but the name
abides with us, and the utterance of it restores them in a moment. Words
are the custodiers of every product of mind less impressive than
themselves. All extensions of human knowledge, all new generalizations,
are fixed and spread, even unintentionally, by the use of words. The
child growing up learns, along with the vocables of his mother-tongue,
that things which he would have believed to be different, are, in
important points, the same. Without any formal instruction, the language
in which we grow up teaches us all the common philosophy of the age. It
directs us to observe and know things which we should have overlooked;
it supplies us with classifications ready made, by which things are
arranged (as far as the light of by-gone generations admits) with the
objects to which they bear the greatest total resemblance. The number of
general names in a language, and the degree of generality of those
names, afford a test of the knowledge of the era, and of the
intellectual insight which is the birthright of any one born into it."

It is not, however, of the functions of Names, considered generally,
that we have here to treat, but only of the manner and degree in which
they are directly instrumental to the investigation of truth; in other
words, to the process of induction.

§ 2. Observation and Abstraction, the operations which formed the
subject of the two foregoing chapters, are conditions indispensable to
induction; there can be no induction where they are not. It has been
imagined that Naming is also a condition equally indispensable. There
are thinkers who have held that language is not solely, according to a
phrase generally current, _an_ instrument of thought, but _the_
instrument: that names, or something equivalent to them, some species of
artificial signs, are necessary to reasoning; that there could be no
inference, and consequently no induction, without them. But if the
nature of reasoning was correctly explained in the earlier part of the
present work, this opinion must be held to be an exaggeration, though of
an important truth. If reasoning be from particulars to particulars, and
if it consist in recognising one fact as a mark of another, or a mark of
a mark of another, nothing is required to render reasoning possible,
except senses and association: senses to perceive that two facts are
conjoined; association, as the law by which one of those two facts
raises up the idea of the other.[6] For these mental phenomena, as well
as for the belief or expectation which follows, and by which we
recognise as having taken place, or as about to take place, that of
which we have perceived a mark, there is evidently no need of language.
And this inference of one particular fact from another is a case of
induction. It is of this sort of induction that brutes are capable: it
is in this shape that uncultivated minds make almost all their
inductions, and that we all do so in the cases in which familiar
experience forces our conclusions upon us without any active process of
inquiry on our part, and in which the belief or expectation follows the
suggestion of the evidence, with the promptitude and certainty of an

§ 3. But though inference of an inductive character is possible without
the use of signs, it could never, without them, be carried much beyond
the very simple cases which we have just described, and which form, in
all probability, the limit of the reasonings of those animals to whom
conventional language is unknown. Without language, or something
equivalent to it, there could only be as much reasoning from experience
as can take place without the aid of general propositions. Now, though
in strictness we may reason from past experience to a fresh individual
case without the intermediate stage of a general proposition, yet
without general propositions we should seldom remember what past
experience we have had, and scarcely ever what conclusions that
experience will warrant. The division of the inductive process into two
parts, the first ascertaining what is a mark of the given fact, the
second whether in the new case that mark exists, is natural, and
scientifically indispensable. It is, indeed, in a majority of cases,
rendered necessary by mere distance of time. The experience by which we
are to guide our judgments may be other people's experience, little of
which can be communicated to us otherwise than by language: when it is
our own, it is generally experience long past; unless, therefore, it
were recorded by means of artificial signs, little of it (except in
cases involving our intenser sensations or emotions, or the subjects of
our daily and hourly contemplation) would be retained in the memory. It
is hardly necessary to add, that when the inductive inference is of any
but the most direct and obvious nature--when it requires several
observations or experiments, in varying circumstances, and the
comparison of one of these with another--it is impossible to proceed a
step, without the artificial memory which words bestow. Without words,
we should, if we had often seen A and B in immediate and obvious
conjunction, expect B whenever we saw A; but to discover their
conjunction when not obvious, or to determine whether it is really
constant or only casual, and whether there is reason to expect it under
any given change of circumstances, is a process far too complex to be
performed without some contrivance to make our remembrance of our own
mental operations accurate. Now, language is such a contrivance. When
that instrument is called to our aid, the difficulty is reduced to that
of making our remembrance of the meaning of words accurate. This being
secured, whatever passes through our minds may be remembered accurately,
by putting it carefully into words, and committing the words either to
writing or to memory.

The function of Naming, and particularly of General Names, in Induction,
may be recapitulated as follows. Every inductive inference which is good
at all, is good for a whole class of cases: and, that the inference may
have any better warrant of its correctness than the mere clinging
together of two ideas, a process of experimentation and comparison is
necessary; in which the whole class of cases must be brought to view,
and some uniformity in the course of nature evolved and ascertained,
since the existence of such an uniformity is required as a
justification for drawing the inference in even a single case. This
uniformity, therefore, may be ascertained once for all; and if, being
ascertained, it can be remembered, it will serve as a formula for
making, in particular cases, all such inferences as the previous
experience will warrant. But we can only secure its being remembered, or
give ourselves even a chance of carrying in our memory any considerable
number of such uniformities, by registering them through the medium of
permanent signs; which (being, from the nature of the case, signs not of
an individual fact, but of an uniformity, that is, of an indefinite
number of facts similar to one another) are general signs; universals;
general names, and general propositions.

§ 4. And here I cannot omit to notice an oversight committed by some
eminent thinkers; who have said that the cause of our using general
names is the infinite multitude of individual objects, which, making it
impossible to have a name for each, compels us to make one name serve
for many. This is a very limited view of the function of general names.
Even if there were a name for every individual object, we should require
general names as much as we now do. Without them we could not express
the result of a single comparison, nor record any one of the
uniformities existing in nature; and should be hardly better off in
respect to Induction than if we had no names at all. With none but names
of individuals, (or in other words, proper names,) we might, by
pronouncing the name, suggest the idea of the object, but we could not
assert any proposition; except the unmeaning ones formed by predicating
two proper names one of another. It is only by means of general names
that we can convey any information, predicate any attribute, even of an
individual, much more of a class. Rigorously speaking we could get on
without any other general names than the abstract names of attributes;
all our propositions might be of the form "such an individual object
possesses such an attribute," or "such an attribute is always (or never)
conjoined with such another attribute." In fact, however, mankind have
always given general names to objects as well as attributes, and indeed
before attributes: but the general names given to objects imply
attributes, derive their whole meaning from attributes; and are chiefly
useful as the language by means of which we predicate the attributes
which they connote.

It remains to be considered what principles are to be adhered to in
giving general names, so that these names, and the general propositions
in which they fill a place, may conduce most to the purposes of



§ 1. In order that we may possess a language perfectly suitable for the
investigation and expression of general truths, there are two principal,
and several minor, requisites. The first is, that every general name
should have a meaning, steadily fixed, and precisely determined. When,
by the fulfilment of this condition, such names as we possess are fitted
for the due performance of their functions, the next requisite, and the
second in order of importance, is that we should possess a name wherever
one is needed; wherever there is anything to be designated by it, which
it is of importance to express.

The former of these requisites is that to which our attention will be
exclusively directed in the present chapter.

§ 2. Every general name, then, must have a certain and knowable meaning.
Now the meaning (as has so often been explained) of a general
connotative name, resides in the connotation; in the attribute on
account of which, and to express which, the name is given. Thus, the
name animal being given to all things which possess the attributes of
sensation and voluntary motion, the word connotes those attributes
exclusively, and they constitute the whole of its meaning. If the name
be abstract, its denotation is the same with the connotation of the
corresponding concrete: it designates directly the attribute, which the
concrete term implies. To give a precise meaning to general names is,
then, to fix with steadiness the attribute or attributes connoted by
each concrete general name, and denoted by the corresponding abstract.
Since abstract names, in the order of their creation, do not precede
but follow concrete ones, as is proved by the etymological fact that
they are almost always derived from them; we may consider their meaning
as determined by, and dependent on, the meaning of their concrete: and
thus the problem of giving a distinct meaning to general language, is
all included in that of giving a precise connotation to all concrete
general names.

This is not difficult in the case of new names; of the technical terms
created by scientific inquirers for the purposes of science or art. But
when a name is in common use, the difficulty is greater; the problem in
this case not being that of choosing a convenient connotation for the
name, but of ascertaining and fixing the connotation with which it is
already used. That this can ever be a matter of doubt, is a sort of
paradox. But the vulgar (including in that term all who have not
accurate habits of thought) seldom know exactly what assertion they
intend to make, what common property they mean to express, when they
apply the same name to a number of different things. All which the name
expresses with them, when they predicate it of an object, is a confused
feeling of resemblance between that object and some of the other things
which they have been accustomed to denote by the name. They have applied
the name Stone to various objects previously seen; they see a new
object, which appears to them somewhat like the former, and they call it
a stone, without asking themselves in what respect it is like, or what
mode or degree of resemblance the best authorities, or even they
themselves, require as a warrant for using the name. This rough general
impression of resemblance is, however, made up of particular
circumstances of resemblance; and into these it is the business of the
logician to analyse it; to ascertain what points of resemblance among
the different things commonly called by the name, have produced in the
common mind this vague feeling of likeness; have given to the things the
similarity of aspect, which has made them a class, and has caused the
same name to be bestowed upon them.

But though general names are imposed by the vulgar without any more
definite connotation than that of a vague resemblance; general
propositions come in time to be made, in which predicates are applied to
those names, that is, general assertions are made concerning the _whole_
of the things which are denoted by the name. And since by each of these
propositions some attribute, more or less precisely conceived, is of
course predicated, the ideas of these various attributes thus become
associated with the name, and in a sort of uncertain way it comes to
connote them; there is a hesitation to apply the name in any new case in
which any of the attributes familiarly predicated of the class do not
exist. And thus, to common minds, the propositions which they are in the
habit of hearing or uttering concerning a class, make up in a loose way
a sort of connotation for the class-name. Let us take, for instance, the
word Civilized. How few could be found, even among the most educated
persons, who would undertake to say exactly what the term Civilized
connotes. Yet there is a feeling in the minds of all who use it, that
they are using it with a meaning; and this meaning is made up, in a
confused manner, of everything which they have heard or read that
civilized men, or civilized communities, are, or may be expected to be.

It is at this stage, probably, in the progress of a concrete name, that
the corresponding abstract name generally comes into use. Under the
notion that the concrete name must of course convey a meaning, or in
other words, that there is some property common to all things which it
denotes, people give a name to this common property; from the concrete
Civilized, they form the abstract Civilization. But since most people
have never compared the different things which are called by the
concrete name, in such a manner as to ascertain what properties these
things have in common, or whether they have any; each is thrown back
upon the marks by which he himself has been accustomed to be guided in
his application of the term: and these, being merely vague hearsays and
current phrases, are not the same in any two persons, nor in the same
person at different times. Hence the word (as Civilization, for example)
which professes to be the designation of the unknown common property,
conveys scarcely to any two minds the same idea. No two persons agree in
the things they predicate of it; and when it is itself predicated of
anything, no other person knows, nor does the speaker himself know with
precision, what he means to assert. Many other words which could be
named, as the word _honour_, or the word _gentleman_, exemplify this
uncertainty still more strikingly.

It needs scarcely be observed, that general propositions of which no one
can tell exactly what they assert, cannot possibly have been brought to
the test of a correct induction. Whether a name is to be used as an
instrument of thinking, or as a means of communicating the result of
thought, it is imperative to determine exactly the attribute or
attributes which it is to express: to give it, in short, a fixed and
ascertained connotation.

§ 3. It would, however, be a complete misunderstanding of the proper
office of a logician in dealing with terms already in use, if we were to
think that because a name has not at present an ascertained connotation,
it is competent to any one to give it such a connotation at his own
choice. The meaning of a term actually in use is not an arbitrary
quantity to be fixed, but an unknown quantity to be sought.

In the first place, it is obviously desirable to avail ourselves, as far
as possible, of the associations already connected with the name; not
enjoining the employment of it in a manner which conflicts with all
previous habits, and especially not so as to require the rupture of
those strongest of all associations between names, which are created by
familiarity with propositions in which they are predicated of one
another. A philosopher would have little chance of having his example
followed, if he were to give such a meaning to his terms as should
require us to call the North American Indians a civilized people, or the
higher classes in France or England savages; or to say that civilized
people live by hunting, and savages by agriculture. Were there no other
reason, the extreme difficulty of effecting so complete a revolution in
speech would be more than a sufficient one. The endeavour should be,
that all generally received propositions into which the term enters,
should be at least as true after its meaning is fixed, as they were
before; and that the concrete name, therefore, should not receive such a
connotation as shall prevent it from denoting things which, in common
language, it is currently affirmed of. The fixed and precise connotation
which it receives, should not be in deviation from, but in agreement (as
far as it goes) with, the vague and fluctuating connotation which the
term already had.

To fix the connotation of a concrete name, or the denotation of the
corresponding abstract, is to define the name. When this can be done
without rendering any received assertions inadmissible, the name can be
defined in accordance with its received use, which is vulgarly called
defining not the name but the thing. What is meant by the improper
expression of defining a thing, (or rather a class of things--for nobody
talks of defining an individual,) is to define the name, subject to the
condition that it shall denote those things. This, of course, supposes a
comparison of the things, feature by feature and property by property,
to ascertain what attributes they agree in; and not unfrequently an
operation strictly inductive, for the purpose of ascertaining some
unobvious agreement, which is the cause of the obvious agreements.

For, in order to give a connotation to a name, consistently with its
denoting certain objects, we have to make our selection from among the
various attributes in which those objects agree. To ascertain in what
they do agree is, therefore, the first logical operation requisite. When
this has been done as far as is necessary or practicable, the question
arises, which of these common attributes shall be selected to be
associated with the name. For if the class which the name denotes be a
Kind, the common properties are innumerable; and even if not, they are
often extremely numerous. Our choice is first limited by the preference
to be given to properties which are well known, and familiarly
predicated of the class; but even these are often too numerous to be all
included in the definition, and, besides, the properties most generally
known may not be those which serve best to mark out the class from all
others. We should therefore select from among the common properties, (if
among them any such are to be found,) those on which it has been
ascertained by experience, or proved by deduction, that many others
depend; or at least which are sure marks of them, and from whence,
therefore, many others will follow by inference. We thus see that to
frame a good definition of a name already in use, is not a matter of
choice but of discussion, and discussion not merely respecting the usage
of language, but respecting the properties of things, and even the
origin of those properties. And hence every enlargement of our knowledge
of the objects to which the name is applied, is liable to suggest an
improvement in the definition. It is impossible to frame a perfect set
of definitions on any subject, until the theory of the subject is
perfect: and as science makes progress, its definitions are also

§ 4. The discussion of Definitions, in so far as it does not turn on the
use of words but on the properties of things, Dr. Whewell calls the
Explication of Conceptions. The act of ascertaining, better than before,
in what particulars any phenomena which are classed together agree, he
calls in his technical phraseology, unfolding the general conception in
virtue of which they are so classed. Making allowance for what appears
to me the darkening and misleading tendency of this mode of expression,
several of his remarks are so much to the purpose, that I shall take the
liberty of transcribing them.

He observes,[8] that many of the controversies which have had an
important share in the formation of the existing body of science, have
"assumed the form of a battle of Definitions. For example, the inquiry
concerning the laws of falling bodies, led to the question whether the
proper definition of a _uniform force_ is that it generates a velocity
proportional to the _space_ from rest, or to the _time_. The controversy
of the _vis viva_ was what was the proper definition of the _measure of
force_. A principal question in the classification of minerals is, what
is the definition of a _mineral species_. Physiologists have endeavoured
to throw light on their subject by defining _organization_, or some
similar term." Questions of the same nature are still open respecting
the definitions of Specific Heat, Latent Heat, Chemical Combination, and

"It is very important for us to observe, that these controversies have
never been questions of insulated and _arbitrary_ definitions, as men
seem often tempted to imagine them to have been. In all cases there is a
tacit assumption of some proposition which is to be expressed by means
of the definition, and which gives it its importance. The dispute
concerning the definition thus acquires a real value, and becomes a
question concerning true and false. Thus in the discussion of the
question, What is a uniform force? it was taken for granted that gravity
is a uniform force. In the debate of the _vis viva_, it was assumed that
in the mutual action of bodies the whole effect of the force is
unchanged. In the zoological definition of species, (that it consists of
individuals which have, or may have, sprung from the same parents,) it
is presumed that individuals so related resemble each other more than
those which are excluded by such a definition; or, perhaps, that species
so defined have permanent and definite differences. A definition of
organization, or of some other term, which was not employed to express
some principle, would be of no value.

"The establishment, therefore, of a right definition of a term, may be a
useful step in the explication of our conceptions; but this will be the
case then only when we have under our consideration some proposition in
which the term is employed. For then the question really is, how the
conception shall be understood and defined in order that the proposition
may be true.

"To unfold our conceptions by means of definitions has never been
serviceable to science, except when it has been associated with an
immediate use of the definitions. The endeavour to define a Uniform
Force was combined with the assertion that gravity is a uniform force:
the attempt to define Accelerating Force was immediately followed by
the doctrine that accelerating forces may be compounded: the process of
defining Momentum was connected with the principle that momenta gained
and lost are equal: naturalists would have given in vain the definition
of Species which we have quoted, if they had not also given the
characters of species so separated.... Definition may be the best mode
of explaining our conception, but that which alone makes it worth while
to explain it in any mode, is the opportunity of using it in the
expression of truth. When a definition is propounded to us as a useful
step in knowledge, we are always entitled to ask what principle it
serves to enunciate."

In giving, then, an exact connotation to the phrase, "an uniform force,"
the condition was understood, that the phrase should continue to denote
gravity. The discussion, therefore, respecting the definition, resolved
itself into this question, What is there of an uniform nature in the
motions produced by gravity? By observations and comparisons, it was
found, that what was uniform in those motions was the ratio of the
velocity acquired to the time elapsed; equal velocities being added in
equal times. An uniform force, therefore, was defined, a force which
adds equal velocities in equal times. So, again, in defining momentum.
It was already a received doctrine, that when two objects impinge upon
one another, the momentum lost by the one is equal to that gained by the
other. This proportion it was deemed necessary to preserve, not from the
motive (which operates in many other cases) that it was firmly fixed in
popular belief; for the proposition in question had never been heard of
by any but the scientifically instructed. But it was felt to contain a
truth: even a superficial observation of the phenomena left no doubt
that in the propagation of motion from one body to another, there was
something of which the one body gained precisely what the other lost;
and the word momentum had been invented to express this unknown
something. The settlement, therefore, of the definition of momentum,
involved the determination of the question, What is that of which a
body, when it sets another body in motion, loses exactly as much as it
communicates? And when experiment had shown that this _something_ was
the product of the velocity of the body by its mass, or quantity of
matter, this became the definition of momentum.

The following remarks,[9] therefore, are perfectly just: "The business
of definition is part of the business of discovery.... To define, so
that our definition shall have any scientific value, requires no small
portion of that sagacity by which truth is detected.... When it has been
clearly seen what ought to be our definition, it must be pretty well
known what truth we have to state. The definition, as well as the
discovery, supposes a decided step in our knowledge to have been made.
The writers on Logic, in the middle ages, made Definition the last stage
in the progress of knowledge; and in this arrangement at least, the
history of science, and the philosophy derived from the history, confirm
their speculative views." For in order to judge finally how the name
which denotes a class may best be defined, we must know all the
properties common to the class, and all the relations of causation or
dependence among those properties.

If the properties which are fittest to be selected as marks of other
common properties are also obvious and familiar, and especially if they
bear a great part in producing that general air of resemblance which was
the original inducement to the formation of the class, the definition
will then be most felicitous. But it is often necessary to define the
class by some property not familiarly known, provided that property be
the best mark of those which are known. M. de Blainville, for instance,
founded his definition of life on the process of decomposition and
recomposition which incessantly takes place in every living body, so
that the particles composing it are never for two instants the same.
This is by no means one of the most obvious properties of living bodies;
it might escape altogether the notice of an unscientific observer. Yet
great authorities (independently of M. de Blainville, who is himself a
first-rate authority) have thought that no other property so well
answers the conditions required for the definition.

§ 5. Having laid down the principles which ought for the most part to be
observed in attempting to give a precise connotation to a term in use, I
must now add, that it is not always practicable to adhere to those
principles, and that even when practicable, it is occasionally not

Cases in which it is impossible to comply with all the conditions of a
precise definition of a name in agreement with usage, occur very
frequently. There is often no one connotation capable of being given to
a word, so that it shall still denote everything it is accustomed to
denote; or that all the propositions into which it is accustomed to
enter, and which have any foundation in truth, shall remain true.
Independently of accidental ambiguities, in which the different meanings
have no connexion with one another; it continually happens that a word
is used in two or more senses derived from each other, but yet radically
distinct. So long as a term is vague, that is, so long as its
connotation is not ascertained and permanently fixed, it is constantly
liable to be applied by _extension_ from one thing to another, until it
reaches things which have little, or even no, resemblance to those which
were first designated by it.

Suppose, says Dugald Stewart, in his _Philosophical Essays_,[10] "that
the letters A, B, C, D, E, denote a series of objects; that A possesses
some one quality in common with B; B a quality in common with C; C a
quality in common with D; D a quality in common with E; while at the
same time, no quality can be found which belongs in common to any
_three_ objects in the series. Is it not conceivable, that the affinity
between A and B may produce a transference of the name of the first to
the second; and that, in consequence of the other affinities which
connect the remaining objects together, the same name may pass in
succession from B to C; from C to D; and from D to E? In this manner, a
common appellation will arise between A and E, although the two objects
may, in their nature and properties, be so widely distant from each
other, that no stretch of imagination can conceive how the thoughts were
led from the former to the latter. The transitions, nevertheless, may
have been all so easy and gradual, that, were they successfully detected
by the fortunate ingenuity of a theorist, we should instantly recognise,
not only the verisimilitude, but the truth of the conjecture: in the
same way as we admit, with the confidence of intuitive conviction, the
certainty of the well-known etymological process which connects the
Latin preposition _e_ or _ex_ with the English substantive _stranger_,
the moment that the intermediate links of the chain are submitted to our

The applications which a word acquires by this gradual extension of it
from one set of objects to another, Stewart, adopting an expression from
Mr. Payne Knight, calls its _transitive_ applications; and after briefly
illustrating such of them as are the result of local or casual
associations, he proceeds as follows:[12]--

"But although by far the greater part of the transitive or derivative
applications of words depend on casual and unaccountable caprices of the
feelings or the fancy, there are certain cases in which they open a very
interesting field of philosophical speculation. Such are those, in which
an analogous transference of the corresponding term may be remarked
universally, or very generally, in other languages; and in which, of
course, the uniformity of the result must be ascribed to the essential
principles of the human frame. Even in such cases, however, it will by
no means be always found, on examination, that the various applications
of the same term have arisen from any common quality or qualities in the
objects to which they relate. In the greater number of instances, they
may be traced to some natural and universal associations of ideas,
founded in the common faculties, common organs, and common condition of
the human race.... According to the different degrees of intimacy and
strength in the associations on which the _transitions_ of language are
founded, very different effects may be expected to arise. Where the
association is slight and casual, the several meanings will remain
distinct from each other, and will often, in process of time, assume the
appearance of capricious varieties in the use of the same arbitrary
sign. _Where the association is so natural and habitual as to become
virtually indissoluble, the transitive meanings will coalesce in one
complex conception; and every new transition will become a more
comprehensive generalization of the term in question._"

I solicit particular attention to the law of mind expressed in the last
sentence, and which is the source of the perplexity so often experienced
in detecting these transitions of meaning. Ignorance of that law is the
shoal on which some of the most powerful intellects which have adorned
the human race have been stranded. The inquiries of Plato into the
definitions of some of the most general terms of moral speculation are
characterized by Bacon as a far nearer approach to a true inductive
method than is elsewhere to be found among the ancients, and are,
indeed, almost perfect examples of the preparatory process of comparison
and abstraction: but, from being unaware of the law just mentioned, he
often wasted the powers of this great logical instrument on inquiries in
which it could realize no result, since the phenomena, whose common
properties he so elaborately endeavoured to detect, had not really any
common properties. Bacon himself fell into the same error in his
speculations on the nature of heat, in which he evidently confounded
under the name hot, classes of phenomena which had no property in
common. Stewart certainly overstates the matter when he speaks of "a
prejudice which has descended to modern times from the scholastic ages,
that when a word admits of a variety of significations, these different
significations must all be species of the same genus, and must
consequently include some essential idea common to every individual to
which the generic term can be applied:"[13] for both Aristotle and his
followers were well aware that there are such things as ambiguities of
language, and delighted in distinguishing them. But they never suspected
ambiguity in the cases where (as Stewart remarks) the association on
which the transition of meaning was founded is so natural and habitual,
that the two meanings blend together in the mind, and a real transition
becomes an apparent generalization. Accordingly they wasted infinite
pains in endeavouring to find a definition which would serve for several
distinct meanings at once: as in an instance noticed by Stewart himself,
that of "causation; the ambiguity of the word which, in the Greek
language, corresponds to the English word _cause_, having suggested to
them the vain attempt of tracing the common idea which, in the case of
any _effect_, belongs to the _efficient_, to the _matter_, to the
_form_, and to the _end_. The idle generalities" (he adds) "we meet with
in other philosophers, about the ideas of the _good_, the _fit_, and the
_becoming_, have taken their rise from the same undue influence of
popular epithets on the speculations of the learned."[14]

Among the words which have undergone so many successive transitions of
meaning that every trace of a property common to all the things they are
applied to, or at least common and also peculiar to those things, has
been lost, Stewart considers the word Beautiful to be one. And (without
attempting to decide a question which in no respect belongs to logic) I
cannot but feel, with him, considerable doubt, whether the word
beautiful connotes the same property when we speak of a beautiful
colour, a beautiful face, a beautiful scene, a beautiful character, and
a beautiful poem. The word was doubtless extended from one of these
objects to another on account of a resemblance between them, or more
probably, between the emotions they excited; and, by this progressive
extension, it has at last reached things very remote from those objects
of sight to which there is no doubt that it was first appropriated; and
it is at least questionable whether there is now any property common to
all the things which, consistently with usage, may be called beautiful,
except the property of agreeableness, which the term certainly does
connote, but which cannot be all that people usually intend to express
by it, since there are many agreeable things which are never called
beautiful. If such be the case, it is impossible to give to the word
Beautiful any fixed connotation, such that it shall denote all the
objects which in common use it now denotes, but no others. A fixed
connotation, however, it ought to have; for, so long as it has not, it
is unfit to be used as a scientific term, and is a perpetual source of
false analogies and erroneous generalizations.

This, then, constitutes a case in exemplification of our remark, that
even when there is a property common to all the things denoted by a
name, to erect that property into the definition and exclusive
connotation of the name is not always desirable. The various things
called beautiful unquestionably resemble one another in being agreeable;
but to make this the definition of beauty, and so extend the word
Beautiful to all agreeable things, would be to drop altogether a portion
of meaning which the word really, though indistinctly, conveys, and to
do what depends on us towards causing those qualities of the objects
which the word previously, though vaguely, pointed at, to be overlooked
and forgotten. It is better, in such a case, to give a fixed connotation
to the term by restricting, than by extending its use; rather excluding
from the epithet Beautiful some things to which it is commonly
considered applicable, than leaving out of its connotation any of the
qualities by which, though occasionally lost sight of, the general mind
may have been habitually guided in the commonest and most interesting
applications of the term. For there is no question that when people
call anything beautiful, they think they are asserting more than that it
is merely agreeable. They think they are ascribing a peculiar _sort_ of
agreeableness, analogous to that which they find in some other of the
things to which they are accustomed to apply the same name. If,
therefore, there be any peculiar sort of agreeableness which is common
though not to all, yet to the principal things which are called
beautiful, it is better to limit the denotation of the term to those
things, than to leave that kind of quality without a term to connote it,
and thereby divert attention from its peculiarities.

§ 6. The last remark exemplifies a rule of terminology, which is of
great importance, and which has hardly yet been recognised as a rule,
but by a few thinkers of the present century. In attempting to rectify
the use of a vague term by giving it a fixed connotation, we must take
care not to discard (unless advisedly, and on the ground of a deeper
knowledge of the subject) any portion of the connotation which the word,
in however indistinct a manner, previously carried with it. For
otherwise language loses one of its inherent and most valuable
properties, that of being the conservator of ancient experience; the
keeper-alive of those thoughts and observations of former ages, which
may be alien to the tendencies of the passing time. This function of
language is so often overlooked or undervalued, that a few observations
on it appear to be extremely required.

Even when the connotation of a term has been accurately fixed, and still
more if it has been left in the state of a vague unanalysed feeling of
resemblance; there is a constant tendency in the word, through familiar
use, to part with a portion of its connotation. It is a well-known law
of the mind, that a word originally associated with a very complex
cluster of ideas, is far from calling up all those ideas in the mind,
every time the word is used: it calls up only one or two, from which the
mind runs on by fresh associations to another set of ideas, without
waiting for the suggestion of the remainder of the complex cluster. If
this were not the case, processes of thought could not take place with
anything like the rapidity which we know they possess. Very often,
indeed, when we are employing a word in our mental operations, we are so
far from waiting until the complex idea which corresponds to the meaning
of the word is consciously brought before us in all its parts, that we
run on to new trains of ideas by the other associations which the mere
word excites, without having realized in our imagination any part
whatever of the meaning: thus using the word, and even using it well and
accurately, and carrying on important processes of reasoning by means of
it, in an almost mechanical manner; so much so, that some
metaphysicians, generalizing from an extreme case, have fancied that all
reasoning is but the mechanical use of a set of terms according to a
certain form. We may discuss and settle the most important interests of
towns or nations, by the application of general theorems or practical
maxims previously laid down, without having had consciously suggested to
us, once in the whole process, the houses and green fields, the thronged
market-places and domestic hearths, of which not only those towns and
nations consist, but which the words town and nation confessedly mean.

Since, then, general names come in this manner to be used (and even to
do a portion of their work well) without suggesting to the mind the
whole of their meaning, and often with the suggestion of a very small,
or no part at all of that meaning; we cannot wonder that words so used
come in time to be no longer capable of suggesting any other of the
ideas appropriated to them, than those with which the association is
most immediate and strongest, or most kept up by the incidents of life:
the remainder being lost altogether; unless the mind, by often
consciously dwelling on them, keeps up the association. Words naturally
retain much more of their meaning to persons of active imagination, who
habitually represent to themselves things in the concrete, with the
detail which belongs to them in the actual world. To minds of a
different description, the only antidote to this corruption of language
is predication. The habit of predicating of the name, all the various
properties which it originally connoted, keeps up the association
between the name and those properties.

But in order that it may do so, it is necessary that the predicates
should themselves retain their association with the properties which
they severally connote. For the propositions cannot keep the meaning of
the words alive, if the meaning of the propositions themselves should
die. And nothing is more common than for propositions to be mechanically
repeated, mechanically retained in the memory, and their truth
undoubtingly assented to and relied on, while yet they carry no meaning
distinctly home to the mind; and while the matter of fact or law of
nature which they originally expressed is as much lost sight of, and
practically disregarded, as if it never had been heard of at all. In
those subjects which are at the same time familiar and complicated, and
especially in those which are so in as great a degree as moral and
social subjects are, it is a matter of common remark how many important
propositions are believed and repeated from habit, while no account
could be given, and no sense is practically manifested, of the truths
which they convey. Hence it is, that the traditional maxims of old
experience, though seldom questioned, have often so little effect on the
conduct of life; because their meaning is never, by most persons, really
felt, until personal experience has brought it home. And thus also it is
that so many doctrines of religion, ethics, and even politics, so full
of meaning and reality to first converts, have manifested (after the
association of that meaning with the verbal formulas has ceased to be
kept up by the controversies which accompanied their first introduction)
a tendency to degenerate rapidly into lifeless dogmas; which tendency,
all the efforts of an education expressly and skilfully directed to
keeping the meaning alive, are barely sufficient to counteract.

Considering, then, that the human mind, in different generations,
occupies itself with different things, and in one age is led by the
circumstances which surround it to fix more of its attention upon one of
the properties of a thing, in another age upon another; it is natural
and inevitable that in every age a certain portion of our recorded and
traditional knowledge, not being continually suggested by the pursuits
and inquiries with which mankind are at that time engrossed, should fall
asleep, as it were, and fade from the memory. It would be in danger of
being totally lost, if the propositions or formulas, the results of the
previous experience, did not remain, as forms of words it may be, but of
words that once really conveyed, and are still supposed to convey, a
meaning: which meaning, though suspended, may be historically traced,
and when suggested, may be recognised by minds of the necessary
endowments as being still matter of fact, or truth. While the formulas
remain, the meaning may at any time revive; and as on the one hand the
formulas progressively lose the meaning they were intended to convey,
so, on the other, when this forgetfulness has reached its height and
begun to produce obvious consequences, minds arise which from the
contemplation of the formulas rediscover the truth, when truth it was,
which was contained in them, and announce it again to mankind, not as a
discovery, but as the meaning of that which they have been taught, and
still profess to believe.

Thus there is a perpetual oscillation in spiritual truths, and in
spiritual doctrines of any significance, even when not truths. Their
meaning is almost always in a process either of being lost or of being
recovered. Whoever has attended to the history of the more serious
convictions of mankind--of the opinions by which the general conduct of
their lives is, or as they conceive ought to be, more especially
regulated--is aware that even when recognising verbally the same
doctrines, they attach to them at different periods a greater or a less
quantity, and even a different kind, of meaning. The words in their
original acceptation connoted, and the propositions expressed, a
complication of outward facts and inward feelings, to different portions
of which the general mind is more particularly alive in different
generations of mankind. To common minds, only that portion of the
meaning is in each generation suggested, of which that generation
possesses the counterpart in its own habitual experience. But the words
and propositions lie ready to suggest to any mind duly prepared the
remainder of the meaning. Such individual minds are almost always to be
found: and the lost meaning, revived by them, again by degrees works its
way into the general mind.

The arrival of this salutary reaction may however be materially
retarded, by the shallow conceptions and incautious proceedings of mere
logicians. It sometimes happens that towards the close of the downward
period, when the words have lost part of their significance, and have
not yet begun to recover it, persons arise whose leading and favourite
idea is the importance of clear conceptions and precise thought, and the
necessity, therefore, of definite language. These persons, in examining
the old formulas, easily perceive that words are used in them without a
meaning; and if they are not the sort of persons who are capable of
rediscovering the lost signification, they naturally enough dismiss the
formula, and define the name without reference to it. In so doing they
fasten down the name to what it connotes in common use at the time when
it conveys the smallest quantity of meaning; and introduce the practice
of employing it, consistently and uniformly, according to that
connotation. The word in this way acquires an extent of denotation far
beyond what it had before; it becomes extended to many things to which
it was previously, in appearance capriciously, refused. Of the
propositions in which it was formerly used, those which were true in
virtue of the forgotten part of its meaning are now, by the clearer
light which the definition diffuses, seen not to be true according to
the definition; which, however, is the recognised and sufficiently
correct expression of all that is perceived to be in the mind of any one
by whom the term is used at the present day. The ancient formulas are
consequently treated as prejudices; and people are no longer taught as
before, though not to understand them, yet to believe that there is
truth in them. They no longer remain in the general mind surrounded by
respect, and ready at any time to suggest their original meaning.
Whatever truths they contain are not only, in these circumstances,
rediscovered far more slowly, but, when rediscovered, the prejudice
with which novelties are regarded is now, in some degree at least,
against them, instead of being on their side.

An example may make these remarks more intelligible. In all ages, except
where moral speculation has been silenced by outward compulsion, or
where the feelings which prompt to it still continue to be satisfied by
the traditional doctrines of an established faith, one of the subjects
which have most occupied the minds of thinking persons is the inquiry,
What is virtue? or, What is a virtuous character? Among the different
theories on the subject which have, at different times, grown up and
obtained partial currency, every one of which reflected as in the
clearest mirror, the express image of the age which gave it birth; there
was one, according to which virtue consists in a correct calculation of
our own personal interests, either in this world only, or also in
another. To make this theory plausible, it was of course necessary that
the only beneficial actions which people in general were accustomed to
see, or were therefore accustomed to praise, should be such as were, or
at least might without contradicting obvious facts be supposed to be,
the result of a prudential regard to self-interest; so that the words
really connoted no more, in common acceptation, than was set down in the

Suppose, now, that the partisans of this theory had contrived to
introduce a consistent and undeviating use of the term according to this
definition. Suppose that they had seriously endeavoured, and had
succeeded in the endeavour, to banish the word disinterestedness from
the language; had obtained the disuse of all expressions attaching odium
to selfishness or commendation to self-sacrifice, or which implied
generosity or kindness to be anything but doing a benefit in order to
receive a greater personal advantage in return. Need we say, that this
abrogation of the old formulas for the sake of preserving clear ideas
and consistency of thought, would have been a great evil? while the very
inconsistency incurred by the coexistence of the formulas with
philosophical opinions which seemed to condemn them as absurdities,
operated as a stimulus to the re-examination of the subject; and thus
the very doctrines originating in the oblivion into which a part of the
truth had fallen, were rendered indirectly, but powerfully, instrumental
to its revival.

The doctrine of the Coleridge school, that the language of any people
among whom culture is of old date, is a sacred deposit, the property of
all ages, and which no one age should consider itself empowered to
alter--borders indeed, as thus expressed, on an extravagance; but it is
grounded on a truth, frequently overlooked by that class of logicians
who think more of having a clear than of having a comprehensive meaning;
and who perceive that every age is adding to the truths which it has
received from its predecessors, but fail to see that a counter process
of losing truths already possessed, is also constantly going on, and
requiring the most sedulous attention to counteract it. Language is the
depository of the accumulated body of experience to which all former
ages have contributed their part, and which is the inheritance of all
yet to come. We have no right to prevent ourselves from transmitting to
posterity a larger portion of this inheritance than we may ourselves
have profited by. However much we may be able to improve on the
conclusions of our forefathers, we ought to be careful not inadvertently
to let any of their premises slip through our fingers. It may be good to
alter the meaning of a word, but it is bad to let any part of the
meaning drop. Whoever seeks to introduce a more correct use of a term
with which important associations are connected, should be required to
possess an accurate acquaintance with the history of the particular
word, and of the opinions which in different stages of its progress it
served to express. To be qualified to define the name, we must know all
that has ever been known of the properties of the class of objects which
are, or originally were, denoted by it. For if we give it a meaning
according to which any proposition will be false which has ever been
generally held to be true, it is incumbent on us to be sure that we know
and have considered all which those, who believed the proposition,
understood by it.



§ 1. It is not only in the mode which has now been pointed out, namely
by gradual inattention to a portion of the ideas conveyed, that words in
common use are liable to shift their connotation. The truth is, that the
connotation of such words is perpetually varying; as might be expected
from the manner in which words in common use acquire their connotation.
A technical term, invented for purposes of art or science, has, from the
first, the connotation given to it by its inventor; but a name which is
in every one's mouth before any one thinks of defining it, derives its
connotation only from the circumstances which are habitually brought to
mind when it is pronounced. Among these circumstances, the properties
common to the things denoted by the name, have naturally a principal
place; and would have the sole place, if language were regulated by
convention rather than by custom and accident. But besides these common
properties, which if they exist are _certainly_ present whenever the
name is employed, any other circumstance may _casually_ be found along
with it, so frequently as to become associated with it in the same
manner, and as strongly, as the common properties themselves. In
proportion as this association forms itself, people give up using the
name in cases in which those casual circumstances do not exist. They
prefer using some other name, or the same name with some adjunct, rather
than employ an expression which will call up an idea they do not want to
excite. The circumstance originally casual, thus becomes regularly a
part of the connotation of the word.

It is this continual incorporation of circumstances originally
accidental, into the permanent signification of words, which is the
cause that there are so few exact synonymes. It is this also which
renders the dictionary meaning of a word, by universal remark so
imperfect an exponent of its real meaning. The dictionary meaning is
marked out in a broad, blunt way, and probably includes all that was
originally necessary for the correct employment of the term; but in
process of time so many collateral associations adhere to words, that
whoever should attempt to use them with no other guide than the
dictionary, would confound a thousand nice distinctions and subtle
shades of meaning which dictionaries take no account of; as we notice in
the use of a language in conversation or writing by a foreigner not
thoroughly master of it. The history of a word, by showing the causes
which determine its use, is in these cases a better guide to its
employment than any definition; for definitions can only show its
meaning at the particular time, or at most the series of its successive
meanings, but its history may show the law by which the succession was
produced. The word _gentleman_, for instance, to the correct employment
of which a dictionary would be no guide, originally meant simply a man
born in a certain rank. From this it came by degrees to connote all such
qualities or adventitious circumstances as were usually found to belong
to persons of that rank. This consideration at once explains why in one
of its vulgar acceptations it means any one who lives without labour, in
another without manual labour, and in its more elevated signification it
has in every age signified the conduct, character, habits, and outward
appearance, in whomsoever found, which, according to the ideas of that
age, belonged or were expected to belong to persons born and educated in
a high social position.

It continually happens that of two words, whose dictionary meanings are
either the same or very slightly different, one will be the proper word
to use in one set of circumstances, another in another, without its
being possible to show how the custom of so employing them originally
grew up. The accident that one of the words was used and not the other
on a particular occasion or in a particular social circle, will be
sufficient to produce so strong an association between the word and some
speciality of circumstances, that mankind abandon the use of it in any
other case, and the speciality becomes part of its signification. The
tide of custom first drifts the word on the shore of a particular
meaning, then retires and leaves it there.

An instance in point is the remarkable change which, in the English
language at least, has taken place in the signification of the word
_loyalty_. That word originally meant in English, as it still means in
the language from whence it came, fair, open dealing, and fidelity to
engagements; in that sense the quality it expressed was part of the
ideal chivalrous or knightly character. By what process, in England, the
term became restricted to the single case of fidelity to the throne, I
am not sufficiently versed in the history of courtly language to be able
to pronounce. The interval between a _loyal chevalier_ and a loyal
subject is certainly great. I can only suppose that the word was, at
some period, the favourite term at court to express fidelity to the oath
of allegiance; until at length those who wished to speak of any other,
and as it was probably deemed, inferior sort of fidelity, either did not
venture to use so dignified a term, or found it convenient to employ
some other in order to avoid being misunderstood.

§ 2. Cases are not unfrequent in which a circumstance, at first casually
incorporated into the connotation of a word which originally had no
reference to it, in time wholly supersedes the original meaning, and
becomes not merely a part of the connotation, but the whole of it. This
is exemplified in the word pagan, _paganus_; which originally, as its
etymology imports, was equivalent to _villager_; the inhabitant of a
_pagus_, or village. At a particular era in the extension of
Christianity over the Roman empire, the adherents of the old religion,
and the villagers or country people, were nearly the same body of
individuals, the inhabitants of the towns having been earliest
converted; as in our own day, and at all times, the greater activity of
social intercourse renders them the earliest recipients of new opinions
and modes, while old habits and prejudices linger longest among the
country people: not to mention that the towns were more immediately
under the direct influence of the government, which at that time had
embraced Christianity. From this casual coincidence, the word _paganus_
carried with it, and began more and more steadily to suggest, the idea
of a worshipper of the ancient divinities; until at length it suggested
that idea so forcibly that people who did not desire to suggest the idea
avoided using the word. But when _paganus_ had come to connote
heathenism, the very unimportant circumstance, with reference to that
fact, of the place of residence, was soon disregarded in the employment
of the word. As there was seldom any occasion for making separate
assertions respecting heathens who lived in the country, there was no
need for a separate word to denote them; and pagan came not only to mean
heathen, but to mean that exclusively.

A case still more familiar to most readers is that of the word _villain_
or _villein_. This term, as everybody knows, had in the middle ages a
connotation as strictly defined as a word could have, being the proper
legal designation for those persons who were the subjects of the less
onerous forms of feudal bondage. The scorn of the semibarbarous military
aristocracy for these their abject dependants, rendered the act of
likening any person to this class of people a mark of the greatest
contumely: the same scorn led them to ascribe to the same people all
manner of hateful qualities, which doubtless also, in the degrading
situation in which they were held, were often not unjustly imputed to
them. These circumstances combined to attach to the term villain, ideas
of crime and guilt in so forcible a manner, that the application of the
epithet even to those to whom it legally belonged became an affront, and
was abstained from whenever no affront was intended. From that time
guilt was part of the connotation; and soon became the whole of it,
since mankind were not prompted by any urgent motive to continue making
a distinction in their language between bad men of servile station and
bad men of any other rank in life.

These and similar instances in which the original signification of a
term is totally lost--another and an entirely distinct meaning being
first engrafted upon the former, and finally substituted for it--afford
examples of the double movement which is always taking place in
language: two counter-movements, one of Generalization, by which words
are perpetually losing portions of their connotation, and becoming of
less meaning and more general acceptation; the other of Specialization,
by which other, or even these same words, are continually taking on
fresh connotation; acquiring additional meaning, by being restricted in
their employment to a part only of the occasions on which they might
properly be used before. This double movement is of sufficient
importance in the natural history of language, (to which natural history
the artificial modifications ought always to have some degree of
reference,) to justify our dwelling a little longer on the nature of the
twofold phenomenon, and the causes to which it owes its existence.

§ 3. To begin with the movement of generalization. It is unnecessary to
dwell on the changes in the meaning of names which take place merely
from their being used ignorantly, by persons who, not having properly
mastered the received connotation of a word, apply it in a looser and
wider sense than belongs to it. This, however, is a real source of
alterations in the language; for when a word, from being often employed
in cases where one of the qualities which it connotes does not exist,
ceases to suggest that quality with certainty, then even those who are
under no mistake as to the proper meaning of the word, prefer expressing
that meaning in some other way, and leave the original word to its fate.
The word 'Squire as standing for an owner of a landed estate; Parson, as
denoting not the rector of the parish, but clergymen in general; Artist,
to denote only a painter or sculptor; are cases in point.[15]
Independently, however, of the generalization of names through their
ignorant misuse, there is a tendency in the same direction, consistently
with a perfect knowledge of their meaning; arising from the fact, that
the number of things known to us, and of which we feel a desire to
speak, multiply faster than the names for them. Except on subjects for
which there has been constructed a scientific terminology, with which
unscientific persons do not meddle, great difficulty is generally found
in bringing a new name into use; and independently of that difficulty,
it is natural to prefer giving to a new object a name which at least
expresses its resemblance to something already known, since by
predicating of it a name entirely new we at first convey no information.
In this manner the name of a species often becomes the name of a genus;
as _salt_, for example, or _oil_; the former of which words originally
denoted only the muriate of soda, the latter, as its etymology
indicates, only olive oil; but which now denote large and diversified
classes of substances resembling these in some of their qualities, and
connote only those common qualities, instead of the whole of the
distinctive properties of olive oil and sea salt. The words _glass_ and
_soap_ are used by modern chemists in a similar manner, to denote genera
of which the substances vulgarly so called are single species. And it
often happens, as in those instances, that the term keeps its special
signification in addition to its more general one, and becomes
ambiguous, that is, two names instead of one.

These changes, by which words in ordinary use become more and more
generalized, and less and less expressive, take place in a still greater
degree with the words which express the complicated phenomena of mind
and society. Historians, travellers, and in general those who speak or
write concerning moral and social phenomena with which they are not
familiarly acquainted, are the great agents in this modification of
language. The vocabulary of all except unusually instructed as well as
thinking persons, is, on such subjects, eminently scanty. They have a
certain small set of words to which they are accustomed, and which they
employ to express phenomena the most heterogeneous, because they have
never sufficiently analysed the facts to which those words correspond in
their own country, to have attached perfectly definite ideas to the
words. The first English conquerors of Bengal, for example, carried with
them the phrase _landed proprietor_ into a country where the rights of
individuals over the soil were extremely different in degree, and even
in nature, from those recognised in England. Applying the term with all
its English associations in such a state of things; to one who had only
a limited right they gave an absolute right, from another because he had
not an absolute right they took away all right, drove whole classes of
people to ruin and despair, filled the country with banditti, created a
feeling that nothing was secure, and produced, with the best intentions,
a disorganization of society which had not been produced in that country
by the most ruthless of its barbarian invaders. Yet the usage of persons
capable of so gross a misapprehension, determines the meaning of
language; and the words they thus misuse grow in generality, until the
instructed are obliged to acquiesce; and to employ those words (first
freeing them from vagueness by giving them a definite connotation) as
generic terms, subdividing the genera into species.

§ 4. While the more rapid growth of ideas than of names thus creates a
perpetual necessity for making the same names serve, even if
imperfectly, on a greater number of occasions; a counter-operation is
going on, by which names become on the contrary restricted to fewer
occasions, by taking on, as it were, additional connotation, from
circumstances not originally included in the meaning, but which have
become connected with it in the mind by some accidental cause. We have
seen above, in the words _pagan_ and _villain_, remarkable examples of
the specialization of the meaning of words from casual associations, as
well as of the generalization of it in a new direction, which often

Similar specializations are of frequent occurrence in the history even
of scientific nomenclature. "It is by no means uncommon," says Dr.
Paris, in his _Pharmacologia_,[16] "to find a word which is used to
express general characters subsequently become the name of a specific
substance in which such characters are predominant; and we shall find
that some important anomalies in nomenclature may be thus explained. The
term _Αρσενίκον_, from which the word Arsenic is derived, was an ancient
epithet applied to those natural substances which possessed strong and
acrimonious properties, and as the poisonous quality of arsenic was
found to be remarkably powerful, the term was especially applied to
Orpiment, the form in which this metal most usually occurred. So the
term _Verbena_ (quasi _Herbena_) originally denoted all those herbs that
were held sacred on account of their being employed in the rites of
sacrifice, as we learn from the poets; but as _one_ herb was usually
adopted upon these occasions, the word Verbena came to denote that
particular herb _only_, and it is transmitted to us to this day under
the same title, viz. Verbena or Vervain, and indeed until lately it
enjoyed the medical reputation which its sacred origin conferred upon
it, for it was worn suspended around the neck as an amulet. _Vitriol_,
in the original application of the word, denoted _any_ crystalline body
with a certain degree of transparency (_vitrum_); it is hardly necessary
to observe that the term is now appropriated to a particular species: in
the same manner, Bark, which is a general term, is applied to express
_one_ genus, and by way of eminence, it has the article _The_ prefixed,
as _The_ bark: the same observation will apply to the word Opium, which,
in its primitive sense, signifies _any_ juice (_ὀπὸς_, _Succus_), while
it now only denotes _one_ species, viz. that of the poppy. So, again,
_Elaterium_ was used by Hippocrates to signify various internal
applications, especially purgatives, of a violent and drastic nature
(from the word _ἐλαύνω_, _agito_, _moveo_, _stimulo_), but by succeeding
authors it was exclusively applied to denote the active matter which
subsides from the juice of the wild cucumber. The word _Fecula_, again,
originally meant to imply _any_ substance which was derived by
spontaneous subsidence from a liquid (from _fæx_, the grounds or
settlement of _any_ liquor); afterwards it was applied to Starch, which
is deposited in this manner by agitating the flour of wheat in water;
and lastly, it has been applied to a peculiar vegetable principle,
which, like starch, is insoluble in cold, but completely soluble in
boiling water, with which it forms a gelatinous solution. This
indefinite meaning of the word _fecula_ has created numerous mistakes in
pharmaceutic chemistry; Elaterium, for instance, is said to be _fecula_,
and, in the original sense of the word, it is properly so called,
inasmuch as it is procured from a vegetable juice by spontaneous
subsidence, but in the limited and modern acceptation of the term, it
conveys an erroneous idea; for instead of the active principle of the
juice residing in _fecula_, it is a peculiar proximate principle, _sui
generis_, to which I have ventured to bestow the name of _Elatin_. For
the same reason, much doubt and obscurity involve the meaning of the
word _Extract_, because it is applied _generally_ to any substance
obtained by the evaporation of a vegetable solution, and _specifically_
to a peculiar proximate principle, possessed of certain characters, by
which it is distinguished from every other elementary body."

A generic term is always liable to become thus limited to a single
species, or even individual, if people have occasion to think and speak
of that individual or species much oftener than of anything else which
is contained in the genus. Thus by cattle, a stage-coachman will
understand horses; beasts, in the language of agriculturists, stands for
oxen; and birds, with some sportsmen, for partridges only. The law of
language which operates in these trivial instances, is the very same in
conformity to which the terms Θεός, Deus, and God, were adopted from
Polytheism by Christianity, to express the single object of its own
adoration. Almost all the terminology of the Christian Church is made
up of words originally used in a much more general acceptation:
_Ecclesia_, Assembly; _Bishop_, Episcopus, Overseer; _Priest_,
Presbyter, Elder; _Deacon_, Diaconus, Administrator; _Sacrament_, a vow
of allegiance; _Evangelium_, good tidings; and some words, as
_Minister_, are still used both in the general and in the limited sense.
It would be interesting to trace the progress by which _author_ came, in
its most familiar sense, to signify a writer, and _ποίητης_, or maker, a

Of the incorporation into the meaning of a term, of circumstances
accidentally connected with it at some particular period, as in the case
of Pagan, instances might easily be multiplied. Physician (_φυσίκος_, or
naturalist) became, in England, synonymous with a healer of diseases,
because until a comparatively late period medical practitioners were the
only naturalists. _Clerc_, or clericus, a scholar, came to signify an
ecclesiastic, because the clergy were for many centuries the only

Of all ideas, however, the most liable to cling by association to
anything with which they have ever been connected by proximity, are
those of our pleasures and pains, or of the things which we habitually
contemplate as sources of our pleasures or pains. The additional
connotation, therefore, which a word soonest and most readily takes on,
is that of agreeableness or painfulness, in their various kinds and
degrees: of being a good or bad thing; desirable or to be avoided; an
object of hatred, of dread, contempt, admiration, hope, or love.
Accordingly there is hardly a single name, expressive of any moral or
social fact calculated to call forth strong affections either of a
favourable or of a hostile nature, which does not carry with it
decidedly and irresistibly a connotation of those strong affections, or,
at the least, of approbation or censure; insomuch that to employ those
names in conjunction with others by which the contrary sentiments were
expressed, would produce the effect of a paradox, or even a
contradiction in terms. The baneful influence of a connotation thus
acquired, on the prevailing habits of thought, especially in morals and
politics, has been well pointed out on many occasions by Bentham. It
gives rise to the fallacy of "question-begging names." The very property
which we are inquiring whether a thing possesses or not, has become so
associated with the name of the thing as to be part of its meaning,
insomuch that by merely uttering the name we assume the point which was
to be made out: one of the most frequent sources of apparently
self-evident propositions.

Without any further multiplication of examples to illustrate the changes
which usage is continually making in the signification of terms, I shall
add, as a practical rule, that the logician, not being able to prevent
such transformations, should submit to them with a good grace when they
are irrevocably effected, and if a definition is necessary, define the
word according to its new meaning; retaining the former as a second
signification, if it is needed, and if there is any chance of being able
to preserve it either in the language of philosophy or in common use.
Logicians cannot _make_ the meaning of any but scientific terms: that of
all other words is made by the collective human race. But logicians can
ascertain clearly what it is which, working obscurely, has guided the
general mind to a particular employment of a name; and when they have
found this, they can clothe it in such distinct and permanent terms,
that mankind shall see the meaning which before they only felt, and
shall not suffer it to be afterwards forgotten or misapprehended.



§ 1. We have, thus far, considered only one of the requisites of a
language adapted for the investigation of truth; that its terms shall
each of them convey a determinate and unmistakeable meaning. There are,
however, as we have already remarked, other requisites; some of them
important only in the second degree, but one which is fundamental, and
barely yields in point of importance, if it yields at all, to the
quality which we have already discussed at so much length. That the
language may be fitted for its purposes, not only should every word
perfectly express its meaning, but there should be no important meaning
without its word. Whatever we have occasion to think of often, and for
scientific purposes, ought to have a name appropriated to it.

This requisite of philosophical language may be considered under three
different heads; that number of separate conditions being involved in

§ 2. First: there ought to be all such names, as are needful for making
such a record of individual observations that the words of the record
shall exactly show what fact it is which has been observed. In other
words, there should be an accurate Descriptive Terminology.

The only things which we can observe directly being our own sensations,
or other feelings, a complete descriptive language would be one in which
there should be a name for every variety of elementary sensation or
feeling. Combinations of sensations or feelings may always be described,
if we have a name for each of the elementary feelings which compose
them; but brevity of description, and clearness (which often depends
very much on brevity,) are greatly promoted by giving distinctive names
not to the elements alone, but also to all combinations which are of
frequent recurrence. On this occasion I cannot do better than quote from
Dr. Whewell[17] some of the excellent remarks which he has made on this
important branch of our subject.

"The meaning of [descriptive] technical terms can be fixed in the first
instance only by convention, and can be made intelligible only by
presenting to the senses that which the terms are to signify. The
knowledge of a colour by its name can only be taught through the eye. No
description can convey to a hearer what we mean by _apple-green_ or
_French-grey_. It might, perhaps, be supposed that, in the first
example, the term _apple_, referring to so familiar an object,
sufficiently suggests the colour intended. But it may easily be seen
that this is not true; for apples are of many different hues of green,
and it is only by a conventional selection that we can appropriate the
term to one special shade. When this appropriation is once made, the
term refers to the sensation, and not to the parts of the term; for
these enter into the compound merely as a help to the memory, whether
the suggestion be a natural connexion as in 'apple-green,' or a casual
one as in 'French-grey.' In order to derive due advantage from technical
terms of this kind, they must be associated _immediately_ with the
perception to which they belong; and not connected with it through the
vague usages of common language. The memory must retain the sensation;
and the technical word must be understood as directly as the most
familiar word, and more distinctly. When we find such terms as
_tin-white_ or _pinchbeck-brown_, the metallic colour so denoted ought
to start up in our memory without delay or search.

"This, which it is most important to recollect with respect to the
simpler properties of bodies, as colour and form, is no less true with
respect to more compound notions. In all cases the term is fixed to a
peculiar meaning by convention; and the student, in order to use the
word, must be completely familiar with the convention, so that he has no
need to frame conjectures from the word itself. Such conjectures would
always be insecure, and often erroneous. Thus the term _papilionaceous_
applied to a flower is employed to indicate, not only a resemblance to a
butterfly, but a resemblance arising from five petals of a certain
peculiar shape and arrangement; and even if the resemblance were much
stronger than it is in such cases, yet, if it were produced in a
different way, as for example, by one petal, or two only, instead of a
'standard,' two 'wings,' and a 'keel' consisting of two parts more or
less united into one, we should be no longer justified in speaking of it
as a 'papilionaceous' flower."

When, however, the thing named is, as in this last case, a combination
of simple sensations, it is not necessary, in order to learn the meaning
of the word, that the student should refer back to the sensations
themselves; it may be communicated to him through the medium of other
words; the terms, in short, may be defined. But the names of elementary
sensations, or elementary feelings of any sort, cannot be defined; nor
is there any mode of making their signification known but by making the
learner experience the sensation, or referring him, through some known
mark, to his remembrance of having experienced it before. Hence it is
only the impressions on the outward senses, or those inward feelings
which are connected in a very obvious and uniform manner with outward
objects, that are really susceptible of an exact descriptive language.
The countless variety of sensations which arise, for instance, from
disease, or from peculiar physiological states, it would be in vain to
attempt to name; for as no one can judge whether the sensation I have is
the same with his, the name cannot have, to us two, real community of
meaning. The same may be said, to a considerable extent, of purely
mental feelings. But in some of the sciences which are conversant with
external objects, it is scarcely possible to surpass the perfection to
which this quality of a philosophical language has been carried.

"The formation[18] of an exact and extensive descriptive language for
botany has been executed with a degree of skill and felicity, which,
before it was attained, could hardly have been dreamt of as attainable.
Every part of a plant has been named; and the form of every part, even
the most minute, has had a large assemblage of descriptive terms
appropriated to it, by means of which the botanist can convey and
receive knowledge of form and structure, as exactly as if each minute
part were presented to him vastly magnified. This acquisition was part
of the Linnæan reform.... 'Tournefort,' says Decandolle, 'appears to
have been the first who really perceived the utility of fixing the sense
of terms in such a way as always to employ the same word in the same
sense, and always to express the same idea by the same words; but it was
Linnæus who really created and fixed this botanical language, and this
is his fairest claim to glory, for by this fixation of language he has
shed clearness and precision over all parts of the science.'

"It is not necessary here to give any detailed account of the terms of
botany. The fundamental ones have been gradually introduced, as the
parts of plants were more carefully and minutely examined. Thus the
flower was necessarily distinguished into the _calyx_, the _corolla_,
the _stamens_, and the _pistils_; the sections of the corolla were
termed _petals_ by Columna; those of the calyx were called _sepals_ by
Necker. Sometimes terms of greater generality were devised; as
_perianth_, to include the calyx and corolla, whether one or both of
these were present; _pericarp_, for the part enclosing the grain, of
whatever kind it be, fruit, nut, pod, &c. And it may easily be imagined,
that descriptive terms may, by definition and combination, become very
numerous and distinct. Thus leaves may be called _pinnatifid_,
_pinnatipartite_, _pinnatisect_, _pinnatilobate_, _palmatifid_,
_palmatipartite_, &c., and each of these words designates different
combinations of the modes and extent of the divisions of the leaf with
the divisions of its outline. In some cases, arbitrary numerical
relations are introduced into the definition: thus, a leaf is called
_bilobate_, when it is divided into two parts by a notch; but if the
notch go to the middle of its length, it is _bifid_; if it go near the
base of the leaf, it is _bipartite_; if to the base, it is _bisect_.
Thus, too, a pod of a cruciferous plant is a _siliqua_, if it is four
times as long as it is broad, but if it be shorter than this it is a
_silicula_. Such terms being established, the form of the very complex
leaf or frond of a fern (Hymenophyllum Wilsoni) is exactly conveyed by
the following phrase:--'fronds rigid pinnate, pinnæ recurved
subunilateral, pinnatifid, the segments linear undivided or bifid

"Other characters, as well as form, are conveyed with the like
precision: Colour by means of a classified scale of colours.... This was
done with most precision by Werner, and his scale of colours is still
the most usual standard of naturalists. Werner also introduced a more
exact terminology with regard to other characters which are important in
mineralogy, as lustre, hardness. But Mohs improved upon this step by
giving a numerical scale of hardness, in which talc is 1, gypsum 2, calc
spar 3, and so on.... Some properties, as specific gravity, by their
definition give at once a numerical measure; and others, as crystalline
form, require a very considerable array of mathematical calculation and
reasoning, to point out their relations and gradations."

§ 3. Thus far of Descriptive Terminology, or of the language requisite
for placing on record our observation of individual instances. But when
we proceed from this to Induction, or rather to that comparison of
observed instances which is the preparatory step towards it, we stand in
need of an additional and a different sort of general names.

Whenever, for purposes of Induction, we find it necessary to introduce
(in Dr. Whewell's phraseology) some new general conception; that is,
whenever the comparison of a set of phenomena leads to the recognition
in them of some common circumstance, which, our attention not having
been directed to it on any former occasion, is to us a new phenomenon;
it is of importance that this new conception, or this new result of
abstraction, should have a name appropriated to it; especially if the
circumstance it involves be one which leads to many consequences, or
which is likely to be found also in other classes of phenomena. No
doubt, in most cases of the kind, the meaning might be conveyed by
joining together several words already in use. But when a thing has to
be often spoken of, there are more reasons than the saving of time and
space, for speaking of it in the most concise manner possible. What
darkness would be spread over geometrical demonstrations, if wherever
the word _circle_ is used, the definition of a circle were inserted
instead of it. In mathematics and its applications, where the nature of
the processes demands that the attention should be strongly
concentrated, but does not require that it should be widely diffused,
the importance of concentration also in the expressions has always been
duly felt; and a mathematician no sooner finds that he shall often have
occasion to speak of the same two things together, than he at once
creates a term to express them whenever combined: just as, in his
algebraical operations, he substitutes for _(a^m + b^n) p/q_, or for
_a/b + b/c + c/d_ + &c., the single letter P, Q, or S; not solely to
shorten his symbolical expressions, but to simplify the purely
intellectual part of his operations, by enabling the mind to give its
exclusive attention to the relation between the quantity S and the other
quantities which enter into the equation, without being distracted by
thinking unnecessarily of the parts of which S is itself composed.

But there is another reason, in addition to that of promoting
perspicuity, for giving a brief and compact name to each of the more
considerable results of abstraction which are obtained in the course of
our intellectual phenomena. By naming them, we fix our attention upon
them; we keep them more constantly before the mind. The names are
remembered, and being remembered, suggest their definition; while if
instead of specific and characteristic names, the meaning had been
expressed by putting together a number of other names, that particular
combination of words already in common use for other purposes would have
had nothing to make itself remembered by. If we want to render a
particular combination of ideas permanent in the mind, there is nothing
which clenches it like a name specially devoted to express it. If
mathematicians had been obliged to speak of "that to which a quantity,
in increasing or diminishing, is always approaching nearer, so that the
difference becomes less than any assignable quantity, but to which it
never becomes exactly equal," instead of expressing all this by the
simple phrase, "the limit of a quantity," we should probably have long
remained without most of the important truths which have been discovered
by means of the relation between quantities of various kinds and their
limits. If instead of speaking of _momentum_, it had been necessary to
say, "the product of the number of units of velocity in the velocity by
the number of units of mass in the mass," many of the dynamical truths
now apprehended by means of this complex idea would probably have
escaped notice, for want of recalling the idea itself with sufficient
readiness and familiarity. And on subjects less remote from the topics
of popular discussion, whoever wishes to draw attention to some new or
unfamiliar distinction among things, will find no way so sure as to
invent or select suitable names for the express purpose of marking it.

A volume devoted to explaining what the writer means by civilization,
does not raise so vivid a conception of it as the single expression,
that Civilization is a different thing from Cultivation; the compactness
of that brief designation for the contrasted quality being an equivalent
for a long discussion. So, if we would impress forcibly upon the
understanding and memory the distinction between the two different
conceptions of a representative government, we cannot more effectually
do so than by saying that Delegation is not Representation. Hardly any
original thoughts on mental or social subjects ever make their way among
mankind, or assume their proper importance in the minds even of their
inventors, until aptly-selected words or phrases have, as it were,
nailed them down and held them fast.

§ 4. Of the three essential parts of a philosophical language, we have
now mentioned two: a terminology suited for describing with precision
the individual facts observed; and a name for every common property of
any importance or interest, which we detect by comparing those facts:
including (as the concretes corresponding to those abstract terms) names
for the classes which we artificially construct in virtue of those
properties, or as many of them, at least, as we have frequent occasion
to predicate anything of.

But there is a sort of classes, for the recognition of which no such
elaborate process is necessary; because each of them is marked out from
all others not by some one property, the detection of which may depend
on a difficult act of abstraction, but by its properties generally. I
mean, the Kinds of things, in the sense which, in this treatise, has
been specially attached to that term. By a Kind, it will be remembered,
we mean one of those classes which are distinguished from all others not
by one or a few definite properties, but by an unknown multitude of
them: the combination of properties on which the class is grounded,
being a mere index to an indefinite number of other distinctive
attributes. The class horse is a Kind, because the things which agree in
possessing the characters by which we recognise a horse, agree in a
great number of other properties, as we know, and, it cannot be doubted,
in many more than we know. Animal, again, is a Kind, because no
definition that could be given of the name animal could either exhaust
the properties common to all animals, or supply premises from which the
remainder of those properties could be inferred. But a combination of
properties which does not give evidence of the existence of any other
independent peculiarities, does not constitute a Kind. White horse,
therefore, is not a Kind; because horses which agree in whiteness, do
not agree in anything else, except the qualities common to all horses,
and whatever may be the causes or effects of that particular colour.

On the principle that there should be a name for everything which we
have frequent occasion to make assertions about, there ought evidently
to be a name for every Kind; for as it is the very meaning of a Kind
that the individuals composing it have an indefinite multitude of
properties in common, it follows that, if not with our present
knowledge, yet with that which we may hereafter acquire, the Kind is a
subject to which there will have to be applied many predicates. The
third component element of a philosophical language, therefore, is that
there shall be a name for every Kind. In other words, there must not
only be a terminology, but also a nomenclature.

The words Nomenclature and Terminology are employed by most authors
almost indiscriminately; Dr. Whewell being, as far as I am aware, the
first writer who has regularly assigned to the two words different
meanings. The distinction however which he has drawn between them being
real and important, his example is likely to be followed; and (as is apt
to be the case when such innovations in language are felicitously made)
a vague sense of the distinction is found to have influenced the
employment of the terms in common practice, before the expediency had
been pointed out of discriminating them philosophically. Every one would
say that the reform effected by Lavoisier and Guyton-Morveau in the
language of chemistry consisted in the introduction of a new
nomenclature, not of a new terminology. Linear, lanceolate, oval, or
oblong, serrated, dentate, or crenate leaves, are expressions forming
part of the terminology of botany, while the names "Viola odorata," and
"Ulex Europæus," belong to its nomenclature.

A nomenclature may be defined, the collection of the names of all the
Kinds with which any branch of knowledge is conversant; or more
properly, of all the lowest Kinds, or _infimæ species_--those which may
be subdivided indeed, but not into Kinds, and which generally accord
with what in natural history are termed simply species. Science
possesses two splendid examples of a systematic nomenclature; that of
plants and animals, constructed by Linnæus and his successors, and that
of chemistry, which we owe to the illustrious group of chemists who
flourished in France towards the close of the eighteenth century. In
these two departments, not only has every known species, or lowest Kind,
a name assigned to it, but when new lowest Kinds are discovered, names
are at once given to them on an uniform principle. In other sciences the
nomenclature is not at present constructed on any system, either because
the species to be named are not numerous enough to require one, (as in
geometry for example,) or because no one has yet suggested a suitable
principle for such a system, as in mineralogy; in which the want of a
scientifically constructed nomenclature is now the principal cause which
retards the progress of the science.

§ 5. A word which carries on its face that it belongs to a nomenclature,
seems at first sight to differ from other concrete general names in
this--that its meaning does not reside in its connotation, in the
attributes implied in it, but in its denotation, that is, in the
particular group of things which it is appointed to designate; and
cannot, therefore, be unfolded by means of a definition, but must be
made known in another way. This opinion, however, appears to me
erroneous. Words belonging to a nomenclature differ, I conceive, from
other words mainly in this, that besides the ordinary connotation, they
have a peculiar one of their own: besides connoting certain attributes,
they also connote that those attributes are distinctive of a Kind. The
term "peroxide of iron," for example, belonging by its form to the
systematic nomenclature of chemistry, bears on its face that it is the
name of a peculiar Kind of substance. It moreover connotes, like the
name of any other class, some portion of the properties common to the
class; in this instance the property of being a compound of iron and the
largest dose of oxygen with which iron will combine. These two things,
the fact of being such a compound, and the fact of being a Kind,
constitute the connotation of the name peroxide of iron. When we say of
the substance before us, that it is the peroxide of iron, we thereby
assert, first, that it is a compound of iron and a maximum of oxygen,
and next, that the substance so composed is a peculiar Kind of

Now, this second part of the connotation of any word belonging to a
nomenclature is as essential a portion of its meaning as the first part,
while the definition only declares the first: and hence the appearance
that the signification of such terms cannot be conveyed by a definition:
which appearance, however, is fallacious. The name Viola odorata denotes
a Kind, of which a certain number of characters, sufficient to
distinguish it, are enunciated in botanical works. This enumeration of
characters is surely, as in other cases, a definition of the name. No,
say some, it is not a definition, for the name Viola odorata does not
mean those characters; it means that particular group of plants, and the
characters are selected from among a much greater number, merely as
marks by which to recognise the group. But to this I reply, that the
name does not mean that group, for it would be applied to that group no
longer than while the group is believed to be an _infima species_; if it
were to be discovered that several distinct Kinds have been confounded
under this one name, no one would any longer apply the name Viola
odorata to the whole of the group, but would apply it, if retained at
all, to one only of the Kinds contained therein. What is imperative,
therefore, is not that the name shall denote one particular collection
of objects, but that it shall denote a Kind, and a lowest Kind. The form
of the name declares that, happen what will, it is to denote an _infima
species_; and that, therefore, the properties which it connotes, and
which are expressed in the definition, are to be connoted by it no
longer than while we continue to believe that those properties, when
found together, indicate a Kind, and that the whole of them are found in
no more than one Kind.

With the addition of this peculiar connotation, implied in the form of
every word which belongs to a systematic nomenclature; the set of
characters which is employed to discriminate each Kind from all other
Kinds (and which is a real definition) constitutes as completely as in
any other case the whole meaning of the term. It is no objection to say
that (as is often the case in natural history) the set of characters
may be changed, and another substituted as being better suited for the
purpose of distinction, while the word, still continuing to denote the
same group of things, is not considered to have changed its meaning. For
this is no more than may happen in the case of any other general name:
we may, in reforming its connotation, leave its denotation untouched;
and it is generally desirable to do so. The connotation, however, is not
the less for this the real meaning, for we at once apply the name
wherever the characters set down in the definition are found; and that
which exclusively guides us in applying the term, must constitute its
signification. If we find, contrary to our previous belief, that the
characters are not peculiar to one species, we cease to use the term
coextensively with the characters; but then it is because the other
portion of the connotation fails; the condition that the class must be a
Kind. The connotation, therefore, is still the meaning; the set of
descriptive characters is a true definition; and the meaning is
unfolded, not indeed (as in other cases) by the definition alone, but by
the definition and the form of the word taken together.

§ 6. We have now analysed what is implied in the two principal
requisites of a philosophical language; first, precision, or
definiteness, and secondly, completeness. Any further remarks on the
mode of constructing a nomenclature must be deferred until we treat of
Classification; the mode of naming the Kinds of things being necessarily
subordinate to the mode of arranging those Kinds into larger classes.
With respect to the minor requisites of terminology, some of them are
well stated and illustrated in the "Aphorisms concerning the Language of
Science," included in Dr. Whewell's _Philosophy of the Inductive
Sciences_. These, as being of secondary importance in the peculiar point
of view of Logic, I shall not further refer to, but shall confine my
observations to one more quality, which, next to the two already treated
of, appears to be the most valuable which the language of science can
possess. Of this quality a general notion may be conveyed by the
following aphorism:

Whenever the nature of the subject permits our reasoning processes to
be, without danger, carried on mechanically, the language should be
constructed on as mechanical principles as possible; while in the
contrary case, it should be so constructed that there shall be the
greatest possible obstacles to a merely mechanical use of it.

I am aware that this maxim requires much explanation, which I shall at
once proceed to give. And first, as to what is meant by using a language
mechanically. The complete or extreme case of the mechanical use of
language, is when it is used without any consciousness of a meaning, and
with only the consciousness of using certain visible or audible marks in
conformity to technical rules previously laid down. This extreme case is
nowhere realized except in the figures of arithmetic and the symbols of
algebra, a language unique in its kind, and approaching as nearly to
perfection, for the purposes to which it is destined, as can, perhaps,
be said of any creation of the human mind. Its perfection consists in
the completeness of its adaptation to a purely mechanical use. The
symbols are mere counters, without even the semblance of a meaning apart
from the convention which is renewed each time they are employed, and
which is altered at each renewal, the same symbol _a_ or _x_ being used
on different occasions to represent things which (except that, like all
things, they are susceptible of being numbered) have no property in
common. There is nothing, therefore, to distract the mind from the set
of mechanical operations which are to be performed upon the symbols,
such as squaring both sides of the equation, multiplying or dividing
them by the same or by equivalent symbols, and so forth. Each of these
operations, it is true, corresponds to a syllogism; represents one step
of a ratiocination relating not to the symbols, but to the things
signified by them. But as it has been found practicable to frame a
technical form, by conforming to which we can make sure of finding the
conclusion of the ratiocination, our end can be completely attained
without our ever thinking of anything but the symbols. Being thus
intended to work merely as mechanism, they have the qualities which
mechanism ought to have. They are of the least possible bulk, so that
they take up scarcely any room, and waste no time in their manipulation;
they are compact, and fit so closely together that the eye can take in
the whole at once of almost every operation which they are employed to

These admirable properties of the symbolical language of mathematics
have made so strong an impression on the minds of many thinkers, as to
have led them to consider the symbolical language in question as the
ideal type of philosophical language generally; to think that names in
general, or (as they are fond of calling them) signs, are fitted for the
purposes of thought in proportion as they can be made to approximate to
the compactness, the entire unmeaningness, and the capability of being
used as counters without a thought of what they represent, which are
characteristic of the _a_ and _b_, the _x_ and _y_, of algebra. This
notion has led to sanguine views of the acceleration of the progress of
science by means which, I conceive, cannot possibly conduce to that end,
and forms part of that exaggerated estimate of the influence of signs,
which has contributed in no small degree to prevent the real laws of our
intellectual operations from being rightly understood.

In the first place, a set of signs by which we reason without
consciousness of their meaning, can be serviceable, at most, only in our
deductive operations. In our direct inductions we cannot for a moment
dispense with a distinct mental image of the phenomena, since the whole
operation turns on a perception of the particulars in which those
phenomena agree and differ. But, further, this reasoning by counters is
only suitable to a very limited portion even of our deductive processes.
In our reasonings respecting numbers, the only general principles which
we ever have occasion to introduce, are these, Things which are equal to
the same thing are equal to one another, and The sums or differences of
equal things are equal, with their various corollaries. Not only can no
hesitation ever arise respecting the applicability of these principles,
since they are true of all magnitudes whatever; but every possible
application of which they are susceptible, may be reduced to a
technical rule; and such, in fact, the rules of the calculus are. But if
the symbols represent any other things than mere numbers, let us say
even straight or curve lines, we have then to apply theorems of geometry
not true of all lines without exception, and to select those which are
true of the lines we are reasoning about. And how can we do this unless
we keep completely in mind what particular lines these are? Since
additional geometrical truths may be introduced into the ratiocination
in any stage of its progress, we cannot suffer ourselves, during even
the smallest part of it, to use the names mechanically (as we use
algebraical symbols) without an image annexed to them. It is only after
ascertaining that the solution of a question concerning lines can be
made to depend on a previous question concerning numbers, or in other
words after the question has been (to speak technically) reduced to an
equation, that the unmeaning signs become available, and that the nature
of the facts themselves to which the investigation relates can be
dismissed from the mind. Up to the establishment of the equation, the
language in which mathematicians carry on their reasoning does not
differ in character from that employed by close reasoners on any other
kind of subject.

I do not deny that every correct ratiocination, when thrown into the
syllogistic shape, is conclusive from the mere form of the expression,
provided none of the terms used be ambiguous; and this is one of the
circumstances which have led some writers to think that if all names
were so judiciously constructed and so carefully defined as not to admit
of any ambiguity, the improvement thus made in language would not only
give to the conclusions of every deductive science the same certainty
with those of mathematics, but would reduce all reasonings to the
application of a technical form, and enable their conclusiveness to be
rationally assented to after a merely mechanical process, as is
undoubtedly the case in algebra. But, if we except geometry, the
conclusions of which are already as certain and exact as they can be
made, there is no science but that of number, in which the practical
validity of a reasoning can be apparent to any person who has looked
only at the form of the process. Whoever has assented to what was said
in the last Book concerning the case of the Composition of Causes, and
the still stronger case of the entire supersession of one set of laws by
another, is aware that geometry and algebra are the only sciences of
which the propositions are categorically true: the general propositions
of all other sciences are true only hypothetically, supposing that no
counteracting cause happens to interfere. A conclusion, therefore,
however correctly deduced, in point of form, from admitted laws of
nature, will have no other than an hypothetical certainty. At every step
we must assure ourselves that no other law of nature has superseded, or
intermingled its operation with, those which are the premises of the
reasoning; and how can this be done by merely looking at the words? We
must not only be constantly thinking of the phenomena themselves, but we
must be constantly studying them; making ourselves acquainted with the
peculiarities of every case to which we attempt to apply our general

The algebraic notation, considered as a philosophical language, is
perfect in its adaptation to the subjects for which it is commonly
employed, namely those of which the investigations have already been
reduced to the ascertainment of a relation between numbers. But,
admirable as it is for its own purpose, the properties by which it is
rendered such are so far from constituting it the ideal model of
philosophical language in general, that the more nearly the language of
any other branch of science approaches to it, the less fit that language
is for its own proper functions. On all other subjects, instead of
contrivances to prevent our attention from being distracted by thinking
of the meaning of our signs, we ought to wish for contrivances to make
it impossible that we should ever lose sight of that meaning even for an

With this view, as much meaning as possible should be thrown into the
formation of the word itself; the aids of derivation and analogy being
made available to keep alive a consciousness of all that is signified
by it. In this respect those languages have an immense advantage which
form their compounds and derivatives from native roots, like the German,
and not from those of a foreign or dead language, as is so much the case
with English, French, and Italian: and the best are those which form
them according to fixed analogies, corresponding to the relations
between the ideas to be expressed. All languages do this more or less,
but especially, among modern European languages, the German; while even
that is inferior to the Greek, in which the relation between the meaning
of a derivative word and that of its primitive is in general clearly
marked by its mode of formation; except in the case of words compounded
with prepositions, which are often, in both those languages, extremely

But all that can be done, by the mode of constructing words, to prevent
them from degenerating into sounds passing through the mind without any
distinct apprehension of what they signify, is far too little for the
necessity of the case. Words, however well constructed originally, are
always tending, like coins, to have their inscription worn off by
passing from hand to hand; and the only possible mode of reviving it is
to be ever stamping it afresh, by living in the habitual contemplation
of the phenomena themselves, and not resting in our familiarity with the
words that express them. If any one, having possessed himself of the
laws of phenomena as recorded in words, whether delivered to him
originally by others, or even found out by himself, is content from
thenceforth to live among these formulæ, to think exclusively of them,
and of applying them to cases as they arise, without keeping up his
acquaintance with the realities from which these laws were
collected--not only will he continually fail in his practical efforts,
because he will apply his formulæ without duly considering whether, in
this case and in that, other laws of nature do not modify or supersede
them; but the formulæ themselves will progressively lose their meaning
to him, and he will cease at last even to be capable of recognising with
certainty whether a case falls within the contemplation of his formula
or not. It is, in short, as necessary, on all subjects not mathematical,
that the things on which we reason should be conceived by us in the
concrete, and "clothed in circumstances," as it is in algebra that we
should keep all individualizing peculiarities sedulously out of view.

With this remark we close our observations on the Philosophy of



§ 1. There is, as has been frequently remarked in this work, a
classification of things, which is inseparable from the fact of giving
them general names. Every name which connotes an attribute, divides, by
that very fact, all things whatever into two classes, those which have
the attribute and those which have it not; those of which the name can
be predicated, and those of which it cannot. And the division thus made
is not merely a division of such things as actually exist, or are known
to exist, but of all such as may hereafter be discovered, and even of
all which can be imagined.

On this kind of Classification we have nothing to add to what has
previously been said. The Classification which requires to be discussed
as a separate act of the mind, is altogether different. In the one, the
arrangement of objects in groups, and distribution of them into
compartments, is a mere incidental effect consequent on the use of names
given for another purpose, namely that of simply expressing some of
their qualities. In the other the arrangement and distribution are the
main object, and the naming is secondary to, and purposely conforms
itself to, instead of governing, that more important operation.

Classification, thus regarded, is a contrivance for the best possible
ordering of the ideas of objects in our minds; for causing the ideas to
accompany or succeed one another in such a way as shall give us the
greatest command over our knowledge already acquired, and lead most
directly to the acquisition of more. The general problem of
Classification, in reference to these purposes, may be stated as
follows: To provide that things shall be thought of in such groups, and
those groups in such an order, as will best conduce to the remembrance
and to the ascertainment of their laws.

Classification thus considered, differs from classification in the wider
sense, in having reference to real objects exclusively, and not to all
that are imaginable: its object being the due co-ordination in our minds
of those things only, with the properties of which we have actually
occasion to make ourselves acquainted. But, on the other hand, it
embraces _all_ really existing objects. We cannot constitute any one
class properly, except in reference to a general division of the whole
of nature; we cannot determine the group in which any one object can
most conveniently be placed, without taking into consideration all the
varieties of existing objects, all at least which have any degree of
affinity with it. No one family of plants or animals could have been
rationally constituted, except as part of a systematic arrangement of
all plants or animals; nor could such a general arrangement have been
properly made, without first determining the exact place of plants and
animals in a general division of nature.

§ 2. There is no property of objects which may not be taken, if we
please, as the foundation for a classification or mental grouping of
those objects; and in our first attempts we are likely to select for
that purpose properties which are simple, easily conceived, and
perceptible on a first view, without any previous process of thought.
Thus Tournefort's arrangement of plants was founded on the shape and
divisions of the corolla; and that which is commonly called the Linnæan
(though Linnæus also suggested another and more scientific arrangement)
was grounded chiefly on the number of the stamens and pistils.

But these classifications, which are at first recommended by the
facility they afford of ascertaining to what class any individual
belongs, are seldom much adapted to the ends of that Classification
which is the subject of our present remarks. The Linnæan arrangement
answers the purpose of making us think together of all those kinds of
plants which possess the same number of stamens and pistils; but to
think of them in that manner is of little use, since we seldom have
anything to affirm in common of the plants which have a given number of
stamens and pistils. If plants of the class Pentandria, order Monogynia,
agreed in any other properties, the habit of thinking and speaking of
the plants under a common designation would conduce to our remembering
those common properties so far as they were ascertained, and would
dispose us to be on the look-out for such of them as were not yet known.
But since this is not the case, the only purpose of thought which the
Linnæan classification serves is that of causing us to remember, better
than we should otherwise have done, the exact number of stamens and
pistils of every species of plants. Now, as this property is of little
importance or interest, the remembering it with any particular accuracy
is of no moment. And, inasmuch as, by habitually thinking of plants in
those groups, we are prevented from habitually thinking of them in
groups which have a greater number of properties in common, the effect
of such a classification, when systematically adhered to, upon our
habits of thought, must be regarded as mischievous.

The ends of scientific classification are best answered, when the
objects are formed into groups respecting which a greater number of
general propositions can be made, and those propositions more important,
than could be made respecting any other groups into which the same
things could be distributed. The properties, therefore, according to
which objects are classified, should, if possible, be those which are
causes of many other properties: or at any rate, which are sure marks of
them. Causes are preferable, both as being the surest and most direct of
marks, and as being themselves the properties on which it is of most use
that our attention should be strongly fixed. But the property which is
the cause of the chief peculiarities of a class, is unfortunately seldom
fitted to serve also as the diagnostic of the class. Instead of the
cause, we must generally select some of its more prominent effects,
which may serve as marks of the other effects and of the cause.

A classification thus formed is properly scientific or philosophical,
and is commonly called a Natural, in contradistinction to a Technical
or Artificial, classification or arrangement. The phrase Natural
Classification seems most peculiarly appropriate to such arrangements as
correspond, in the groups which they form, to the spontaneous tendencies
of the mind, by placing together the objects most similar in their
general aspect: in opposition to those technical systems which,
arranging things according to their agreement in some circumstance
arbitrarily selected, often throw into the same group objects which in
the general aggregate of their properties present no resemblance, and
into different and remote groups, others which have the closest
similarity. It is one of the most valid recommendations of any
classification to the character of a scientific one, that it shall be a
natural classification in this sense also; for the test of its
scientific character is the number and importance of the properties
which can be asserted in common of all objects included in a group; and
properties on which the general aspect of the things depends, are, if
only on that ground, important, as well as, in most cases, numerous.
But, though a strong recommendation, this circumstance is not a _sine
quâ non_; since the most obvious properties of things may be of trifling
importance compared with others that are not obvious. I have seen it
mentioned as a great absurdity in the Linnæan classification, that it
places (which by the way it does not) the violet by the side of the oak:
it certainly dissevers natural affinities, and brings together things
quite as unlike as the oak and the violet are. But the difference,
apparently so wide, which renders the juxtaposition of those two
vegetables so suitable an illustration of a bad arrangement, depends, to
the common eye, mainly on mere size and texture; now if we made it our
study to adopt the classification which would involve the least peril of
similar _rapprochements_, we should return to the obsolete division into
trees, shrubs, and herbs, which though of primary importance with regard
to more general aspect, yet (compared even with so petty and unobvious a
distinction as that into dicotyledons and monocotyledons) answers to so
few differences in the other properties of plants, that a classification
founded on it (independently of the indistinctness of the lines of
demarcation) would be as completely artificial and technical as the

Our natural groups, therefore, must often be founded not on the obvious,
but on the unobvious properties of things, when these are of greater
importance. But in such cases it is essential that there should be some
other property or set of properties, more readily recognisable by the
observer, which coexist with, and may be received as marks of, the
properties which are the real groundwork of the classification. A
natural arrangement, for example, of animals, must be founded in the
main on their internal structure, but (as has been justly remarked) it
would be absurd that we should not be able to determine the genus and
species of an animal without first killing it. On this ground, the
preference, among zoological classifications, is probably due to that of
M. de Blainville, founded on the differences in the external
integuments; differences which correspond, much more accurately than
might be supposed, to the really important varieties, both in the other
parts of the structure, and in the habits and history of the animals.

This shows, more strongly than ever, how extensive a knowledge of the
properties of objects is necessary for making a good classification of
them. And as it is one of the uses of such a classification that by
drawing attention to the properties on which it is founded, and which if
the classification be good are marks of many others, it facilitates the
discovery of those others; we see in what manner our knowledge of
things, and our classification of them, tend mutually and indefinitely
to the improvement of each other.

We said just now that the classification of objects should follow those
of their properties which indicate not only the most numerous, but also
the most important peculiarities. What is here meant by importance? It
has reference to the particular end in view; and the same objects,
therefore, may admit with propriety of several different
classifications. Each science or art forms its classification of things
according to the properties which fall within its special cognizance, or
of which it must take account in order to accomplish its peculiar
practical end. A farmer does not divide plants, like a botanist, into
dicotyledonous and monocotyledonous, but into useful plants and weeds. A
geologist divides fossils, not like a zoologist, into families
corresponding to those of living species, but into fossils of the
secondary and of the tertiary periods, above the coal and below the
coal, &c. Whales are or are not fish, according to the purpose for which
we are considering them. "If we are speaking of the internal structure
and physiology of the animal, we must not call them fish; for in these
respects they deviate widely from fishes: they have warm blood, and
produce and suckle their young as land quadrupeds do. But this would not
prevent our speaking of the _whale fishery_, and calling such animals
_fish_ on all occasions connected with this employment; for the
relations thus rising depend upon the animal's living in the water, and
being caught in a manner similar to other fishes. A plea that human laws
which mention fish do not apply to whales, would be rejected at once by
an intelligent judge."[19]

These different classifications are all good, for the purposes of their
own particular departments of knowledge or practice. But when we are
studying objects not for any special practical end, but for the sake of
extending our knowledge of the whole of their properties and relations,
we must consider as the most important attributes, those which
contribute most, either by themselves or by their effects, to render the
things like one another, and unlike other things; which give to the
class composed of them the most marked individuality; which fill, as it
were, the largest space in their existence, and would most impress the
attention of a spectator who knew all their properties but was not
specially interested in any. Classes formed on this principle may be
called, in a more emphatic manner than any others, natural groups.

§ 3. On the subject of these groups Dr. Whewell lays down a theory,
grounded on an important truth, which he has, in some respects,
expressed and illustrated very felicitously; but also, as it appears to
me, with some admixture of error. It will be advantageous, for both
these reasons, to extract the statement of his doctrine in the very
words he has used.

"Natural groups," according to this theory,[20] are "given by Type, not
by Definition." And this consideration accounts for that "indefiniteness
and indecision which we frequently find in the descriptions of such
groups, and which must appear so strange and inconsistent to any one who
does not suppose these descriptions to assume any deeper ground of
connexion than an arbitrary choice of the botanist. Thus in the family
of the rose-tree, we are told that the _ovules_ are _very rarely_ erect,
the _stigmata usually_ simple. Of what use, it might be asked, can such
loose accounts be? To which the answer is, that they are not inserted in
order to distinguish the species, but in order to describe the family,
and the total relations of the ovules and the stigmata of the family are
better known by this general statement. A similar observation may be
made with regard to the Anomalies of each group, which occur so
commonly, that Mr. Lindley, in his _Introduction to the Natural System
of Botany_, makes the 'Anomalies' an article in each family. Thus, part
of the character of the Rosaceæ is, that they have alternate _stipulate_
leaves, and that the _albumen_ is _obliterated_; but yet in _Lowea_, one
of the genera of this family, the stipulæ are _absent_; and the albumen
is _present_ in another, _Neillia_. This implies, as we have already
seen, that the artificial character (or _diagnosis_, as Mr. Lindley
calls it,) is imperfect. It is, though very nearly, yet not exactly,
commensurate with the natural group: and hence in certain cases this
character is made to yield to the general weight of natural affinities.

"These views,--of classes determined by characters which cannot be
expressed in words,--of propositions which state, not what happens in
all cases, but only usually,--of particulars which are included in a
class, though they transgress the definition of it, may probably
surprise the reader. They are so contrary to many of the received
opinions respecting the use of definitions, and the nature of scientific
propositions, that they will probably appear to many persons highly
illogical and unphilosophical. But a disposition to such a judgment
arises in a great measure from this, that the mathematical and
mathematico-physical sciences have, in a great degree, determined men's
views of the general nature and form of scientific truth; while Natural
History has not yet had time or opportunity to exert its due influence
upon the current habits of philosophizing. The apparent indefiniteness
and inconsistency of the classifications and definitions of Natural
History belongs, in a far higher degree, to all other except
mathematical speculations; and the modes in which approximations to
exact distinctions and general truths have been made in Natural History,
may be worthy our attention, even for the light they throw upon the best
modes of pursuing truth of all kinds.

"Though in a Natural group of objects a definition can no longer be of
any use as a regulative principle, classes are not therefore left quite
loose, without any certain standard or guide. The class is steadily
fixed, though not precisely limited; it is given, though not
circumscribed; it is determined, not by a boundary line without, but by
a central point within; not by what it strictly excludes, but by what it
eminently includes; by an example, not by a precept; in short, instead
of a Definition we have a Type for our director.

"A Type is an example of any class, for instance a species of a genus,
which is considered as eminently possessing the character of the class.
All the species which have a greater affinity with this type-species
than with any others, form the genus, and are arranged about it,
deviating from it in various directions and different degrees. Thus a
genus may consist of several species which approach very near the type,
and of which the claim to a place with it is obvious; while there may be
other species which straggle further from this central knot, and which
yet are clearly more connected with it than with any other. And even if
there should be some species of which the place is dubious, and which
appear to be equally bound to two generic types, it is easily seen that
this would not destroy the reality of the generic groups, any more than
the scattered trees of the intervening plain prevent our speaking
intelligibly of the distinct forests of two separate hills.

"The type-species of every genus, the type-genus of every family, is,
then, one which possesses all the characters and properties of the genus
in a marked and prominent manner. The type of the Rose family has
alternate stipulate leaves, wants the albumen, has the ovules not erect,
has the stigmata simple, and besides these features, which distinguish
it from the exceptions or varieties of its class, it has the features
which make it prominent in its class. It is one of those which possess
clearly several leading attributes; and thus, though we cannot say of
any one genus that it _must_ be the type of the family, or of any one
species that it _must_ be the type of the genus, we are still not wholly
to seek; the type must be connected by many affinities with most of the
others of its group; it must be near the centre of the crowd, and not
one of the stragglers."

In this passage (the latter part of which especially I cannot help
noticing as an admirable example of philosophic style) Dr. Whewell has
stated very clearly and forcibly, but (I think) without making all
necessary distinctions, one of the principles of a Natural
Classification. What this principle is, what are its limits, and in what
manner he seems to me to have overstepped them, will appear when we have
laid down another rule of Natural Arrangement, which appears to me still
more fundamental.

§ 4. The reader is by this time familiar with the general truth (which I
restate so often on account of the great confusion in which it is
commonly involved), that there are in nature distinctions of Kind;
distinctions not consisting in a given number of definite properties,
_plus_ the effects which follow from those properties, but running
through the whole nature, through the attributes generally, of the
things so distinguished. Our knowledge of the properties of a Kind is
never complete. We are always discovering, and expecting to discover,
new ones. Where the distinction between two classes of things is not one
of Kind, we expect to find their properties alike, except where there is
some reason for their being different. On the contrary, when the
distinction is in Kind, we expect to find the properties different
unless there be some cause for their being the same. All knowledge of a
Kind must be obtained by observation and experiment upon the Kind
itself; no inference respecting its properties from the properties of
things not connected with it by Kind, goes for more than the sort of
presumption usually characterized as an analogy, and generally in one of
its fainter degrees.

Since the common properties of a true Kind, and consequently the general
assertions which can be made respecting it, or which are certain to be
made hereafter as our knowledge extends, are indefinite and
inexhaustible; and since the very first principle of natural
classification is that of forming the classes so that the objects
composing each may have the greatest number of properties in common;
this principle prescribes that every such classification shall recognise
and adopt into itself all distinctions of Kind, which exist among the
objects it professes to classify. To pass over any distinctions of Kind,
and substitute definite distinctions, which, however considerable they
may be, do not point to ulterior unknown differences, would be to
replace classes with more by classes with fewer attributes in common;
and would be subversive of the Natural Method of Classification.

Accordingly all natural arrangements, whether the reality of the
distinction of Kinds was felt or not by their framers, have been led, by
the mere pursuit of their own proper end, to conform themselves to the
distinctions of Kind, so far as these had been ascertained at the time.
The Species of Plants are not only real Kinds, but are probably,[21]
all of them, real lowest Kinds, Infimæ Species; which if we were to
subdivide, as of course it is open to us to do, into subclasses, the
subdivision would necessarily be founded on _definite_ distinctions, not
pointing (apart from what may be known of their causes or effects) to
any difference beyond themselves.

In so far as a natural classification is grounded on real Kinds, its
groups are certainly not conventional; it is perfectly true that they do
not depend upon an arbitrary choice of the naturalist. But it does not
follow, nor, I conceive, is it true, that these classes are determined
by a type, and not by characters. To determine them by a type would be
as sure a way of missing the Kind, as if we were to select a set of
characters arbitrarily. They are determined by characters, but these are
not arbitrary. The problem is, to find a few definite characters which
point to the multitude of indefinite ones. Kinds are Classes between
which there is an impassable barrier; and what we have to seek is, marks
whereby we may determine on which side of the barrier an object takes
its place. The characters which will best do this should be chosen: if
they are also important in themselves, so much the better. When we have
selected the characters, we parcel out the objects according to those
characters, and not, I conceive, according to resemblance to a type. We
do not compose the species Ranunculus acris, of all plants which bear a
satisfactory degree of resemblance to a model-buttercup, but of those
which possess certain characters selected as marks by which we might
recognise the possibility of a common parentage; and the enumeration of
those characters is the definition of the species.

The question next arises, whether, as all Kinds must have a place among
the classes, so all the classes in a natural arrangement must be Kinds?
And to this I answer, certainly not. The distinctions of Kinds are not
numerous enough to make up the whole of a classification. Very few of
the genera of plants, or even of the families, can be pronounced with
certainty to be Kinds. The great distinctions of Vascular and Cellular,
Dicotyledonous or Exogenous and Monocotyledonous or Endogenous plants,
are perhaps differences of Kind; the lines of demarcation which divide
those classes seem (though even on this I would not pronounce
positively) to go through the whole nature of the plants. But the
different species of a genus, or genera of a family, usually have in
common only a limited number of characters. A Rose does not seem to
differ from a Rubus, or the Umbelliferæ from the Ranunculaceæ, in much
else than the characters botanically assigned to those genera or those
families. Unenumerated differences certainly do exist in some cases;
there are families of plants which have peculiarities of chemical
composition, or yield products having peculiar effects on the animal
economy. The Cruciferæ and Fungi contain an unusual proportion of
nitrogen; the Labiatæ are the chief sources of essential oils, the
Solaneæ are very commonly narcotic, &c. In these and similar cases there
are possibly distinctions of Kind; but it is by no means indispensable
that there should be. Genera and Families may be eminently natural,
though marked out from one another by properties limited in number;
provided those properties are important, and the objects contained in
each genus or family resemble each other more than they resemble
anything which is excluded from the genus or family.

After the recognition and definition, then, of the _infimæ species_, the
next step is to arrange those _infimæ species_ into larger groups:
making these groups correspond to Kinds wherever it is possible, but in
most cases without any such guidance. And in doing this it is true that
we are naturally and properly guided, in most cases at least, by
resemblance to a type. We form our groups round certain selected Kinds,
each of which serves as a sort of exemplar of its group. But though the
groups are suggested by types, I cannot think that a group when formed
is _determined_ by the type; that in deciding whether a species belongs
to the group, a reference is made to the type, and not to the
characters; that the characters "cannot be expressed in words." This
assertion is inconsistent with Dr. Whewell's own statement of the
fundamental principle of classification, namely, that "general
assertions shall be possible." If the class did not possess any
characters in common, what general assertions would be possible
respecting it? Except that they all resemble each other more than they
resemble anything else, nothing whatever could be predicated of the

The truth is, on the contrary, that every genus or family is framed with
distinct reference to certain characters, and is composed, first and
principally, of species which agree in possessing all those characters.
To these are added, as a sort of appendix, such other species, generally
in small number, as possess _nearly_ all the properties selected;
wanting some of them one property, some another, and which, while they
agree with the rest _almost_ as much as these agree with one another, do
not resemble in an equal degree any other group. Our conception of the
class continues to be grounded on the characters; and the class might be
defined, those things which _either_ possess that set of characters,
_or_ resemble the things that do so, more than they resemble anything

And this resemblance itself is not, like resemblance between simple
sensations, an ultimate fact, unsusceptible of analysis. Even the
inferior degree of resemblance is created by the possession of common
characters. Whatever resembles the genus Rose more than it resembles any
other genus, does so because it possesses a greater number of the
characters of that genus, than of the characters of any other genus. Nor
can there be any real difficulty in representing, by an enumeration of
characters, the nature and degree of the resemblance which is strictly
sufficient to include any object in the class. There are always some
properties common to all things which are included. Others there often
are, to which some things, which are nevertheless included, are
exceptions. But the objects which are exceptions to one character are
not exceptions to another: the resemblance which fails in some
particulars must be made up for in others. The class, therefore, is
constituted by the possession of _all_ the characters which are
universal, and _most_ of those which admit of exceptions. If a plant had
the ovules erect, the stigmata divided, possessed the albumen, and was
without stipules, it possibly would not be classed among the Rosaceæ.
But it may want any one, or more than one of those characters, and not
be excluded. The ends of a scientific classification are better answered
by including it. Since it agrees so nearly, in its known properties,
with the sum of the characters of the class, it is likely to resemble
that class more than any other in those of its properties which are
still undiscovered.

Not only, therefore, are natural groups, no less than any artificial
classes, determined by characters; they are constituted in contemplation
of, and by reason of, characters. But it is in contemplation not of
those characters only which are rigorously common to all the objects
included in the group, but of the entire body of characters, all of
which are found in most of those objects, and most of them in all. And
hence our conception of the class, the image in our minds which is
representative of it, is that of a specimen complete in all the
characters; most naturally a specimen which, by possessing them all in
the greatest degree in which they are ever found, is the best fitted to
exhibit clearly, and in a marked manner, what they are. It is by a
mental reference to this standard, not instead of, but in illustration
of, the definition of the class, that we usually and advantageously
determine whether any individual or species belongs to the class or not.
And this, as it seems to me, is the amount of truth contained in the
doctrine of Types.

We shall see presently that where the classification is made for the
express purpose of a special inductive inquiry, it is not optional, but
necessary for fulfilling the conditions of a correct Inductive Method,
that we should establish a type-species or genus, namely, the one which
exhibits in the most eminent degree the particular phenomenon under
investigation. But of this hereafter. It remains, for completing the
theory of natural groups, that a few words should be said on the
principles of the nomenclature adapted to them.

§ 5. A Nomenclature in science, is, as we have said, a system of the
names of Kinds. These names, like other class-names, are defined by the
enumeration of the characters distinctive of the class. The only merit
which a set of names can have beyond this, is to convey, by the mode of
their construction, as much information as possible: so that a person
who knows the thing, may receive all the assistance which the name can
give in remembering what he knows, while he who knows it not, may
receive as much knowledge respecting it as the case admits of, by merely
being told its name.

There are two modes of giving to the name of a Kind this sort of
significance. The best, but which unfortunately is seldom practicable,
is when the word can be made to indicate, by its formation, the very
properties which it is designed to connote. The name of a Kind does not,
of course, connote all the properties of the Kind, since these are
inexhaustible, but such of them as are sufficient to distinguish it;
such as are sure marks of all the rest. Now, it is very rarely that one
property, or even any two or three properties, can answer this purpose.
To distinguish the common daisy from all other species of plants would
require the specification of many characters. And a name cannot, without
being too cumbrous for use, give indication, by its etymology or mode of
construction, of more than a very small number of these. The
possibility, therefore, of an ideally perfect Nomenclature, is probably
confined to the one case in which we are happily in possession of
something nearly approaching to it; the Nomenclature of elementary
Chemistry. The substances, whether simple or compound, with which
chemistry is conversant, are Kinds, and, as such, the properties which
distinguish each of them from the rest are innumerable; but in the case
of compound substances (the simple ones are not numerous enough to
require a systematic nomenclature), there is one property, the chemical
composition, which is of itself sufficient to distinguish the Kind; and
is (with certain reservations not yet thoroughly understood) a sure mark
of all the other properties of the compound. All that was needful,
therefore, was to make the name of every compound express, on the first
hearing, its chemical composition; that is, to form the name of the
compound, in some uniform manner, from the names of the simple
substances which enter into it as elements. This was done, most
skilfully and successfully, by the French chemists. The only thing left
unexpressed by them was the exact proportion in which the elements were
combined; and even this, since the establishment of the atomic theory,
it has been found possible to express by a simple adaptation of their

But where the characters which must be taken into consideration in order
sufficiently to designate the Kind, are too numerous to be all signified
in the derivation of the name, and where no one of them is of such
preponderant importance as to justify its being singled out to be so
indicated, we may avail ourselves of a subsidiary resource. Though we
cannot indicate the distinctive properties of the Kind, we may indicate
its nearest natural affinities, by incorporating into its name the name
of the proximate natural group of which it is one of the species. On
this principle is founded the admirable binary nomenclature of botany
and zoology. In this nomenclature the name of every species consists of
the name of the genus, or natural group next above it, with a word added
to distinguish the particular species. The last portion of the compound
name is sometimes taken from some _one_ of the peculiarities in which
that species differs from others of the genus; as Clematis
_integrifolia_, Potentilla _alba_, Viola _palustris_, Artemisia
_vulgaris_; sometimes from a circumstance of an historical nature, as
Narcissus _poeticus_, Potentilla _tormentilla_ (indicating that the
plant was formerly known by the latter name), Exacum _Candollii_ (from
the fact that De Candolle was its first discoverer); and sometimes the
word is purely conventional, as Thlaspi _bursa-pastoris_, Ranunculus
_thora_; it is of little consequence which; since the second, or as it
is usually called, the specific name, could at most express,
independently of convention, no more than a very small portion of the
connotation of the term. But by adding to this the name of the superior
genus, we may make the best amends we can for the impossibility of so
contriving the name as to express all the distinctive characters of the
Kind. We make it, at all events, express as many of those characters as
are common to the proximate natural group in which the Kind is included.
If even those common characters are so numerous or so little familiar as
to require a further extension of the same resource, we might, instead
of a binary, adopt a ternary nomenclature, employing not only the name
of the genus, but that of the next natural group in order of generality
above the genus, commonly called the Family. This was done in the
mineralogical nomenclature proposed by Professor Mohs. "The names framed
by him were not composed of two, but of three elements, designating
respectively the Species, the Genus, and the Order; thus he has such
species as _Rhombohedral Lime Haloide_, _Octohedral Fluor Haloide_,
_Prismatic Hal Baryte_."[22] The binary construction, however, has been
found sufficient in botany and zoology, the only sciences in which this
general principle has hitherto been successfully adopted in the
construction of a nomenclature.

Besides the advantage which this principle of nomenclature possesses, in
giving to the names of species the greatest quantity of independent
significance which the circumstances of the case admit of, it answers
the further end of immensely economizing the use of names, and
preventing an otherwise intolerable burden on the memory. When the names
of species become extremely numerous, some artifice (as Dr. Whewell[23]
observes) becomes absolutely necessary to make it possible to recollect
or apply them. "The known species of plants, for example, were ten
thousand in the time of Linnæus, and are now probably sixty thousand. It
would be useless to endeavour to frame and employ separate names for
each of these species. The division of the objects into a subordinated
system of classification enables us to introduce a Nomenclature which
does not require this enormous number of names. Each of the genera has
its name, and the species are marked by the addition of some epithet to
the name of the genus. In this manner about seventeen hundred generic
names, with a moderate number of specific names, were found by Linnæus
sufficient to designate with precision all the species of vegetables
known at his time." And though the number of generic names has since
greatly increased, it has not increased in anything like the proportion
of the multiplication of known species.



§ 1. Thus far, we have considered the principles of scientific
classification so far only as relates to the formation of natural
groups; and at this point most of those who have attempted a theory of
natural arrangement, including, among the rest, Dr. Whewell, have
stopped. There remains, however, another, and a not less important
portion of the theory, which has not yet, as far as I am aware, been
systematically treated of by any writer except M. Comte. This is, the
arrangement of the natural groups into a natural series.[24]

The end of Classification, as an instrument for the investigation of
nature, is (as before stated) to make us think of those objects
together, which have the greatest number of important common properties;
and which therefore we have oftenest occasion, in the course of our
inductions, for taking into joint consideration. Our ideas of objects
are thus brought into the order most conducive to the successful
prosecution of inductive inquiries generally. But when the purpose is to
facilitate some particular inductive inquiry, more is required. To be
instrumental to that purpose, the classification must bring those
objects together, the simultaneous contemplation of which is likely to
throw most light upon the particular subject. That subject being the
laws of some phenomenon or some set of connected phenomena; the very
phenomenon or set of phenomena in question must be chosen as the
groundwork of the classification.

The requisites of a classification intended to facilitate the study of a
particular phenomenon, are, first, to bring into one class all Kinds of
things which exhibit that phenomenon, in whatever variety of forms or
degrees; and secondly, to arrange those Kinds in a series according to
the degree in which they exhibit it, beginning with those which exhibit
most of it, and terminating with those which exhibit least. The
principal example, as yet, of such a classification, is afforded by
comparative anatomy and physiology, from which, therefore, our
illustrations shall be taken.

§ 2. The object being supposed to be, the investigation of the laws of
animal life; the first step, after forming the most distinct conception
of the phenomenon itself, possible in the existing state of our
knowledge, is to erect into one great class (that of animals) all the
known Kinds of beings where that phenomenon presents itself; in however
various combinations with other properties, and in however different
degrees. As some of these Kinds manifest the general phenomenon of
animal life in a very high degree, and others in an insignificant
degree, barely sufficient for recognition; we must, in the next place,
arrange the various Kinds in a series, following one another according
to the degrees in which they severally exhibit the phenomenon; beginning
therefore with man, and ending with the most imperfect kinds of

This is merely saying that we should put the instances, from which the
law is to be inductively collected, into the order which is implied in
one of the four Methods of Experimental Inquiry discussed in the
preceding Book; the fourth Method, that of Concomitant Variations. As
formerly remarked, this is often the only method to which recourse can
be had, with assurance of a true conclusion, in cases in which we have
but limited means of effecting, by artificial experiments, a separation
of circumstances usually conjoined. The principle of the method is, that
facts which increase or diminish together, and disappear together, are
either cause and effect, or effects of a common cause. When it has been
ascertained that this relation really subsists between the variations, a
connexion between the facts themselves may be confidently laid down,
either as a law of nature or only as an empirical law, according to

That the application of this Method must be preceded by the formation of
such a series as we have described, is too obvious to need being pointed
out; and the mere arrangement of a set of objects in a series, according
to the degrees in which they exhibit some fact of which we are seeking
the law, is too naturally suggested by the necessities of our inductive
operations, to require any lengthened illustration here. But there are
cases in which the arrangement required for the special purpose, becomes
the determining principle of the classification of the same objects for
general purposes. This will naturally and properly happen, when those
laws of the objects which are sought in the special inquiry enact so
principal a part in the general character and history of those
objects--exercise so much influence in determining all the phenomena of
which they are either the agents or the theatre--that all other
differences existing among the objects are fittingly regarded as mere
modifications of the one phenomenon sought; effects determined by the
co-operation of some incidental circumstance with the laws of that
phenomenon. Thus in the case of animated beings, the differences between
one class of animals and another may reasonably be considered as mere
modifications of the general phenomenon, animal life; modifications
arising either from the different degrees in which that phenomenon is
manifested in different animals, or from the intermixture of the effects
of incidental causes peculiar to the nature of each, with the effects
produced by the general laws of life; those laws still exercising a
predominant influence over the result. Such being the case, no other
inductive inquiry respecting animals can be successfully carried on,
except in subordination to the great inquiry into the universal laws of
animal life. And the classification of animals best suited to that one
purpose, is the most suitable to all the other purposes of zoological

§ 3. To establish a classification of this sort, or even to apprehend it
when established, requires the power of recognising the essential
similarity of a phenomenon, in its minuter degrees and obscurer forms,
with what is called the _same_ phenomenon in the greatest perfection of
its development; that is, of identifying with each other all phenomena
which differ only in degree, and in properties which we suppose to be
caused by difference of degree. In order to recognise this identity, or
in other words, this exact similarity of quality, the assumption of a
type-species is indispensable. We must consider as the type of the
class, that among the Kinds included in it, which exhibits the
properties constitutive of the class, in the highest degree; conceiving
the other varieties as instances of degeneracy, as it were, from that
type; deviations from it by inferior intensity of the characteristic
property or properties. For every phenomenon is best studied (_cæteris
paribus_) where it exists in the greatest intensity. It is there that
the effects which either depend on it, or depend on the same causes with
it, will also exist in the greatest degree. It is there, consequently,
and only there, that those effects of it, or joint effects with it, can
become fully known to us, so that we may learn to recognise their
smaller degrees, or even their mere rudiments, in cases in which the
direct study would have been difficult or even impossible. Not to
mention that the phenomenon in its higher degrees may be attended by
effects or collateral circumstances which in its smaller degrees do not
occur at all, requiring for their production in any sensible amount a
greater degree of intensity of the cause than is there met with. In man,
for example, (the species in which both the phenomenon of animal and
that of organic life exist in the highest degree,) many subordinate
phenomena develop themselves in the course of his animated existence,
which the inferior varieties of animals do not show. The knowledge of
these properties may nevertheless be of great avail towards the
discovery of the conditions and laws of the general phenomenon of life,
which is common to man with those inferior animals. And they are, even,
rightly considered as properties of animated nature itself; because they
may evidently be affiliated to the general laws of animated nature;
because we may fairly presume that some rudiments or feeble degrees of
those properties would be recognised in all animals by more perfect
organs, or even by more perfect instruments, than ours; and because
those may be correctly termed properties of a class, which a thing
exhibits exactly in proportion as it belongs to the class, that is, in
proportion as it possesses the main attributes constitutive of the

§ 4. It remains to consider how the internal distribution of the series
may most properly take place: in what manner it should be divided into
Orders, Families, and Genera.

The main principle of division must of course be natural affinity; the
classes formed must be natural groups: and the formation of these has
already been sufficiently treated of. But the principles of natural
grouping must be applied in subordination to the principle of a natural
series. The groups must not be so constituted as to place in the same
group things which ought to occupy different points of the general
scale. The precaution necessary to be observed for this purpose is, that
the _primary_ divisions must be grounded not on all distinctions
indiscriminately, but on those which correspond to variations in the
degree of the main phenomenon. The series of Animated Nature should be
broken into parts at the points where the variation in the degree of
intensity of the main phenomenon (as marked by its principal characters,
Sensation, Thought, Voluntary Motion, &c.) begins to be attended by
conspicuous changes in the miscellaneous properties of the animal. Such
well-marked changes take place, for example, where the class Mammalia
ends; at the points where Fishes are separated from Insects, Insects
from Mollusca, &c. When so formed, the primary natural groups will
compose the series by mere juxtaposition, without redistribution; each
of them corresponding to a definite portion of the scale. In like manner
each family should, if possible, be so subdivided, that one portion of
it shall stand higher and the other lower, though of course contiguous,
in the general scale; and only when this is impossible is it allowable
to ground the remaining subdivisions on characters having no
determinable connexion with the main phenomenon.

Where the principal phenomenon so far transcends in importance all other
properties on which a classification could be grounded, as it does in
the case of animated existence, any considerable deviation from the rule
last laid down is in general sufficiently guarded against by the first
principle of a natural arrangement, that of forming the groups according
to the most important characters. All attempts at a scientific
classification of animals, since first their anatomy and physiology were
successfully studied, have been framed with a certain degree of
instinctive reference to a natural series, and have accorded in many
more points than they have differed, with the classification which would
most naturally have been grounded on such a series. But the accordance
has not always been complete; and it still is often a matter of
discussion, which of several classifications best accords with the true
scale of intensity of the main phenomenon. Cuvier, for example, has been
justly criticized for having formed his natural groups with an undue
degree of reference to the mode of alimentation, a circumstance directly
connected only with organic life, and not lending to the arrangement
most appropriate for the purposes of an investigation of the laws of
animal life, since both carnivorous and herbivorous or frugivorous
animals are found at almost every degree in the scale of animal
perfection. Blainville's classification has been considered by high
authorities to be free from this defect; as representing correctly, by
the mere order of the principal groups, the successive degeneracy of
animal nature from its highest to its most imperfect exemplification.

§ 5. A classification of any large portion of the field of nature in
conformity to the foregoing principles, has hitherto been found
practicable only in one great instance, that of animals. In the case
even of vegetables, the natural arrangement has not been carried beyond
the formation of natural groups. Naturalists have found, and probably
will continue to find it impossible to form those groups into any
series, the terms of which correspond to real gradations in the
phenomenon of vegetative or organic life. Such a difference of degree
may be traced between the class of Vascular Plants and that of Cellular,
which includes lichens, algæ, and other substances whose organization is
simpler and more rudimentary than that of the higher order of
vegetables, and which therefore approach nearer to mere inorganic
nature. But when we rise much above this point, we do not find any
sufficient difference in the degree in which different plants possess
the properties of organization and life. The dicotyledons are of more
complex structure, and somewhat more perfect organization, than the
monocotyledons: and some dicotyledonous families, such as the Compositæ,
are rather more complex in their organization than the rest. But the
differences are not of a marked character, and do not promise to throw
any particular light upon the conditions and laws of vegetable life and
development. If they did, the classification of vegetables would have to
be made, like that of animals, with reference to the scale or series

Although the scientific arrangements of organic nature afford as yet the
only complete example of the true principles of rational classification,
whether as to the formation of groups or of series, those principles are
applicable to all cases in which mankind are called upon to bring the
various parts of any extensive subject into mental co-ordination. They
are as much to the point when objects are to be classed for purposes of
art or business, as for those of science. The proper arrangement, for
example, of a code of laws, depends on the same scientific conditions as
the classifications in natural history; nor could there be a better
preparatory discipline for that important function, than the study of
the principles of a natural arrangement, not only in the abstract, but
in their actual application to the class of phenomena for which they
were first elaborated, and which are still the best school for learning
their use. Of this the great authority on codification, Bentham, was
perfectly aware: and his early _Fragment on Government_, the admirable
introduction to a series of writings unequalled in their department,
contains clear and just views (as far as they go) on the meaning of a
natural arrangement, such as could scarcely have occurred to any one who
lived anterior to the age of Linnæus and Bernard de Jussieu.


[1] Supra, book iii. ch. ii. § 3, 4, 5.

[2] Mr. Bailey has given by far the best statement of this theory. "The
general name," he says, "raises up the image sometimes of one individual
of the class formerly seen, sometimes of another, not unfrequently of
many individuals in succession; and it sometimes suggests an image made
up of elements from several different objects, by a latent process of
which I am not conscious." (Letters on the Philosophy of the Human Mind,
1st series, letter 22.) But Mr. Bailey must allow that we carry on
inductions and ratiocinations respecting the class, by means of this
idea or conception of some one individual in it. This is all I require.
The name of a class calls up some idea, through which we can, to all
intents and purposes, think of the class as such, and not solely of an
individual member of it.

[3] I have entered rather fully into this question in chap. xvii. of _An
Examination of Sir William Hamilton's Philosophy_, headed "The Doctrine
of Concepts or General Notions," which contains my last views on the

[4] Other examples of inappropriate conceptions are given by Dr. Whewell
(_Phil. Ind. Sc._ ii. 185) as follows:--"Aristotle and his followers
endeavoured in vain to account for the mechanical relation of forces in
the lever, by applying the _inappropriate_ geometrical conceptions of
the properties of the circle: they failed in explaining the _form_ of
the luminous spot made by the sun shining through a hole, because they
applied the _inappropriate_ conception of a circular _quality_ in the
sun's light: they speculated to no purpose about the elementary
composition of bodies, because they assumed the _inappropriate_
conception of _likeness_ between the elements and the compound, instead
of the genuine notion of elements merely _determining_ the qualities of
the compound." But in these cases there is more than an inappropriate
conception; there is a false conception; one which has no prototype in
nature, nothing corresponding to it in facts. This is evident in the
last two examples, and is equally true in the first; the "properties of
the circle" which were referred to, being purely fantastical. There is,
therefore, an error beyond the wrong choice of a principle of
generalization; there is a false assumption of matters of fact. The
attempt is made to resolve certain laws of nature into a more general
law, that law not being one which, though real, is inappropriate, but
one wholly imaginary.

[5] Professor Bain.

[6] This sentence having been erroneously understood as if I had meant
to assert that belief is nothing but an irresistible association, I
think it necessary to observe that I express no theory respecting the
ultimate analysis either of reasoning or of belief, two of the most
obscure points in analytical psychology. I am speaking not of the powers
themselves, but of the previous conditions necessary to enable those
powers to exert themselves: of which conditions I am contending that
language is not one, senses and association being sufficient without it.

[7] Mr. Bailey agrees with me in thinking that whenever "from something
actually present to my senses conjoined with past experience, I feel
satisfied that something has happened, or will happen, or is happening,
beyond the sphere of my personal observation," I may with strict
propriety be said to reason: and of course to reason inductively, for
demonstrative reasoning is excluded by the circumstances of the case.
(_The Theory of Reasoning_, 2nd ed. p. 27.)

[8] _Novum Organum Renovatum_, pp. 35-37.

[9] _Nov. Org. Renov._, pp. 39, 40.

[10] P. 217, 4to edition.

[11] "E, ex, extra, extraneus, étranger, stranger."

Another etymological example sometimes cited is the derivation of the
English _uncle_ from the Latin _avus_. It is scarcely possible for two
words to bear fewer outward marks of relationship, yet there is but one
step between them; _avus_, _avunculus_, _uncle_.

So _pilgrim_, from _ager_: _per agrum_, _peragrinus_, _peregrinus_,
_pellegrino_, _pilgrim_.

[12] P. 226-7.

[13] _Essays_, p. 214.

[14] Ibid. 215.

[15] Such cases give a clear insight into the process of the
degeneration of languages in periods of history when literary culture
was suspended; and we are now in danger of experiencing a similar evil
through the superficial extension of the same culture. So many persons
without anything deserving the name of education have become writers by
profession, that written language may almost be said to be principally
wielded by persons ignorant of the proper use of the instrument, and who
are spoiling it more and more for those who understand it. Vulgarisms,
which creep in nobody knows how, are daily depriving the English
language of valuable modes of expressing thought. To take a present
instance: the verb _transpire_ formerly conveyed very expressively its
correct meaning, viz. to _become known_ through unnoticed channels--to
exhale, as it were, into publicity through invisible pores, like a
vapour or gas disengaging itself. But of late a practice has commenced
of employing this word, for the sake of finery, as a mere synonym of _to
happen_: "the events which have _transpired_ in the Crimea," meaning the
incidents of the war. This vile specimen of bad English is already seen
in the despatches of noblemen and viceroys: and the time is apparently
not far distant when nobody will understand the word if used in its
proper sense. It is a great error to think that these corruptions of
language do no harm. Those who are struggling with the difficulty (and
who know by experience how great it already is) of expressing oneself
clearly with precision, find their resources continually narrowed by
illiterate writers, who seize and twist from its purpose some form of
speech which once served to convey briefly and compactly an unambiguous
meaning. It would hardly be believed how often a writer is compelled to
a circumlocution by the single vulgarism, introduced during the last few
years, of using the word _alone_ as an adverb, _only_ not being fine
enough for the rhetoric of ambitious ignorance. A man will say "to which
I am not alone bound by honour but also by law," unaware that what he
has unintentionally said is, that he is _not alone_ bound, some other
person being bound with him. Formerly if any one said, "I am not alone
responsible for this," he was understood to mean, (what alone his words
mean in correct English,) that he is not the sole person responsible;
but if he now used such an expression, the reader would be confused
between that and two other meanings; that he is not _only responsible_
but something more; or that he is responsible _not only for this_ but
for something besides. The time is coming when Tennyson's Œnone could
not say "I will not die alone," lest she should be supposed to mean that
she would not only die but do something else.

The blunder of writing _predicate_ for _predict_ has become so widely
diffused that it bids fair to render one of the most useful terms in the
scientific vocabulary of Logic unintelligible. The mathematical and
logical term "to eliminate" is undergoing a similar destruction. All who
are acquainted either with the proper use of the word or with its
etymology, know that to eliminate a thing is to thrust it out; but those
who know nothing about it, except that it is a fine-looking phrase, use
it in a sense precisely the reverse, to denote, not turning anything
out, but bringing it in. They talk of _eliminating_ some truth, or other
useful result, from a mass of details. I suspect that this error must at
first have arisen from some confusion between _to eliminate_ and _to

Though no such evil consequences as take place in these instances, are
likely to arise from the modern freak of writing _sanatory_ instead of
sanitary, it deserves notice as a charming specimen of pedantry
engrafted upon ignorance. Those who thus undertake to correct the
spelling of the classical English writers, are not aware that the
meaning of _sanatory_, if there were such a word in the language, would
have reference not to the preservation of health, but to the cure of

[16] _Historical Introduction_, vol. i. pp. 66-8.

[17] _History of Scientific Ideas_, ii. 110, 111.

[18] _Hist. Sc. Id._ ii. 111-113.

[19] _Nov. Org. Renov._ pp. 286, 287.

[20] _Hist. Sc. Id._ ii. 120-122.

[21] I say probably, not certainly, because this is not the
consideration by which a botanist determines what shall or shall not be
admitted as a species. In natural history those objects belong to the
same species, which are, or consistently with experience might have
been, produced from the same stock. But this distinction, in most, and
probably in all cases, happily accords with the other. It seems to be a
law of physiology, that animals and plants do really, in the
philosophical as well as the popular sense, propagate their kind;
transmitting to their descendants all the distinctions of Kind (down to
the most special or lowest Kind) which they themselves possess.

[22] _Nov. Org. Renov._ p. 274.

[23] _Hist. Sc. Id._ i. 133.

[24] Dr. Whewell, in his reply (_Philosophy of Discovery_, p. 270) says
that he "stopped short of, or rather passed by, the doctrine of a series
of organized beings," because he "thought it bad and narrow philosophy."
If he did, it was evidently without understanding this form of the
doctrine; for he proceeds to quote a passage from his "History," in
which the doctrine he condemns is designated as that of "a mere linear
progression in nature, which would place each genus in contact only with
the preceding and succeeding ones." Now the series treated of in the
text agrees with this linear progression in nothing whatever but in
being a progression.

It would surely be possible to arrange all _places_ (for example) in the
order of their distance from the North Pole, though there would be not
merely a plurality, but a whole circle of places at every single
gradation in the scale.



"Errare non modo affirmando et negando, sed etiam sentiendo, et in
tacitâ hominum cogitatione contingit."--HOBBES, _Computatio sive
Logica_, ch. v.

"Il leur semble qu'il n'y a qu'à douter par fantaisie, et qu'il n'y a
qu'à dire en général que notre nature est infirme; que notre esprit est
plein d'aveuglement; qu'il faut avoir un grand soin de se défaire de ses
préjugés, et autres choses semblables. Ils pensent que cela suffit pour
ne plus se laisser séduire à ses sens, et pour ne plus se tromper du
tout. Il ne suffit pas de dire que l'esprit est foible, il faut lui
faire sentir ses foiblesses. Ce n'est pas assez de dire qu'il est sujet
à l'erreur, il faut lui découvrir en quoi consistent ses
erreurs."--MALEBRANCHE, _Recherche de la Vérité_.



§ 1. It is a maxim of the schoolmen, that "contrariorum eadem est
scientia:" we never really know what a thing is, unless we are also able
to give a sufficient account of its opposite. Conformably to this maxim,
one considerable section, in most treatises on Logic, is devoted to the
subject of Fallacies; and the practice is too well worthy of observance,
to allow of our departing from it. The philosophy of reasoning, to be
complete, ought to comprise the theory of bad as well as of good

We have endeavoured to ascertain the principles by which the sufficiency
of any proof can be tested, and by which the nature and amount of
evidence needful to prove any given conclusion can be determined
beforehand. If these principles were adhered to, then although the
number and value of the truths ascertained would be limited by the
opportunities, or by the industry, ingenuity, and patience, of the
individual inquirer, at least error would not be embraced instead of
truth. But the general consent of mankind, founded on their experience,
vouches for their being far indeed from even this negative kind of
perfection in the employment of their reasoning powers.

In the conduct of life--in the practical business of mankind--wrong
inferences, incorrect interpretations of experience, unless after much
culture of the thinking faculty, are absolutely inevitable: and with
most people, after the highest degree of culture they ever attain, such
erroneous inferences, producing corresponding errors in conduct, are
lamentably frequent. Even in the speculations to which eminent
intellects have systematically devoted themselves, and in reference to
which the collective mind of the scientific world is always at hand to
aid the efforts and correct the aberrations of individuals, it is only
from the more perfect sciences, from those of which the subject-matter
is the least complicated, that opinions not resting on a correct
induction have at length, generally speaking, been expelled. In the
departments of inquiry relating to the more complex phenomena of nature,
and especially those of which the subject is man, whether as a moral and
intellectual, a social, or even as a physical being; the diversity of
opinions still prevalent among instructed persons, and the equal
confidence with which those of the most contrary ways of thinking cling
to their respective tenets, are proof not only that right modes of
philosophizing are not yet generally adopted on those subjects, but that
wrong ones are: that inquirers have not only in general missed the
truth, but have often embraced error; that even the most cultivated
portion of our species have not yet learned to abstain from drawing
conclusions which the evidence does not warrant.

The only complete safeguard against reasoning ill, is the habit of
reasoning well; familiarity with the principles of correct reasoning,
and practice in applying those principles. It is, however, not
unimportant to consider what are the most common modes of bad reasoning;
by what appearances the mind is most likely to be seduced from the
observance of true principles of induction; what, in short, are the most
common and most dangerous varieties of Apparent Evidence, whereby
persons are misled into opinions for which there does not exist evidence
really conclusive.

A catalogue of the varieties of apparent evidence which are not real
evidence, is an enumeration of Fallacies. Without such an enumeration,
therefore, the present work would be wanting in an essential point. And
while writers who included in their theory of reasoning nothing more
than ratiocination, have, in consistency with this limitation, confined
their remarks to the fallacies which have their seat in that portion of
the process of investigation; we, who profess to treat of the whole
process, must add to our directions for performing it rightly, warnings
against performing it wrongly in any of its parts: whether the
ratiocinative or the experimental portion of it be in fault, or the
fault lie in dispensing with ratiocination and induction altogether.

§ 2. In considering the sources of unfounded inference, it is
unnecessary to reckon the errors which arise, not from a wrong method,
nor even from ignorance of the right one, but from a casual lapse,
through hurry or inattention, in the application of the true principles
of induction. Such errors, like the accidental mistakes in casting up a
sum, do not call for philosophical analysis or classification;
theoretical considerations can throw no light upon the means of avoiding
them. In the present treatise our attention is required, not to mere
inexpertness in performing the operation in the right way, (the only
remedies for which are increased attention and more sedulous practice,)
but to the modes of performing it in a way fundamentally wrong; the
conditions under which the human mind persuades itself that it has
sufficient grounds for a conclusion which it has not arrived at by any
of the legitimate methods of induction--which it has not even carelessly
or overhastily, endeavoured to test by those legitimate methods.

§ 3. There is another branch of what may be called the Philosophy of
Error, which must be mentioned here, though only to be excluded from our
subject. The sources of erroneous opinions are twofold, moral and
intellectual. Of these, the moral do not fall within the compass of this
work. They may be classed under two general heads; Indifference to the
attainment of truth, and Bias: of which last the most common case is
that in which we are biassed by our wishes; but the liability is almost
as great to the undue adoption of a conclusion which is disagreeable to
us, as of one which is agreeable, if it be of a nature to bring into
action any of the stronger passions. Persons of timid character are the
more predisposed to believe any statement, the more it is calculated to
alarm them. Indeed it is a psychological law, deducible from the most
general laws of the mental constitution of man, that any strong passion
renders us credulous as to the existence of objects suitable to excite

But the moral causes of opinions, though with most persons the most
powerful of all, are but remote causes: they do not act directly, but by
means of the intellectual causes; to which they bear the same relation
that the circumstances called, in the theory of medicine, _predisposing_
causes, bear to _exciting_ causes. Indifference to truth cannot, in and
by itself, produce erroneous belief; it operates by preventing the mind
from collecting the proper evidences, or from applying to them the test
of a legitimate and rigid induction; by which omission it is exposed
unprotected to the influence of any species of apparent evidence which
offers itself spontaneously, or which is elicited by that smaller
quantity of trouble which the mind may be willing to take. As little is
Bias a direct source of wrong conclusions. We cannot believe a
proposition only by wishing, or only by dreading, to believe it. The
most violent inclination to find a set of propositions true, will not
enable the weakest of mankind to believe them without a vestige of
intellectual grounds--without any, even apparent, evidence. It acts
indirectly, by placing the intellectual grounds of belief in an
incomplete or distorted shape before his eyes. It makes him shrink from
the irksome labour of a rigorous induction, when he has a misgiving that
its result may be disagreeable; and in such examination as he does
institute, it makes him exert that which is in a certain measure
voluntary, his attention, unfairly, giving a larger share of it to the
evidence which seems favourable to the desired conclusion, a smaller to
that which seems unfavourable. It operates, too, by making him look out
eagerly for reasons, or apparent reasons, to support opinions which are
conformable, or resist those which are repugnant, to his interests or
feelings; and when the interests or feelings are common to great numbers
of persons, reasons are accepted and pass current, which would not for a
moment be listened to in that character, if the conclusion had nothing
more powerful than its reasons to speak in its behalf. The natural or
acquired partialities of mankind are continually throwing up
philosophical theories, the sole recommendation of which consists in
the premises they afford for proving cherished doctrines, or justifying
favourite feelings: and when any one of these theories has been so
thoroughly discredited as no longer to serve the purpose, another is
always ready to take its place. This propensity, when exercised in
favour of any widely-spread persuasion or sentiment, is often decorated
with complimentary epithets; and the contrary habit of keeping the
judgment in complete subordination to evidence, is stigmatized by
various hard names, as scepticism, immorality, coldness,
hard-heartedness, and similar expressions according to the nature of the
case. But though the opinions of the generality of mankind, when not
dependent on mere habit and inculcation, have their root much more in
the inclinations than in the intellect, it is a necessary condition to
the triumph of the moral bias that it should first pervert the
understanding. Every erroneous inference, though originating in moral
causes, involves the intellectual operation of admitting insufficient
evidence as sufficient; and whoever was on his guard against all kinds
of inconclusive evidence which can be mistaken for conclusive, would be
in no danger of being led into error even by the strongest bias. There
are minds so strongly fortified on the intellectual side, that they
could not blind themselves to the light of truth, however really
desirous of doing so; they could not, with all the inclination in the
world, pass off upon themselves bad arguments for good ones. If the
sophistry of the intellect could be rendered impossible, that of the
feelings, having no instrument to work with, would be powerless. A
comprehensive classification of all those things which, not being
evidence, are liable to appear such to the understanding, will,
therefore, of itself include all errors of judgment arising from moral
causes, to the exclusion only of errors of practice committed against
better knowledge.

To examine, then, the various kinds of apparent evidence which are not
evidence at all, and of apparently conclusive evidence which do not
really amount to conclusiveness, is the object of that part of our
inquiry into which we are about to enter.

The subject is not beyond the compass of classification and
comprehensive survey. The things, indeed, which are not evidence of any
given conclusion, are manifestly endless, and this negative property,
having no dependence on any positive ones, cannot be made the groundwork
of a real classification. But the things which, not being evidence, are
susceptible of being mistaken for it, are capable of a classification
having reference to the positive property which they possess, of
appearing to be evidence. We may arrange them, at our choice, on either
of two principles; according to the cause which makes them appear to be
evidence, not being so; or according to the particular kind of evidence
which they simulate. The Classification of Fallacies which will be
attempted in the ensuing chapter, is founded on these considerations



§ 1. In attempting to establish certain general distinctions which shall
mark out from one another the various kinds of Fallacious Evidence, we
propose to ourselves an altogether different aim from that of several
eminent thinkers, who have given, under the name of Political or other
Fallacies, a mere enumeration of a certain number of erroneous opinions;
false general propositions which happen to be often met with; _loci
communes_ of bad arguments on some particular subject. Logic is not
concerned with the false opinions which people happen to entertain, but
with the manner in which they come to entertain them. The question is
not, what facts have at any time been erroneously supposed to be proof
of certain other facts, but what property in the facts it was which led
any one to this mistaken supposition.

When a fact is supposed, though incorrectly, to be evidentiary of, or a
mark of, some other fact, there must be a cause of the error; the
supposed evidentiary fact must be connected in some particular manner
with the fact of which it is deemed evidentiary,--must stand in some
particular relation to it, without which relation it would not be
regarded in that light. The relation may either be one resulting from
the simple contemplation of the two facts side by side with one another,
or it may depend on some process of mind, by which a previous
association has been established between them. Some peculiarity of
relation, however, there must be; the fact which can, even by the
wildest aberration, be supposed to prove another fact, must stand in
some special position with regard to it; and if we could ascertain and
define that special position, we should perceive the origin of the

We cannot regard one fact as evidentiary of another, unless we believe
that the two are always, or in the majority of cases, conjoined. If we
believe A to be evidentiary of B, if when we see A we are inclined to
infer B from it, the reason is because we believe that wherever A is, B
also either always or for the most part exists, either as an antecedent,
a consequent, or a concomitant. If when we see A we are inclined not to
expect B--if we believe A to be evidentiary of the absence of B--it is
because we believe that where A is, B either is never, or at least
seldom, found. Erroneous conclusions, in short, no less than correct
conclusions, have an invariable relation to a general formula, either
expressed or tacitly implied. When we infer some fact from some other
fact which does not really prove it, we either have admitted, or, if we
maintained consistency, ought to admit, some groundless general
proposition respecting the conjunction of the two phenomena.

For every property, therefore, in facts, or in our mode of considering
facts, which leads us to believe that they are habitually conjoined when
they are not, or that they are not when in reality they are, there is a
corresponding kind of Fallacy; and an enumeration of fallacies would
consist in a specification of those properties in facts, and those
peculiarities in our mode of considering them, which give rise to this
erroneous opinion.

§ 2. To begin, then; the supposed connexion, or repugnance, between the
two facts, may either be a conclusion from evidence (that is, from some
other proposition or propositions) or may be admitted without any such
ground; admitted, as the phrase is, on its own evidence; embraced as
self-evident, as an axiomatic truth. This gives rise to the first great
distinction, that between Fallacies of Inference, and Fallacies of
Simple Inspection. In the latter division must be included not only all
cases in which a proposition is believed and held for true, literally
without any extrinsic evidence, either of specific experience or general
reasoning; but those more frequent cases in which simple inspection
creates a _presumption_ in favour of a proposition; not sufficient for
belief, but sufficient to cause the strict principles of a regular
induction to be dispensed with, and creating a predisposition to believe
it on evidence which would be seen to be insufficient if no such
presumption existed. This class, comprehending the whole of what may be
termed Natural Prejudices, and which I shall call indiscriminately
Fallacies of Simple Inspection or Fallacies _à priori_, shall be placed
at the head of our list.

Fallacies of Inference, or erroneous conclusions from supposed evidence,
must be subdivided according to the nature of the apparent evidence from
which the conclusions are drawn; or (what is the same thing) according
to the particular kind of sound argument which the fallacy in question
simulates. But there is a distinction to be first drawn, which does not
answer to any of the divisions of sound arguments, but arises out of the
nature of bad ones. We may know exactly what our evidence is, and yet
draw a false conclusion from it; we may conceive precisely what our
premises are, what alleged matters of fact, or general principles, are
the foundation of our inference; and yet, because the premises are
false, or because we have inferred from them what they will not support,
our conclusion may be erroneous. But a case, perhaps even more frequent,
is that in which the error arises from not conceiving our premises with
due clearness, that is, (as shown in the preceding Book,[1]) with due
fixity: forming one conception of our evidence when we collect or
receive it, and another when we make use of it; or unadvisedly, and in
general unconsciously, substituting, as we proceed, different premises
in the place of those with which we set out, or a different conclusion
for that which we undertook to prove. This gives existence to a class of
fallacies which may be justly termed (in a phrase borrowed from Bentham)
Fallacies of Confusion; comprehending, among others, all those which
have their source in language, whether arising from the vagueness or
ambiguity of our terms, or from casual associations with them.

When the fallacy is not one of Confusion, that is, when the proposition
believed, and the evidence on which it is believed, are steadily
apprehended and unambiguously expressed, there remain to be made two
cross divisions. The Apparent Evidence may be either particular facts,
or foregone generalizations; that is, the process may simulate either
simple Induction, or Deduction; and again, the evidence, whether
consisting of supposed facts or of general propositions, may be false in
itself, or, being true, may fail to bear out the conclusion attempted to
be founded on it. This gives us first, Fallacies of Induction and
Fallacies of Deduction, and then a subdivision of each of these,
according as the supposed evidence is false, or true but inconclusive.

Fallacies of Induction, where the facts on which the induction proceeds
are erroneous, may be termed Fallacies of Observation. The term is not
strictly accurate, or rather, not accurately coextensive with the class
of fallacies which I propose to designate by it. Induction is not always
grounded on facts immediately observed, but sometimes on facts inferred:
and when these last are erroneous, the error may not be, in the literal
sense of the term, an instance of bad observation, but of bad inference.
It will be convenient, however, to make only one class of all the
inductions of which the error lies in not sufficiently ascertaining the
facts on which the theory is grounded; whether the cause of failure be
mal-observation, or simple non-observation, and whether the
mal-observation be direct, or by means of intermediate marks which do
not prove what they are supposed to prove. And in the absence of any
comprehensive term to denote the ascertainment, by whatever means, of
the facts on which an induction is grounded, I will venture to retain
for this class of fallacies, under the explanation now given, the title
of Fallacies of Observation.

The other class of inductive fallacies, in which the facts are correct,
but the conclusion not warranted by them, are properly denominated
Fallacies of Generalization: and these, again, fall into various
subordinate classes or natural groups, some of which will be enumerated
in their proper place.

When we now turn to Fallacies of Deduction, namely those modes of
incorrect argumentation in which the premises, or some of them, are
general propositions, and the argument a ratiocination; we may of course
subdivide these also into two species similar to the two preceding,
namely, those which proceed on false premises, and those of which the
premises, though true, do not support the conclusion. But of these
species, the first must necessarily fall under some one of the heads
already enumerated. For the error must be either in those premises which
are general propositions, or in those which assert individual facts. In
the former case it is an Inductive Fallacy, of one or the other class;
in the latter it is a Fallacy of Observation: unless, in either case,
the erroneous premise has been assumed on simple inspection, in which
case the fallacy is _à priori_. Or finally, the premises, of whichever
kind they are, may never have been conceived in so distinct a manner as
to produce any clear consciousness by what means they were arrived at;
as in the case of what is called reasoning in a circle: and then the
fallacy is one of Confusion.

There remain, therefore, as the only class of fallacies having properly
their seat in deduction, those in which the premises of the
ratiocination do not bear out its conclusion; the various cases, in
short, of vicious argumentation, provided against by the rules of the
syllogism. We shall call these, Fallacies of Ratiocination.

We have thus five distinguishable classes of fallacy, which may be
expressed in the following synoptic table:--


    of Simple Inspection            1. Fallacies _à priori_.

    of Inference

      from evidence distinctly

        Inductive Fallacies         2. Fallacies of Observation.
                                    3. Fallacies of Generalization.

        Deductive Fallacies         4. Fallacies of Ratiocination.

      from evidence indistinctly
          conceived                 5. Fallacies of Confusion.

§ 3. We must not, however, expect to find that men's actual errors
always, or even commonly, fall so unmistakeably under some one of these
classes, as to be incapable of being referred to any other. Erroneous
arguments do not admit of such a sharply cut division as valid arguments
do. An argument fully stated, with all its steps distinctly set out, in
language not susceptible of misunderstanding, must, if it be erroneous,
be so in some one of these five modes unequivocally: or indeed of the
first four, since the fifth, on such a supposition, would vanish. But it
is not in the nature of bad reasoning to express itself thus
unambiguously. When a sophist, whether he is imposing on himself or
attempting to impose on others, can be constrained to throw his
sophistry into so distinct a form, it needs, in a large proportion of
cases, no further exposure.

In all arguments, everywhere but in the schools, some of the links are
suppressed; _à fortiori_ when the arguer either intends to deceive, or
is a lame and inexpert thinker, little accustomed to bring his reasoning
processes to any test: and it is in those steps of the reasoning which
are made in this tacit and half-conscious, or even wholly unconscious
manner, that the error oftenest lurks. In order to detect the fallacy,
the proposition thus silently assumed must be supplied; but the
reasoner, most likely, has never really asked himself what he was
assuming: his confuter, unless permitted to extort it from him by the
Socratic mode of interrogation, must himself judge what the suppressed
premise ought to be in order to support the conclusion. And hence, in
the words of Archbishop Whately, "it must be often a matter of doubt, or
rather, of arbitrary choice, not only to which genus each _kind_ of
fallacy should be referred, but even to which kind to refer any one
_individual_ fallacy; for since, in any course of argument, _one_
premise is usually suppressed, it frequently happens in the case of a
fallacy, that the hearers are left to the alternative of supplying
_either_ a premise which is _not true_, or _else_, one which _does not
prove_ the conclusion: _e. g._ if a man expatiates on the distress of
the country, and thence argues that the government is tyrannical, we
must suppose him to assume _either_ that 'every distressed country is
under a tyranny,' which is a manifest falsehood, _or_ merely that 'every
country under a tyranny is distressed,' which, however true, proves
nothing, the middle term being undistributed." The former would be
ranked, in our distribution, among fallacies of generalization, the
latter among those of ratiocination. "Which are we to suppose the
speaker meant us to understand? Surely" (if he understood himself) "just
whichever each of his hearers might happen to prefer: some might assent
to the false premise; others allow the unsound syllogism."

Almost all fallacies, therefore, might in strictness be brought under
our fifth class, Fallacies of Confusion. A fallacy can seldom be
absolutely referred to any of the other classes; we can only say, that
if all the links were filled up which should be capable of being
supplied in a valid argument, it would either stand thus (forming a
fallacy of one class), or thus (a fallacy of another); or at furthest we
may say, that the conclusion is most _likely_ to have originated in a
fallacy of such and such a class. Thus in the illustration just quoted,
the error committed may be traced with most probability to a fallacy of
generalization; that of mistaking an uncertain mark, or piece of
evidence, for a certain one; concluding from an effect to some one of
its possible causes, when there are others which would have been equally
capable of producing it.

Yet, though the five classes run into each other, and a particular error
often seems to be arbitrarily assigned to one of them rather than to any
of the rest, there is considerable use in so distinguishing them. We
shall find it convenient to set apart, as Fallacies of Confusion, those
of which confusion is the most obvious characteristic; in which no other
cause can be assigned for the mistake committed, than neglect or
inability to state the question properly, and to apprehend the evidence
with definiteness and precision. In the remaining four classes I shall
place not only the cases in which the evidence is clearly seen to be
what it is, and yet a wrong conclusion drawn from it, but also those in
which, although there be confusion, the confusion is not the sole cause
of the error, but there is some shadow of a ground for it in the nature
of the evidence itself. And in distributing these cases of partial
confusion among the four classes, I shall, when there can be any
hesitation as to the precise seat of the fallacy, suppose it to be in
that part of the process in which, from the nature of the case, and the
tendencies of the human mind, an error would in the particular
circumstances be the most probable.

After these observations we shall proceed, without further preamble, to
consider the five classes in their order.



§ 1. The tribe of errors of which we are to treat in the first instance,
are those in which no actual inference takes place at all: the
proposition (it cannot in such cases be called a conclusion) being
embraced, not as proved, but as requiring no proof; as a self-evident
truth; or else as having such intrinsic verisimilitude, that external
evidence not in itself amounting to proof, is sufficient in aid of the
antecedent presumption.

An attempt to treat this subject comprehensively would be a
transgression of the bounds prescribed to this work, since it would
necessitate the inquiry which, more than any other, is the grand
question of what is called metaphysics, viz. What are the propositions
which may reasonably be received without proof? That there must be some
such propositions all are agreed, since there cannot be an infinite
series of proof, a chain suspended from nothing. But to determine what
these propositions are, is the _opus magnum_ of the more recondite
mental philosophy. Two principal divisions of opinion on the subject
have divided the schools of philosophy from its first dawn. The one
recognises no ultimate premises but the facts of our subjective
consciousness; our sensations, emotions, intellectual states of mind,
and volitions. These, and whatever by strict rules of induction can be
derived from these, it is possible, according to this theory, for us to
know; of all else we must remain in ignorance. The opposite school hold
that there are other existences, suggested indeed to our minds by these
subjective phenomena, but not inferrible from them, by any process
either of deduction or of induction; which, however, we must, by the
constitution of our mental nature recognise as realities; and
realities, too, of a higher order than the phenomena of our
consciousness, being the efficient causes and necessary substrata of all
Phenomena. Among these entities they reckon Substances, whether matter
or spirit; from the dust under our feet to the soul, and from that to
Deity. All these, according to them, are preternatural or supernatural
beings, having no likeness in experience, though experience is entirely
a manifestation of their agency. Their existence, together with more or
less of the laws to which they conform in their operations, are, on this
theory, apprehended and recognised as real by the mind itself
intuitively: experience (whether in the form of sensation or of mental
feeling) having no other part in the matter than as affording facts
which are consistent with these necessary postulates of reason, and
which are explained and accounted for by them.

As it is foreign to the purpose of the present treatise to decide
between these conflicting theories, we are precluded from inquiring into
the existence, or defining the extent and limits, of knowledge _à
priori_, and from characterizing the kind of correct assumption which
the fallacy of incorrect assumption, now under consideration, simulates.
Yet since it is allowed on both sides that such assumptions are often
made improperly, we may find it practicable, without entering into the
ultimate metaphysical grounds of the discussion, to state some
speculative propositions, and suggest some practical cautions,
respecting the forms in which such unwarranted assumptions are most
likely to be made.

§ 2. In the cases in which, according to the thinkers of the ontological
school, the mind apprehends, by intuition, things, and the laws of
things, not cognizable by our sensitive faculty; those intuitive, or
supposed intuitive, perceptions are undistinguishable from what the
opposite school are accustomed to call ideas of the mind. When they
themselves say that they perceive the things by an immediate act of a
faculty given for that purpose by their Creator, it would be said of
them by their opponents that they find an idea or conception in their
own minds, and from the idea or conception, infer the existence of a
corresponding objective reality. Nor would this be an unfair statement,
but a mere version into other words of the account given by many of
themselves; and one to which the more clear-sighted of them might, and
generally do, without hesitation, subscribe. Since, therefore, in the
cases which lay the strongest claims to be examples of knowledge _à
priori_, the mind proceeds from the idea of a thing to the reality of
the thing itself, we cannot be surprised by finding that illicit
assumptions _à priori_ consist in doing the same thing erroneously: in
mistaking subjective facts for objective, laws of the percipient mind
for laws of the perceived object, properties of the ideas or conceptions
for properties of the things conceived.

Accordingly, a large proportion of the erroneous thinking which exists
in the world proceeds on a tacit assumption, that the same order must
obtain among the objects in nature which obtains among our ideas of
them. That if we always think of two things together, the two things
must always exist together. That if one thing makes us think of another
as preceding or following it, that other must precede it or follow it in
actual fact. And conversely, that when we cannot conceive two things
together they cannot exist together, and that their combination may,
without further evidence, be rejected from the list of possible

Few persons, I am inclined to think, have reflected on the great extent
to which this fallacy has prevailed, and prevails, in the actual beliefs
and actions of mankind. For a first illustration of it, we may refer to
a large class of popular superstitions. If any one will examine in what
circumstances most of those things agree, which in different ages and by
different portions of the human race have been considered as omens or
prognostics of some interesting event, whether calamitous or fortunate;
they will be found very generally characterized by this peculiarity,
that they cause the mind to _think_ of that, of which they are therefore
supposed to forebode the actual occurrence. "Talk of the devil, and he
will appear," has passed into a proverb. Talk of the devil, that is,
raise the idea, and the reality will follow. In times when the
appearance of that personage in a visible form was thought to be no
unfrequent occurrence, it has doubtless often happened to persons of
vivid imagination and susceptible nerves, that talking of the devil has
caused them to fancy they saw him; as, even in our more incredulous
days, listening to ghost stories predisposes us to see ghosts; and thus,
as a prop to the _à priori_ fallacy, there might come to be added an
auxiliary fallacy of mal-observation, with one of false generalization
grounded on it. Fallacies of different orders often herd or cluster
together in this fashion, one smoothing the way for another. But the
origin of the superstition is evidently that which we have assigned. In
like manner it has been universally considered unlucky to speak of
misfortune. The day on which any calamity happened has been considered
an unfortunate day, and there has been a feeling everywhere, and in some
nations a religious obligation, against transacting any important
business on that day. For on such a day our thoughts are likely to be of
misfortune. For a similar reason, any untoward occurrence in commencing
an undertaking has been considered ominous of failure; and often,
doubtless, has really contributed to it, by putting the persons engaged
in the enterprise more or less out of spirits: but the belief has
equally prevailed where the disagreeable circumstance was, independently
of superstition, too insignificant to depress the spirits by any
influence of its own. All know the story of Cæsar's accidentally
stumbling in the act of landing on the African coast; and the presence
of mind with which he converted the direful presage into a favourable
one by exclaiming, "Africa, I embrace thee." Such omens, it is true,
were often conceived as warnings of the future, given by a friendly or a
hostile deity; but this very superstition grew out of a pre-existing
tendency; the god was supposed to send, as an indication of what was to
come, something which people were already disposed to consider in that
light. So in the case of lucky or unlucky names. Herodotus tells us how
the Greeks, on the way to Mycale, were encouraged in their enterprise by
the arrival of a deputation from Samos, one of the members of which was
named Hegesistratus, the leader of armies.

Cases may be pointed out in which something which could have no real
effect but to make persons _think_ of misfortune, was regarded not
merely as a prognostic, but as something approaching to an actual cause
of it. The _εὐφήμει_ of the Greeks, and _favete linguis_, or _bona verba
quæso_, of the Romans, evince the care with which they endeavoured to
repress the utterance of any word expressive or suggestive of ill
fortune; not from notions of delicate politeness, to which their general
mode of conduct and feeling had very little reference, but from _bonâ
fide_ alarm lest the event so suggested to the imagination should in
fact occur. Some vestige of a similar superstition has been known to
exist among uneducated persons even in our own day: it is thought an
unchristian thing to talk of, or suppose, the death of any person while
he is alive. It is known how careful the Romans were to avoid, by an
indirect mode of speech, the utterance of any word directly expressive
of death or other calamity: how instead of _mortuus est_ they said
_vixit_; and "be the event fortunate or _otherwise_" instead of
_adverse_. The name Maleventum, of which Salmasius so sagaciously
detected the Thessalian origin (_Μαλόεις_, _Μαλοέντος_), they changed
into the highly propitious denomination, Beneventum; Egesta into
Segesta; and Epidamnus, a name so interesting in its associations to the
reader of Thucydides, they exchanged for Dyrrhachium, to escape the
perils of a word suggestive of _damnum_ or detriment.

"If an hare cross the highway," says Sir Thomas Browne,[2] "there are
few above threescore that are not perplexed thereat; which
notwithstanding is but an augurial terror, according to that received
expression, _Inauspicatum dat iter oblatus lepus_. And the ground of the
conceit was probably no greater than this, that a fearful animal passing
by us portended unto us something to be feared; as upon the like
consideration the meeting of a fox presaged some future imposture." Such
superstitions as these last must be the result of study; they are too
recondite for natural or spontaneous growth. But when the attempt was
once made to construct a science of predictions, any association, though
ever so faint or remote, by which an object could be connected in
however far-fetched a manner with ideas either of prosperity or of
danger and misfortune, was enough to determine its being classed among
good or evil omens.

An example of rather a different kind from any of these, but falling
under the same principle, is the famous attempt on which so much labour
and ingenuity were expended by the alchemists, to make gold potable. The
motive to this was a conceit that potable gold could be no other than
the universal medicine: and why gold? Because it was so precious. It
must have all marvellous properties as a physical substance, because the
mind was already accustomed to marvel at it.

From a similar feeling, "every substance," says Dr. Paris,[3] "whose
origin is involved in mystery, has at different times been eagerly
applied to the purposes of medicine. Not long since, one of those
showers which are now known to consist of the excrements of insects,
fell in the north of Italy; the inhabitants regarded it as manna, or
some supernatural panacea, and they swallowed it with such avidity, that
it was only by extreme address that a small quantity was obtained for a
chemical examination." The superstition, in this instance, though
doubtless partly of a religious character, probably in part also arose
from the prejudice that a wonderful thing must of course have wonderful

§ 3. The instances of _à priori_ fallacy which we have hitherto cited
belong to the class of vulgar errors, and do not now, nor in any but a
rude age ever could, impose upon minds of any considerable attainments.
But those to which we are about to proceed, have been, and still are,
all but universally prevalent among thinkers. The same disposition to
give objectivity to a law of the mind--to suppose that what is true of
our ideas of things must be true of the things themselves--exhibits
itself in many of the most accredited modes of philosophical
investigation, both on physical and on metaphysical subjects. In one of
its most undisguised manifestations, it embodies itself in two maxims,
which lay claim to axiomatic truth: Things which we cannot think of
together, cannot coexist; and Things which we cannot help thinking of
together, must coexist. I am not sure that the maxims were ever
expressed in these precise words, but the history both of philosophy and
of popular opinions abounds with exemplifications of both forms of the

To begin with the latter of them: Things which we cannot think of except
together, must exist together. This is assumed in the generally received
and accredited mode of reasoning which concludes that A must accompany B
in point of fact, because "it is involved in the idea." Such thinkers do
not reflect that the idea, being a result of abstraction, ought to
conform to the facts, and cannot make the facts conform to it. The
argument is at most admissible as an appeal to authority; a surmise,
that what is now part of the idea, must, before it became so, have been
found by previous inquirers in the facts. Nevertheless, the philosopher
who more than all others made professions of rejecting authority,
Descartes, constructed his system on this very basis. His favourite
device for arriving at truth, even in regard to outward things, was by
looking into his own mind for it. "Credidi me," says his celebrated
maxim, "pro regulâ generali sumere posse, omne id quod valdè dilucidè et
distinctè concipiebam, verum esse;" whatever can be very clearly
conceived, must certainly exist; that is, as he afterwards explains it,
if the idea includes existence. And on this ground he infers that
geometrical figures really exist, because they can be distinctly
conceived. Whenever existence is "involved in an idea," a thing
conformable to the idea must really exist; which is as much as to say,
whatever the idea contains must have its equivalent in the thing; and
what we are not able to leave out of the idea cannot be absent from the
reality.[4] This assumption pervades the philosophy not only of
Descartes, but of all the thinkers who received their impulse mainly
from him, in particular the two most remarkable among them, Spinoza and
Leibnitz, from whom the modern German metaphysical philosophy is
essentially an emanation. I am indeed disposed to think that the fallacy
now under consideration has been the cause of two-thirds of the bad
philosophy, and especially of the bad metaphysics, which the human mind
has never ceased to produce. Our general ideas contain nothing but what
has been put into them, either by our passive experience, or by our
active habits of thought; and the metaphysicians in all ages, who have
attempted to construct the laws of the universe by reasoning from our
supposed necessities of thought, have always proceeded, and only could
proceed, by laboriously finding in their own minds what they themselves
had formerly put there, and evolving from their ideas of things what
they had first _involved_ in those ideas. In this way all deeply-rooted
opinions and feelings are enabled to create apparent demonstrations of
their truth and reasonableness, as it were out of their own substance.

The other form of the fallacy; Things which we cannot think of together
cannot exist together,--including as one of its branches, that what we
cannot think of as existing cannot exist at all,--may thus be briefly
expressed: Whatever is inconceivable must be false.

Against this prevalent doctrine I have sufficiently argued in a former
Book,[5] and nothing is required in this place but examples. It was
long held that Antipodes were impossible because of the difficulty which
was found in conceiving persons with their heads in the same direction
as our feet. And it was one of the received arguments against the
Copernican system, that we cannot conceive so great a void space as that
system supposes to exist in the celestial regions. When men's
imaginations had always been used to conceive the stars as firmly set in
solid spheres, they naturally found much difficulty in imagining them in
so different, and, as it doubtless appeared to them, so precarious a
situation. But they had no right to mistake the limitation (whether
natural, or, as it in fact proved, only artificial) of their own
faculties, for an inherent limitation of the possible modes of existence
in the universe.

It may be said in objection, that the error in these cases was in the
minor premise, not the major; an error of fact, not of principle; that
it did not consist in supposing that what is inconceivable cannot be
true, but in supposing antipodes to be inconceivable, when present
experience proves that they can be conceived. Even if this objection
were allowed, and the proposition that what is inconceivable cannot be
true were suffered to remain unquestioned as a speculative truth, it
would be a truth on which no practical consequence could ever be
founded, since, on this showing, it is impossible to affirm of any
proposition, not being a contradiction in terms, that it is
inconceivable. Antipodes were really, not fictitiously, inconceivable to
our ancestors: they are indeed conceivable to us; and as the limits of
our power of conception have been so largely extended, by the extension
of our experience and the more varied exercise of our imagination, so
may posterity find many combinations perfectly conceivable to them which
are inconceivable to us. But, as beings of limited experience, we must
always and necessarily have limited conceptive powers; while it does not
by any means follow that the same limitation obtains in the
possibilities of nature, nor even in her actual manifestations.

Rather more than a century and a half ago it was a scientific maxim,
disputed by no one, and which no one deemed to require any proof, that
"a thing cannot act where it is not." With this weapon the Cartesians
waged a formidable war against the theory of gravitation, which,
according to them, involving so obvious an absurdity, must be rejected
_in limine_: the sun could not possibly act upon the earth, not being
there. It was not surprising that the adherents of the old systems of
astronomy should urge this objection against the new; but the false
assumption imposed equally on Newton himself, who in order to turn the
edge of the objection, imagined a subtle ether which filled up the space
between the sun and the earth, and by its intermediate agency was the
proximate cause of the phenomena of gravitation. "It is inconceivable,"
said Newton, in one of his letters to Dr. Bentley,[6] "that inanimate
brute matter should, without the mediation of something else, which is
not material, operate upon and affect other matter _without mutual
contact_.... That gravity should be innate, inherent, and essential to
matter, so that one body may act on another, at a distance, through a
vacuum, without the mediation of anything else, by and through which
their action and force may be conveyed from one to another, is to me so
great an absurdity, that I believe no man, who in philosophical matters
has a competent faculty of thinking, can ever fall into it." This
passage should be hung up in the cabinet of every cultivator of science
who is ever tempted to pronounce a fact impossible because it appears to
him inconceivable. In our own day one would be more tempted, though with
equal injustice, to reverse the concluding observation, and consider the
seeing any absurdity at all in a thing so simple and natural, to be what
really marks the absence of "a competent faculty of thinking." No one
now feels any difficulty in conceiving gravity to be, as much as any
other property is, "inherent, and essential to matter," nor finds the
comprehension of it facilitated in the smallest degree by the
supposition of an ether (though some recent inquirers do give this as an
explanation of it); nor thinks it at all incredible that the celestial
bodies can and do act where they, in actual bodily presence, are not.
To us it is not more wonderful that bodies should act upon one another
"without mutual contact," than that they should do so when in contact;
we are familiar with both these facts, and we find them equally
inexplicable, but equally easy to believe. To Newton, the one, because
his imagination was familiar with it, appeared natural and a matter of
course, while the other, for the contrary reason, seemed too absurd to
be credited.

It is strange that any one, after such a warning, should rely implicitly
on the evidence _à priori_ of such propositions as these, that matter
cannot think; that space, or extension, is infinite; that nothing can be
made out of nothing (_ex nihilo nihil fit_). Whether these propositions
are true or not this is not the place to determine, nor even whether the
questions are soluble by the human faculties. But such doctrines are no
more self-evident truths, than the ancient maxim that a thing cannot act
where it is not, which probably is not now believed by any educated
person in Europe.[7] Matter cannot think; why? because we _cannot
conceive_ thought to be annexed to any arrangement of material
particles. Space is infinite, because having never known any part of it
which had not other parts beyond it, we _cannot conceive_ an absolute
termination. _Ex nihilo nihil fit_, because having never known any
physical product without a pre-existing physical material, we _cannot_,
or think we cannot, _imagine_ a creation out of nothing. But these
things may in themselves be as conceivable as gravitation without an
intervening medium, which Newton thought too great an absurdity for any
person of a competent faculty of philosophical thinking to admit: and
even supposing them not conceivable, this, for aught we know, may be
merely one of the limitations of our very limited minds, and not in
nature at all.

No writer has more directly identified himself with the fallacy now
under consideration, or has embodied it in more distinct terms, than
Leibnitz. In his view, unless a thing was not merely conceivable, but
even explainable, it could not exist in nature. All _natural_ phenomena,
according to him, must be susceptible of being accounted for _à priori_.
The only facts of which no explanation could be given but the will of
God, were miracles properly so called. "Je reconnais," says he,[8]
"qu'il n'est pas permis de nier ce qu'on n'entend pas; mais j'ajoute
qu'on a droit de nier (au moins dans l'ordre naturel) ce qui absolument
n'est point intelligible ni explicable. Je soutiens aussi ... qu'enfin
la conception des créatures n'est pas la mesure du pouvoir de Dieu, mais
que leur conceptivité, ou force de concevoir, est la mesure du pouvoir
de la nature, tout ce qui est conforme à l'ordre naturel pouvant être
conçu ou entendu par quelque créature."

Not content with assuming that nothing can be true which we are unable
to conceive, scientific inquirers have frequently given a still further
extension to the doctrine, and held that, even of things not altogether
inconceivable, that which we can conceive with the greatest ease is
likeliest to be true. It was long an admitted axiom, and is not yet
entirely discredited, that "nature always acts by the simplest means,"
_i.e._ by those which are most easily conceivable.[9] A large proportion
of all the errors ever committed in the investigation of the laws of
nature, have arisen from the assumption that the most familiar
explanation or hypothesis must be the truest. One of the most
instructive facts in scientific history is the pertinacity with which
the human mind clung to the belief that the heavenly bodies must move in
circles, or be carried round by the revolution of spheres; merely
because those were in themselves the simplest suppositions: though, to
make them accord with the facts which were ever contradicting them more
and more, it became necessary to add sphere to sphere and circle to
circle, until the original simplicity was converted into almost
inextricable complication.

§ 4. We pass to another _à priori_ fallacy or natural prejudice, allied
to the former, and originating as that does, in the tendency to presume
an exact correspondence between the laws of the mind and those of things
external to it. The fallacy may be enunciated in this general
form--Whatever can be thought of apart exists apart: and its most
remarkable manifestation consists in the personification of
abstractions. Mankind in all ages have had a strong propensity to
conclude that wherever there is a name, there must be a distinguishable
separate entity corresponding to the name; and every complex idea which
the mind has formed for itself by operating upon its conceptions of
individual things, was considered to have an outward objective reality
answering to it. Fate, Chance, Nature, Time, Space, were real beings,
nay, even gods. If the analysis of qualities in the earlier part of this
work be correct, names of qualities and names of substances stand for
the very same sets of facts or phenomena; _whiteness_ and _a white
thing_ are only different phrases, required by convenience for speaking
of the same external fact under different relations. Not such, however,
was the notion which this verbal distinction suggested of old, either to
the vulgar or to the scientific. Whiteness was an entity, inhering or
sticking in the white substance: and so of all other qualities. So far
was this carried, that even concrete general terms were supposed to be,
not names of indefinite numbers of individual substances, but names of a
peculiar kind of entities termed Universal Substances. Because we can
think and speak of man in general, that is, of all persons in so far as
possessing the common attributes of the species, without fastening our
thoughts permanently on some one individual person; therefore man in
general was supposed to be, not an aggregate of individual persons, but
an abstract or universal man, distinct from these.

It may be imagined what havoc metaphysicians trained in these habits
made with philosophy, when they came to the largest generalizations of
all. _Substantiæ Secundæ_ of any kind were bad enough, but such
Substantiæ Secundæ as _τὸ ὄν_, for example, and _τὸ ἕν_, standing for
peculiar entities supposed to be inherent in all things which _exist_,
or which are said to be _one_, were enough to put an end to all
intelligible discussion; especially since, with a just perception that
the truths which philosophy pursues are _general_ truths, it was soon
laid down that these general substances were the only subjects of
science, being immutable, while individual substances cognizable by the
senses, being in a perpetual flux, could not be the subject of real
knowledge. This misapprehension of the import of general language
constitutes Mysticism, a word so much oftener written and spoken than
understood. Whether in the Vedas, in the Platonists, or in the
Hegelians, mysticism is neither more nor less than ascribing objective
existence to the subjective creations of our own faculties, to ideas or
feelings of the mind; and believing that by watching and contemplating
these ideas of its own making, it can read in them what takes place in
the world without.

§ 5. Proceeding with the enumeration of _à priori_ fallacies, and
endeavouring to arrange them with as much reference as possible to their
natural affinities, we come to another, which is also nearly allied to
the fallacy preceding the last, standing in the same relation to one
variety of it as the fallacy last mentioned does to the other. This,
too, represents nature as under incapacities corresponding to those of
our intellect; but instead of only asserting that nature cannot do a
thing because we cannot conceive it done, goes the still greater length
of averring that nature does a particular thing, on the sole ground that
we can see no reason why she should not. Absurd as this seems when so
plainly stated, it is a received principle among scientific authorities
for demonstrating _à priori_ the laws of physical phenomena. A
phenomenon must follow a certain law, because we see no reason why it
should deviate from that law in one way rather than in another. This is
called the Principle of the Sufficient Reason;[10] and by means of it
philosophers often flatter themselves that they are able to establish,
without any appeal to experience, the most general truths of
experimental physics.

Take, for example, two of the most elementary of all laws, the law of
inertia and the first law of motion. A body at rest cannot, it is
affirmed, begin to move unless acted upon by some external force:
because, if it did, it must either move up or down, forward or backward,
and so forth; but if no outward force acts upon it, there can be _no
reason_ for its moving up rather than down, or down rather than up, &c.,
_ergo_, it will not move at all.

This reasoning I conceive to be entirely fallacious, as indeed Dr.
Brown, in his treatise on Cause and Effect, has shown with great
acuteness and justness of thought. We have before remarked, that almost
every fallacy may be referred to different genera by different modes of
filling up the suppressed steps; and this particular one may, at our
option, be brought under _petitio principii_. It supposes that nothing
can be a "sufficient reason" for a body's moving in one particular
direction, except some external force. But this is the very thing to be
proved. Why not some _internal_ force? Why not the law of the thing's
own nature? Since these philosophers think it necessary to prove the law
of inertia, they of course do not suppose _it_ to be self-evident; they
must, therefore, be of opinion that, previously to all proof, the
supposition of a body's moving by internal impulse is an admissible
hypothesis; but if so, why is not the hypothesis also admissible, that
the internal impulse acts naturally in some one particular direction,
not in another? If spontaneous motion might have been the law of matter,
why not spontaneous motion towards the sun, towards the earth, or
towards the zenith? Why not, as the ancients supposed, towards a
particular place in the universe, appropriated to each particular kind
of substance? Surely it is not allowable to say that spontaneity of
motion is credible in itself, but not credible if supposed to take place
in any determinate direction.

Indeed, if any one chose to assert that all bodies when uncontrolled set
out in a direct line towards the north pole, he might equally prove his
point by the principle of the Sufficient Reason. By what right is it
assumed that a state of rest is the particular state which cannot be
deviated from without special cause? Why not a state of motion, and of
some particular sort of motion? Why may we not say that the natural
state of a horse left to himself is to amble, because otherwise he must
either trot, gallop, or stand still, and because we know no reason why
he should do one of these rather than another? If this is to be called
an unfair use of the "sufficient reason," and the other a fair one,
there must be a tacit assumption that a state of rest is more natural to
a horse than a state of ambling. If this means that it is the state
which the animal will assume when left to himself, that is the very
point to be proved; and if it does not mean this, it can only mean that
a state of rest is the simplest state, and therefore the most likely to
prevail in nature, which is one of the fallacies or natural prejudices
we have already examined.

So again of the First Law of Motion; that a body once moving will, if
left to itself, continue to move uniformly in a straight line. An
attempt is made to prove this law by saying, that if not, the body must
deviate either to the right or to the left, and that there is no reason
why it should do one more than the other. But who could know,
antecedently to experience, whether there was a reason or not? Might it
not be the nature of bodies, or of some particular bodies, to deviate
towards the right? or if the supposition is preferred, towards the east,
or south? It was long thought that bodies, terrestrial ones at least,
had a natural tendency to deflect downwards; and there is no shadow of
anything objectionable in the supposition, except that it is not true.
The pretended proof of the law of motion is even more manifestly
untenable than that of the law of inertia, for it is flagrantly
inconsistent; it assumes that the continuance of motion in the direction
first taken is more natural than deviation either to the right or to the
left, but denies that one of these can possibly be more natural than the
other. All these fancies of the possibility of knowing what is natural
or not natural by any other means than experience, are, in truth,
entirely futile. The real and only proof of the laws of motion, or of
any other law of the universe, is experience; it is simply that no
other suppositions explain or are consistent with the facts of universal

Geometers have, in all ages, been open to the imputation of endeavouring
to prove the most general facts of the outward world by sophistical
reasoning, in order to avoid appeals to the senses. Archimedes, says
Professor Playfair,[11] established some of the elementary propositions
of statics by a process in which he "borrows no principle from
experiment, but establishes his conclusion entirely by reasoning _à
priori_. He assumes, indeed, that equal bodies, at the ends of the equal
arms of a lever, will balance one another; and also that a cylinder or
parallelopiped of homogeneous matter, will be balanced about its centre
of magnitude. These, however, are not inferences from experience; they
are, properly speaking, conclusions deduced from the principle of the
Sufficient Reason." And to this day there are few geometers who would
not think it far more scientific to establish these or any other
premises in this way, than to rest their evidence on that familiar
experience which in the case in question might have been so safely
appealed to.

§ 6. Another natural prejudice, of most extensive prevalence, and which
had a great share in producing the errors fallen into by the ancients in
their physical inquiries, was this: That the differences in nature must
correspond to our received distinctions; that effects which we are
accustomed, in popular language, to call by different names, and arrange
in different classes, must be of different natures, and have different
causes. This prejudice, so evidently of the same origin with those
already treated of, marks more especially the earliest stage of science,
when it has not yet broken loose from the trammels of every-day
phraseology. The extraordinary prevalence of the fallacy among the Greek
philosophers may be accounted for by their generally knowing no other
language than their own; from which it was a consequence that their
ideas followed the accidental or arbitrary combinations of that
language, more completely than can happen among the moderns to any but
illiterate persons. They had great difficulty in distinguishing between
things which their language confounded, or in putting mentally together
things which it distinguished; and could hardly combine the objects in
nature, into any classes but those which were made for them by the
popular phrases of their own country: or at least could not help
fancying those classes to be natural, and all others arbitrary and
artificial. Accordingly, scientific investigation among the Greek
schools of speculation and their followers in the middle ages, was
little more than a mere sifting and analysing of the notions attached to
common language. They thought that by determining the meaning of words,
they could become acquainted with facts. "They took for granted," says
Dr. Whewell,[12] "that philosophy must result from the relations of
those notions which are involved in the common use of language, and they
proceeded to seek it by studying such notions." In his next chapter, Dr.
Whewell has so well illustrated and exemplified this error, that I shall
take the liberty of quoting him at some length.

"The propensity to seek for principles in the common usages of language
may be discerned at a very early period. Thus we have an example of it
in a saying which is reported of Thales, the founder of Greek
philosophy. When he was asked, 'What is the _greatest_ thing?' he
replied '_Place_; for all other things are _in_ the world, but the world
is _in_ it.' In Aristotle we have the consummation of this mode of
speculation. The usual point from which he starts in his inquiries is,
that _we say_ thus or thus in common language. Thus, when he has to
discuss the question whether there be, in any part of the universe, a
void, or space in which there is nothing, he inquires first in how many
senses we say that one thing is _in_ another. He enumerates many of
these; we say the part is in the whole, as the finger is _in_ the hand;
again we say, the species is in the genus, as man is included _in_
animal; again, the government of Greece is _in_ the king; and various
other senses are described and exemplified, but of all these _the most
proper_ is when we say a thing is _in_ a vessel, and generally _in
place_. He next examines what _place_ is, and comes to this conclusion,
that 'if about a body there be another body including it, it is in
place, and if not, not.' A body moves when it changes its place; but he
adds, that if water be in a vessel, the vessel being at rest, the parts
of the water may still move, for they are included by each other; so
that while the whole does not change its place, the parts may change
their place in a circular order. Proceeding then to the question of a
_void_, he as usual examines the different senses in which the term is
used, and adopts as the most proper, _place without matter_: with no
useful result.

"Again, in a question concerning mechanical action, he says, 'When a man
moves a stone by pushing it with a stick, _we say_ both that the man
moves the stone, and that the stick moves the stone, but the latter
_more properly_.'

"Again, we find the Greek philosophers applying themselves to extract
their dogmas from the most general and abstract notions which they could
detect; for example, from the conception of the Universe as One or as
Many things. They tried to determine how far we may, or must, combine
with these conceptions that of a whole, of parts, of number, of limits,
of place, of beginning or end, of full or void, of rest, or motion, of
cause and effect, and the like. The analysis of such conceptions with
such a view, occupies, for instance, almost the whole of Aristotle's
Treatise on the Heavens."

The following paragraph merits particular attention:--"Another mode of
reasoning, very widely applied in these attempts, was the _doctrine of
contrarieties_, in which it was assumed, that adjectives or substances
which are in common language, or in some abstract mode of conception,
opposed to each other, must point at some fundamental antithesis in
nature, which it is important to study. Thus Aristotle says that the
Pythagoreans, from the contrasts which number suggests, collected ten
principles--Limited and Unlimited, Odd and Even, One and Many, Right and
Left, Male and Female, Rest and Motion, Straight and Curved, Light and
Darkness, Good and Evil, Square and Oblong.... Aristotle himself deduced
the doctrine of four elements and other dogmas by oppositions of the
same kind."

Of the manner in which, from premises obtained in this way, the ancients
attempted to deduce laws of nature, an example is given in the same work
a few pages further on. "Aristotle decides that there is no void, on
such arguments as this. In a void there could be no difference of up and
down; for as in nothing there are no differences, so there are none in a
privation or negation; but a void is merely a privation or negation of
matter; therefore, in a void, bodies could not move up and down, which
it is in their nature to do. It is easily seen" (Dr. Whewell very justly
adds) "that such a mode of reasoning elevates the familiar forms of
language, and the intellectual connexions of terms, to a supremacy over
facts; making truth depend upon whether terms are or are not privative,
and whether we say that bodies fall _naturally_."

The propensity to assume that the same relations obtain between objects
themselves, which obtain between our ideas of them, is here seen in the
extreme stage of its development. For the mode of philosophizing,
exemplified in the foregoing instances, assumes no less than that the
proper way of arriving at knowledge of nature, is to study nature itself
subjectively; to apply our observation and analysis not to the facts,
but to the common notions entertained of the facts.

Many other equally striking examples may be given of the tendency to
assume that things which for the convenience of common life are placed
in different classes, must differ in every respect. Of this nature was
the universal and deeply-rooted prejudice of antiquity and the middle
ages, that celestial and terrestrial phenomena must be essentially
different, and could in no manner or degree depend on the same laws. Of
the same kind, also, was the prejudice against which Bacon contended,
that nothing produced by nature could be successfully imitated by man:
"Calorem solis et ignis toto genere differre; ne scilicet homines
putent se per opera ignis, aliquid simile iis quæ in Natura fiunt,
educere et formare posse:" and again, "Compositionem tantum opus
Hominis, Mistionem vero opus solius Naturæ esse: ne scilicet homines
sperent aliquam ex arte Corporum naturalium generationem aut
transformationem."[13] The grand distinction in the ancient scientific
speculations, between natural and violent motions, though not without a
plausible foundation in the appearances themselves, was doubtless
greatly recommended to adoption by its conformity to this prejudice.

§ 7. From the fundamental error of the scientific inquirers of
antiquity, we pass, by a natural association, to a scarcely less
fundamental one of their great rival and successor, Bacon. It has
excited the surprise of philosophers that the detailed system of
inductive logic, which this extraordinary man laboured to construct, has
been turned to so little direct use by subsequent inquirers, having
neither continued, except in a few of its generalities, to be recognised
as a theory, nor having conducted in practice to any great scientific
results. But this, though not unfrequently remarked, has scarcely
received any plausible explanation; and some, indeed, have preferred to
assert that all rules of induction are useless, rather than suppose that
Bacon's rules are grounded on an insufficient analysis of the inductive
process. Such, however, will be seen to be the fact, as soon as it is
considered, that Bacon entirely overlooked Plurality of Causes. All his
rules tacitly imply the assumption, so contrary to all we now know of
nature, that a phenomenon cannot have more than one cause.

When he is inquiring into what he terms the _forma calidi aut frigidi_,
_gravis aut levis_, _sicci aut humidi_, and the like, he never for an
instant doubts that there is some one thing, some invariable condition
or set of conditions, which is present in all cases of heat, or cold, or
whatever other phenomenon he is considering; the only difficulty being
to find what it is; which accordingly he tries to do by a process of
elimination, rejecting or excluding, by negative instances, whatever is
not the _forma_ or cause, in order to arrive at what is. But, that this
_forma_ or cause is _one_ thing, and that it is the same in all hot
objects, he has no more doubt of, than another person has that there is
always some cause _or other_. In the present state of knowledge it could
not be necessary, even if we had not already treated so fully of the
question, to point out how widely this supposition is at variance with
the truth. It is particularly unfortunate for Bacon that, falling into
this error, he should have fixed almost exclusively upon a class of
inquiries in which it was especially fatal; namely, inquiries into the
causes of the sensible qualities of objects. For his assumption,
groundless in every case, is false in a peculiar degree with respect to
those sensible qualities. In regard to scarcely any of them has it been
found possible to trace any unity of cause, any set of conditions
invariably accompanying the quality. The conjunctions of such qualities
with one another constitute the variety of Kinds, in which, as already
remarked, it has not been found possible to trace any law. Bacon was
seeking for what did not exist. The phenomenon of which he sought for
the one cause has oftenest no cause at all, and when it has, depends (as
far as hitherto ascertained) on an unassignable variety of distinct

And on this rock every one must split, who represents to himself as the
first and fundamental problem of science to ascertain what is the cause
of a given effect, rather than what are the effects of a given cause. It
was shown, in an early stage of our inquiry into the nature of
Induction,[14] how much more ample are the resources which science
commands for the latter than for the former inquiry, since it is upon
the latter only that we can throw any direct light by means of
experiment; the power of artificially producing an effect, implying a
previous knowledge of at least one of its causes. If we discover the
causes of effects, it is generally by having previously discovered the
effects of causes: the greatest skill in devising crucial instances for
the former purpose may only end, as Bacon's physical inquiries did, in
no result at all. Was it that his eagerness to acquire the power of
producing for man's benefit effects of practical importance to human
life, rendering him impatient of pursuing that end by a circuitous
route, made even him, the champion of experiment, prefer the direct
mode, though one of mere observation, to the indirect, in which alone
experiment was possible? Or had even Bacon not entirely cleared his mind
from the notion of the ancients, that "rerum cognoscere _causas_" was
the sole object of philosophy, and that to inquire into the _effects_ of
things belonged to servile and mechanical arts?

It is worth remarking that, while the only efficient mode of cultivating
speculative science was missed from an undue contempt of manual
operations, the false speculative views thus engendered gave in their
turn a false direction to such practical and mechanical aims as were
suffered to exist. The assumption universal among the ancients and in
the middle ages, that there were _principles_ of heat and cold, dryness
and moisture, &c., led directly to a belief in alchemy; in a
transmutation of substances, a change from one Kind into another. Why
should it not be possible to make gold? Each of the characteristic
properties of gold has its _forma_, its essence, its set of conditions,
which if we could discover, and learn how to realize, we could
superinduce that particular property upon any other substance, upon
wood, or iron, or lime, or clay. If, then, we could effect this with
respect to every one of the essential properties of the precious metal,
we should have converted the other substance into gold. Nor did this, if
once the premises were granted, appear to transcend the real powers of
mankind. For daily experience showed that almost every one of the
distinctive sensible properties of any object, its consistence, its
colour, its taste, its smell, its shape, admitted of being totally
changed by fire, or water, or some other chemical agent. The _formæ_ of
all those qualities seeming, therefore, to be within human power either
to produce or to annihilate, not only did the transmutation of
substances appear abstractedly possible, but the employment of the
power, at our choice, for practical ends, seemed by no means

A prejudice, universal in the ancient world, and from which Bacon was so
far from being free, that it pervaded and vitiated the whole practical
part of his system of logic, may with good reason be ranked high in the
order of Fallacies of which we are now treating.

§ 8. There remains one _à priori_ fallacy or natural prejudice, the most
deeply-rooted, perhaps, of all which we have enumerated: one which not
only reigned supreme in the ancient world, but still possesses almost
undisputed dominion over many of the most cultivated minds; and some of
the most remarkable of the numerous instances by which I shall think it
necessary to exemplify it, will be taken from recent thinkers. This is,
that the conditions of a phenomenon must, or at least probably will,
resemble the phenomenon itself.

Conformably to what we have before remarked to be of frequent
occurrence, this fallacy might without much impropriety have been placed
in a different class, among Fallacies of Generalization: for experience
does afford a certain degree of countenance to the assumption. The cause
does, in very many cases, resemble its effect; like produces like. Many
phenomena have a direct tendency to perpetuate their own existence, or
to give rise to other phenomena similar to themselves. Not to mention
forms actually moulded on one another, as impressions on wax and the
like, in which the closest resemblance between the effect and its cause
is the very law of the phenomenon; all motion tends to continue itself,
with its own velocity, and in its own original direction; and the motion
of one body tends to set others in motion, which is indeed the most
common of the modes in which the motions of bodies originate. We need
scarcely refer to contagion, fermentation, and the like; or to the
production of effects by the growth or expansion of a germ or rudiment
resembling on a smaller scale the completed phenomenon, as in the growth
of a plant or animal from an embryo, that embryo itself deriving its
origin from another plant or animal of the same kind. Again, the
thoughts, or reminiscences, which are effects of our past sensations,
resemble those sensations; feelings produce similar feelings by way of
sympathy; acts produce similar acts by involuntary or voluntary
imitation. With so many appearances in its favour, no wonder if a
presumption naturally grew up, that causes must _necessarily_ resemble
their effects, and that like could _only_ be produced by like.

This principle of fallacy has usually presided over the fantastical
attempts to influence the course of nature by conjectural means, the
choice of which was not directed by previous observation and experiment.
The guess almost always fixed upon some means which possessed features
of real or apparent resemblance to the end in view. If a charm was
wanted, as by Ovid's Medea, to prolong life, all long-lived animals, or
what were esteemed such, were collected and brewed into a broth:--

             ... nec defuit illic
     Squamea Cinyphii tenuis membrana chelydri
     Vivacisque jecur cervi: quibus insuper addit
     Ora caputque novem cornicis sæcula passæ.

A similar notion was embodied in the celebrated medical theory called
the "Doctrine of Signatures," "which is no less," says Dr. Paris,[16]
"than a belief that every natural substance which possesses any
medicinal virtue indicates by an obvious and well-marked external
character the disease for which it is a remedy, or the object for which
it should be employed." This outward character was generally some
feature of resemblance, real or fantastical, either to the effect it
was supposed to produce, or to the phenomenon over which its power was
thought to be exercised. "Thus the lungs of a fox must be a specific for
asthma, because that animal is remarkable for its strong powers of
respiration. Turmeric has a brilliant yellow colour, which indicates
that it has the power of curing the jaundice; for the same reason,
poppies must relieve diseases of the head; Agaricus those of the
bladder; _Cassia fistula_ the affections of the intestines, and
Aristolochia the disorders of the uterus: the polished surface and stony
hardness which so eminently characterize the seeds of the Lithospermum
officinale (common gromwell) were deemed a certain indication of their
efficacy in calculous and gravelly disorders; for a similar reason, the
roots of the Saxifraga granulata (white saxifrage) gained reputation in
the cure of the same disease; and the Euphrasia (eye-bright) acquired
fame, as an application in complaints of the eye, because it exhibits a
black spot in its corolla resembling the pupil. The blood-stone, the
Heliotropium of the ancients, from the occasional small specks or points
of a blood-red colour exhibited on its green surface, is even at this
very day employed in many parts of England and Scotland, to stop a
bleeding from the nose; and nettle tea continues a popular remedy for
the cure of _Urticaria_. It is also asserted that some substances bear
the _signatures_ of the humours, as the petals of the red rose that of
the blood, and the roots of rhubarb and the flowers of saffron that of
the bile."

The early speculations respecting the chemical composition of bodies
were rendered abortive by no circumstance more, than by their invariably
taking for granted that the properties of the elements must resemble
those of the compounds which were formed from them.

To descend to more modern instances; it was long thought, and was
stoutly maintained by the Cartesians and even by Leibnitz against the
Newtonian system, (nor did Newton himself, as we have seen, contest the
assumption, but eluded it by an arbitrary hypothesis), that nothing (of
a physical nature at least) could account for motion, except previous
motion; the impulse or impact of some other body. It was very long
before the scientific world could prevail upon itself to admit
attraction and repulsion (_i. e._ spontaneous tendencies of particles to
approach or recede from one another) as ultimate laws, no more requiring
to be accounted for than impulse itself, if indeed the latter were not,
in truth, resolvable into the former. From the same source arose the
innumerable hypotheses devised to explain those classes of motions which
appeared more mysterious than others because there was no obvious mode
of attributing them to impulse, as for example the voluntary motions of
the human body. Such were the interminable systems of vibrations
propagated along the nerves, or animal spirits rushing up and down
between the muscles and the brain; which, if the facts could have been
proved, would have been an important addition to our knowledge of
physiological laws; but the mere invention, or arbitrary supposition of
them, could not unless by the strongest delusion be supposed to render
the phenomena of animal life more comprehensible, or less mysterious.
Nothing, however, seemed satisfactory, but to make out that motion was
caused by motion; by something like itself. If it was not one kind of
motion, it must be another. In like manner it was supposed that the
physical qualities of objects must arise from some similar quality, or
perhaps only some quality bearing the same name, in the particles or
atoms of which the objects were composed; that a sharp taste, for
example, must arise from sharp particles. And reversing the inference,
the effects produced by a phenomenon must, it was supposed, resemble in
their physical attributes the phenomenon itself. The influences of the
planets were supposed to be analogous to their visible peculiarities:
Mars, being of a red colour, portended fire and slaughter; and the like.

Passing from physics to metaphysics, we may notice among the most
remarkable fruits of this _à priori_ fallacy, two closely analogous
theories, employed in ancient and modern times to bridge over the chasm
between the world of mind and that of matter: the _species sensibiles_
of the Epicureans, and the modern doctrine of perception by means of
ideas. These theories are indeed, probably, indebted for their existence
not solely to the fallacy in question, but to that fallacy combined
with another natural prejudice already adverted to, that a thing cannot
act where it is not. In both doctrines it is assumed that the phenomenon
which takes place _in us_ when we see or touch an object, and which we
regard as an effect of that object, or rather as its presence to our
organs, must of necessity resemble very closely the outward object
itself. To fulfil this condition, the Epicureans supposed that objects
were constantly projecting in all directions impalpable images of
themselves, which entered at the eyes and penetrated to the mind; while
modern metaphysicians, though they rejected this hypothesis, agreed in
deeming it necessary to suppose that not the thing itself, but a mental
image or representation of it, was the direct object of perception. Dr.
Reid had to employ a world of argument and illustration to familiarize
people with the truth, that the sensations or impressions on our minds
need not necessarily be copies of, or bear any resemblance to, the
causes which produce them; in opposition to the natural prejudice which
led people to assimilate the action of bodies upon our senses, and
through them upon our minds, to the transfer of a given form from one
object to another by actual moulding. The works of Dr. Reid are even now
the most effectual course of study for detaching the mind from the
prejudice of which this was an example. And the value of the service
which he thus rendered to popular philosophy, is not much diminished
although we may hold, with Brown, that he went too far in imputing the
"ideal theory" as an actual tenet, to the generality of the philosophers
who preceded him, and especially to Locke and Hume: for if they did not
themselves consciously fall into the error, unquestionably they often
led their readers into it.

The prejudice, that the conditions of a phenomenon must resemble the
phenomenon, is occasionally exaggerated, at least verbally, into a still
more palpable absurdity; the conditions of the thing are spoken of as if
they _were_ the very thing itself. In Bacon's model-inquiry, which
occupies so great a space in the _Novum Organum_, the _inquisitio in
formam calidi_, the conclusion which he favours is that heat is a kind
of motion; meaning of course not the feeling of heat, but the
conditions of the feeling; meaning, therefore, only that wherever there
is heat, there must first be a particular kind of motion; but he makes
no distinction in his language between these two ideas, expressing
himself as if heat, and the conditions of heat, were one and the same
thing. So Darwin, in the beginning of his _Zoonomia_, says, "The word
_idea_ has various meanings in the writers of metaphysic: it is here
used simply for those notions of external things which our organs of
sense bring us acquainted with originally," (thus far the proposition,
though vague, is unexceptionable in meaning,) "and is defined a
contraction, a motion, or configuration, of the fibres which constitute
the immediate organ of sense." Our _notions_, a configuration of the
fibres! What kind of logician must he be who thinks that a phenomenon is
_defined_ to _be_ the condition on which he supposes it to depend?
Accordingly he says soon after, not that our ideas are caused by, or
consequent on, certain organic phenomena, but "our ideas _are_ animal
motions of the organs of sense." And this confusion runs through the
four volumes of the _Zoonomia_; the reader never knows whether the
writer is speaking of the effect, or of its supposed cause; of the idea,
a state of mental consciousness, or of the state of the nerves and brain
which he considers it to presuppose.

I have given a variety of instances in which the natural prejudice, that
causes and their effects must resemble one another, has operated in
practice so as to give rise to serious errors. I shall now go further,
and produce from writings even of the present or very recent times,
instances in which this prejudice is laid down as an established
principle. M. Victor Cousin, in the last of his celebrated lectures on
Locke, enunciates the maxim in the following unqualified terms. "Tout ce
qui est vrai de l'effet est vrai de la cause." A doctrine to which,
unless in some peculiar and technical meaning of the words cause and
effect, it is not to be imagined that any person would literally adhere:
but he who could so write must be far enough from seeing, that the very
reverse might be the fact; that there is nothing impossible in the
supposition that no one property which is true of the effect might be
true of the cause. Without going quite so far in point of expression,
Coleridge, in his _Biographia Literaria_,[17] affirms as an "evident
truth," that "the law of causality holds only between homogeneous
things, _i. e._ things having some common property," and therefore
"cannot extend from one world into another, its opposite:" hence, as
mind and matter have no common property, mind cannot act upon matter,
nor matter upon mind. What is this but the _à priori_ fallacy of which
we are speaking? The doctrine, like many others of Coleridge, is taken
from Spinoza, in the first book of whose _Ethica (De Deo)_ it stands as
the Third Proposition, "Quæ res nihil commune inter se habent, earum una
alterius causa esse non potest," and is there proved from two so-called
axioms, equally gratuitous with itself: but Spinoza, ever systematically
consistent, pursued the doctrine to its inevitable consequence, the
materiality of God.

The same conception of impossibility led the ingenious and subtle mind
of Leibnitz to his celebrated doctrine of a pre-established harmony. He,
too, thought that mind could not act upon matter, nor matter upon mind,
and that the two, therefore, must have been arranged by their Maker like
two clocks, which, though unconnected with one another, strike
simultaneously, and always point to the same hour. Malebranche's equally
famous theory of Occasional Causes was another form of the same
conception: instead of supposing the clocks originally arranged to
strike together, he held that when the one strikes, God interposes, and
makes the other strike in correspondence with it.

Descartes, in like manner, whose works are a rich mine of almost every
description of _à priori_ fallacy, says that the Efficient Cause must at
least have all the perfections of the effect, and for this singular
reason: "Si enim ponamus aliquid in ideâ reperiri quod non fuerit in
ejus causâ, hoc igitur habet a nihilo;" of which it is scarcely a parody
to say, that if there be pepper in the soup there must be pepper in the
cook who made it, since otherwise the pepper would be without a cause. A
similar fallacy is committed by Cicero in his second book _De Finibus_,
where, speaking in his own person against the Epicureans, he charges
them with inconsistency in saying that the pleasures of the mind had
their origin from those of the body, and yet that the former were more
valuable, as if the effect could surpass the cause. "Animi voluptas
oritur propter voluptatem corporis, et major est animi voluptas quam
corporis? ita fit ut gratulator lætior sit quam is cui gratulatur." Even
that, surely, is not an impossibility: a person's good fortune has often
given more pleasure to others than it gave to the person himself.

Descartes, with no less readiness, applies the same principle the
converse way, and infers the nature of the effects from the assumption
that they must, in this or that property or in all their properties,
resemble their cause. To this class belong his speculations, and those
of so many others after him, tending to infer the order of the universe,
not from observation, but by _à priori_ reasoning from supposed
qualities of the Godhead. This sort of inference was probably never
carried to a greater length than it was in one particular instance by
Descartes, when, as a proof of one of his physical principles, that the
quantity of motion in the universe is invariable, he had recourse to the
immutability of the Divine Nature. Reasoning of a very similar character
is however nearly as common now as it was in his time, and does duty
largely as a means of fencing off disagreeable conclusions. Writers have
not yet ceased to oppose the theory of divine benevolence to the
evidence of physical facts, to the principle of population for example.
And people seem in general to think that they have used a very powerful
argument, when they have said, that to suppose some proposition true,
would be a reflection on the goodness or wisdom of the Deity. Put into
the simplest possible terms, their argument is, "If it had depended on
me, I would not have made the proposition true, therefore it is not
true." Put into other words it stands thus: "God is perfect, therefore
(what I think) perfection must obtain in nature." But since in reality
every one feels that nature is very far from perfect, the doctrine is
never applied consistently. It furnishes an argument which (like many
others of a similar character) people like to appeal to when it makes
for their own side. Nobody is convinced by it, but each appears to think
that it puts religion on his side of the question, and that it is a
useful weapon of offence for wounding an adversary.

Although several other varieties of _à priori_ fallacy might probably be
added to those here specified, these are all against which it seems
necessary to give any special caution. Our object is to open, without
attempting or affecting to exhaust, the subject. Having illustrated,
therefore, this first class of Fallacies at sufficient length, I shall
proceed to the second.



§ 1. From the fallacies which are properly Prejudices, or presumptions
antecedent to, and superseding, proof, we pass to those which lie in the
incorrect performance of the proving process. And as Proof, in its
widest extent, embraces one or more, or all, of three processes,
Observation, Generalization, and Deduction; we shall consider in their
order the errors capable of being committed in these three operations.
And first, of the first mentioned.

A fallacy of misobservation may be either negative or positive; either
Non-observation or Mal-observation. It is non-observation, when all the
error consists in overlooking, or neglecting, facts or particulars which
ought to have been observed. It is mal-observation, when something is
not simply unseen, but seen wrong; when the fact or phenomenon, instead
of being recognised for what it is in reality, is mistaken for something

§ 2. Non-observation may either take place by overlooking instances, or
by overlooking some of the circumstances of a given instance. If we were
to conclude that a fortune-teller was a true prophet, from not adverting
to the cases in which his predictions had been falsified by the event,
this would be non-observation of instances; but if we overlooked or
remained ignorant of the fact that in cases where the predictions had
been fulfilled, he had been in collusion with some one who had given him
the information on which they were grounded, this would be
non-observation of circumstances.

The former case, in so far as the act of induction from insufficient
evidence is concerned, does not fall under this second class of
Fallacies, but under the third, Fallacies of Generalization. In every
such case, however, there are two defects or errors instead of one:
there is the error of treating the insufficient evidence as if it were
sufficient, which is a Fallacy of the third class; and there is the
insufficiency itself; the not having better evidence; which, when such
evidence, or in other words, when other instances, were to be had, is
Non-observation: and the erroneous inference, so far as it is to be
attributed to this cause, is a Fallacy of the second class.

It belongs not to our purpose to treat of non-observation as arising
from casual inattention, from general slovenliness of mental habits,
want of due practice in the use of the observing faculties, or
insufficient interest in the subject. The question pertinent to logic
is--Granting the want of complete competency in the observer, on what
points is that insufficiency on his part likely to lead him wrong? or
rather, what sorts of instances, or of circumstances in any given
instance, are most likely to escape the notice of observers generally;
of mankind at large.

§ 3. First, then, it is evident that when the instances on one side of a
question are more likely to be remembered and recorded than those on the
other; especially if there be any strong motive to preserve the memory
of the first, but not of the latter; these last are likely to be
overlooked, and escape the observation of the mass of mankind. This is
the recognised explanation of the credit given, in spite of reason and
evidence, to many classes of impostors: to quack doctors, and
fortune-tellers in all ages; to the "cunning man" of modern times and
the oracles of old. Few have considered the extent to which this fallacy
operates in practice, even in the teeth of the most palpable negative
evidence. A striking example of it is the faith which the uneducated
portion of the agricultural classes, in this and other countries,
continue to repose in the prophecies as to weather supplied by almanac
makers: though every season affords to them numerous cases of
completely erroneous prediction; but as every season also furnishes some
cases in which the prediction is fulfilled, this is enough to keep up
the credit of the prophet, with people who do not reflect on the number
of instances requisite for what we have called, in our inductive
terminology, the Elimination of Chance; since a certain number of casual
coincidences not only may but will happen, between any two unconnected

Coleridge, in one of the essays in the _Friend_, has illustrated the
matter we are now considering, in discussing the origin of a proverb,
"which, differently worded, is to be found in all the languages of
Europe," viz. "Fortune favours fools." He ascribes it partly to the
"tendency to exaggerate all effects that seem disproportionate to their
visible cause, and all circumstances that are in any way strongly
contrasted with our notions of the persons under them." Omitting some
explanations which would refer the error to mal-observation, or to the
other species of non-observation (that of circumstances), I take up the
quotation farther on. "Unforeseen coincidences may have greatly helped a
man, yet if they have done for him only what possibly from his own
abilities he might have effected for himself, his good luck will excite
less attention, and the instances be less remembered. That clever men
should attain their objects seems natural, and we neglect the
circumstances that perhaps produced that success of themselves, without
the intervention of skill or foresight; but we dwell on the fact and
remember it, as something strange, when the same happens to a weak or
ignorant man. So too, though the latter should fail in his undertakings
from concurrences that might have happened to the wisest man, yet his
failure being no more than might have been expected and accounted for
from his folly, it lays no hold on our attention, but fleets away among
the other undistinguished waves in which the stream of ordinary life
murmurs by us, and is forgotten. Had it been as true as it was
notoriously false, that those all-embracing discoveries, which have shed
a dawn of _science_ on the _art_ of chemistry, and give no obscure
promise of some one great constitutive law, in the light of which dwell
dominion and the power of prophecy; if these discoveries, instead of
having been, as they really were, preconcerted by meditation, and
evolved out of his own intellect, had occurred by a set of lucky
_accidents_ to the illustrious father and founder of philosophic
alchemy; if they had presented themselves to Professor Davy exclusively
in consequence of his _luck_ in possessing a particular galvanic
battery; if this battery, as far as Davy was concerned, had itself been
an _accident_, and not (as in point of fact it was) desired and obtained
by him for the purpose of ensuring the testimony of experience to his
principles, and in order to bind down material nature under the
inquisition of reason, and force from her, as by torture, unequivocal
answers to _prepared_ and _preconceived_ questions,--yet still they
would not have been talked of or described as instances of _luck_, but
as the natural results of his admitted genius and known skill. But
should an accident have disclosed similar discoveries to a mechanic at
Birmingham or Sheffield, and if the man should grow rich in consequence,
and partly by the envy of his neighbours and partly with good reason, be
considered by them as a man _below par_ in the general powers of his
understanding; then, 'O what a lucky fellow! Well, Fortune _does_ favour
fools--that's for certain!--It is always so!' And forthwith the
exclaimer relates half a dozen similar instances. Thus accumulating the
one sort of facts and never collecting the other, we do, as poets in
their diction, and quacks of all denominations do in their reasoning,
put a part for the whole."

This passage very happily sets forth the manner in which, under the
loose mode of induction which proceeds _per enumerati onem simplicem_,
not seeking for instances of such a kind as to be decisive of the
question, but generalizing from any which occur, or rather which are
remembered, opinions grow up with the apparent sanction of experience,
which have no foundation in the laws of nature at all. "Itaque recte
respondit ille," (we may say with Bacon,[18]) "qui cum suspensa tabula
in templo ei monstraretur eorum, qui vota solverant, quod naufragii
periculo elapsi sint, atque interrogando premeretur, anne tum quidem
Deorum numen agnosceret, quæsivit denuo, _At ubi sunt illi depicti qui
post vota nuncupata perierunt?_ Eadem ratio est fere omnis
superstitionis, ut in Astrologicis, in Somniis, Ominibus, Nemesibus, et
hujusmodi; in quibus, homines delectati hujusmodi vanitatibus, advertunt
eventus, ubi implentur; ast ubi fallunt, licet multo frequentius, tamen
negligunt, et prætereunt." And he proceeds to say, that independently of
the love of the marvellous, or any other bias in the inclinations, there
is a natural tendency in the intellect itself to this kind of fallacy;
since the mind is more moved by affirmative instances, though negative
ones are of most use in philosophy; "Is tamen humano intellectui error
est proprius et perpetuus, ut magis moveatur et excitetur Affirmativis
quam Negativis; cum rite et ordine æquum se utrique præbere debeat; quin
contra, in omni Axiomate vero constituendo, major vis est instantiæ

But the greatest of all causes of non-observation is a preconceived
opinion. This it is which, in all ages, has made the whole race of
mankind, and every separate section of it, for the most part unobservant
of all facts, however abundant, even when passing under their own eyes,
which are contradictory to any first appearance, or any received tenet.
It is worth while to recal occasionally to the oblivious memory of
mankind some of the striking instances in which opinions that the
simplest experiment would have shown to be erroneous, continued to be
entertained because nobody ever thought of trying that experiment. One
of the most remarkable of these was exhibited in the Copernican
controversy. The opponents of Copernicus argued that the earth did not
move, because if it did, a stone let fall from the top of a high tower
would not reach the ground at the foot of the tower, but at a little
distance from it, in a contrary direction to the earth's course; in the
same manner (said they) as, if a ball is let drop from the mast-head
while the ship is in full sail, it does not fall exactly at the foot of
the mast, but nearer to the stern of the vessel. The Copernicans would
have silenced these objectors at once if they had _tried_ dropping a
ball from the mast-head, since they would have found that it does fall
exactly at the foot, as the theory requires: but no; they admitted the
spurious fact, and struggled vainly to make out a difference between the
two cases. "The ball was no _part_ of the ship--and the motion forward
was not _natural_, either to the ship or to the ball. The stone, on the
other hand, let fall from the top of the tower, was a _part_ of the
earth; and therefore, the diurnal and annular revolutions which were
_natural_ to the earth, were also _natural_ to the stone: the stone
would, therefore, retain the same motion with the tower, and strike the
ground precisely at the bottom of it."[19]

Other examples, scarcely less striking, are recorded by Dr. Whewell,[20]
where imaginary laws of nature have continued to be received as real,
merely because no person had steadily looked at facts which almost every
one had the opportunity of observing. "A vague and loose mode of looking
at facts very easily observable, left men for a long time under the
belief that a body ten times as heavy as another falls ten times as
fast; that objects immersed in water are always magnified, without
regard to the form of the surface; that the magnet exerts an
irresistible force; that crystal is always found associated with ice;
and the like. These and many others are examples how blind and careless
man can be even in observation of the plainest and commonest
appearances; and they show us that the mere faculties of perception,
although constantly exercised upon innumerable objects, may long fail in
leading to any exact knowledge."

If even on physical facts, and these of the most obvious character, the
observing faculties of mankind can be to this degree the passive slaves
of their preconceived impressions, we need not be surprised that this
should be so lamentably true as all experience attests it to be, on
things more nearly connected with their stronger feelings--on moral,
social, and religious subjects. The information which an ordinary
traveller brings back from a foreign country, as the result of the
evidence of his senses, is almost always such as exactly confirms the
opinions with which he set out. He has had eyes and ears for such things
only as he expected to see. Men read the sacred books of their religion,
and pass unobserved therein, multitudes of things utterly
irreconcileable with even their own notions of moral excellence. With
the same authorities before them, different historians, alike innocent
of intentional misrepresentation, see only what is favourable to
Protestants or Catholics, royalists or republicans, Charles I. or
Cromwell; while others, having set out with the preconception that
extremes must be in the wrong, are incapable of seeing truth and justice
when these are wholly on one side.

The influence of a preconceived theory is well exemplified in the
superstitions of barbarians respecting the virtues of medicaments and
charms. The negroes, among whom coral, as of old among ourselves, is
worn as an amulet, affirm, according to Dr. Paris,[21] that its colour
"is always affected by the state of health of the wearer, it becoming
paler in disease." On a matter open to universal observation, a general
proposition which has not the smallest vestige of truth is received as a
result of experience; the preconceived opinion preventing, it would
seem, any observation whatever on the subject.

§ 4. For illustration of the first species of non-observation, that of
Instances, what has now been stated may suffice. But there may also be
non-observation of some material circumstances, in instances which have
not been altogether overlooked--nay, which may be the very instances on
which the whole superstructure of a theory has been founded. As, in the
cases hitherto examined, a general proposition was too rashly adopted,
on the evidence of particulars, true indeed, but insufficient to support
it; so in the cases to which we now turn, the particulars themselves
have been imperfectly observed, and the singular propositions on which
the generalization is grounded, or some at least of those singular
propositions, are false.

Such, for instance, was one of the mistakes committed in the celebrated
phlogistic theory; a doctrine which accounted for combustion by the
extrication of a substance called phlogiston, supposed to be contained
in all combustible matter. The hypothesis accorded tolerably well with
superficial appearances: the ascent of flame naturally suggests the
escape of a substance; and the visible residuum of ashes, in bulk and
weight, generally falls extremely short of the combustible material. The
error was, non-observation of an important portion of the actual
residue, namely, the gaseous products of combustion. When these were at
last noticed and brought into account, it appeared to be an universal
law, that all substances gain instead of losing weight by undergoing
combustion; and, after the usual attempt to accommodate the old theory
to the new fact by means of an arbitrary hypothesis (that phlogiston had
the quality of positive levity instead of gravity), chemists were
conducted to the true explanation, namely, that instead of a substance
separated, there was on the contrary a substance absorbed.

Many of the absurd practices which have been deemed to possess medicinal
efficacy, have been indebted for their reputation to non-observance of
some accompanying circumstance which was the real agent in the cures
ascribed to them. Thus, of the sympathetic powder of Sir Kenelm Digby:
"Whenever any wound had been inflicted, this powder was applied to the
weapon that had inflicted it, which was, moreover, covered with
ointment, and dressed two or three times a day. The wound itself, in the
meantime, was directed to be brought together, and carefully bound up
with clean linen rags, but _above all, to be let alone_ for seven days,
at the end of which period the bandages were removed, when the wound was
generally found perfectly united. The triumph of the cure was decreed to
the mysterious agency of the sympathetic powder which had been so
assiduously applied to the weapon, whereas it is hardly necessary to
observe that the promptness of the cure depended on the total exclusion
of air from the wound, and upon the sanative operations of nature not
having received any disturbance from the officious interference of art.
The result, beyond all doubt, furnished the first hint which led
surgeons to the improved practice of healing wounds by what is
technically called the _first intention_."[22] "In all records," adds
Dr. Paris, "of extraordinary cures performed by mysterious agents, there
is a great desire to conceal the remedies and other curative means which
were simultaneously administered with them; thus Oribasius commends in
high terms a necklace of Pæony root for the cure of epilepsy; but we
learn that he always took care to accompany its use with copious
evacuations, although he assigns to them no share of credit in the cure.
In later times we have a good specimen of this species of deception,
presented to us in a work on Scrofula by Mr. Morley, written, as we are
informed, for the sole purpose of restoring the much injured character
and use of the Vervain; in which the author directs the root of this
plant to be tied with a yard of white satin riband around the neck,
where it is to remain until the patient is cured; but mark--during this
interval he calls to his aid the most active medicines in the materia

In other cases the cures really produced by rest, regimen, and
amusement, have been ascribed to the medicinal, or occasionally to the
supernatural, means which were put in requisition. "The celebrated John
Wesley, while he commemorates the triumph of sulphur and supplication
over his bodily infirmity, forgets to appreciate the resuscitating
influence of four months' repose from his apostolic labours; and such is
the disposition of the human mind to place confidence in the operation
of mysterious agents, that we find him more disposed to attribute his
cure to a brown paper plaister of egg and brimstone, than to Dr.
Fothergill's salutary prescription of country air, rest, asses' milk,
and horse exercise."[24]

In the following example, the circumstance overlooked was of a somewhat
different character. "When the yellow fever raged in America, the
practitioners trusted exclusively to the copious use of mercury; at
first this plan was deemed so universally efficacious, that, in the
enthusiasm of the moment, it was triumphantly proclaimed that death
never took place after the mercury had evinced its effect upon the
system: all this was very true, but it furnished no proof of the
efficacy of that metal, since the disease in its aggravated form was so
rapid in its career, that it swept away its victims long before the
system could be brought under mercurial influence, while in its milder
shape it passed off equally well without any assistance from art."[25]

In these examples the circumstance overlooked was cognizable by the
senses. In other cases, it is one the knowledge of which could only be
arrived at by reasoning; but the fallacy may still be classed under the
head to which, for want of a more appropriate name, we have given the
appellation Fallacies of Non-observation. It is not the nature of the
faculties which ought to have been employed, but the non-employment of
them, which constitutes this Natural Order of Fallacies. Wherever the
error is negative, not positive; wherever it consists especially in
_overlooking_, in being ignorant or unmindful of some fact which, if
known and attended to, would have made a difference in the conclusion
arrived at; the error is properly placed in the Class which we are
considering. In this Class, there is not, as in all other fallacies
there is, a positive mis-estimate of evidence actually had. The
conclusion would be just, if the portion which is seen of the case were
the whole of it; but there is another portion overlooked, which vitiates
the result.

For instance, there is a remarkable doctrine which has occasionally
found a vent in the public speeches of unwise legislators, but which
only in one instance that I am aware of has received the sanction of a
philosophical writer, namely M. Cousin, who, in his preface to the
_Gorgias_ of Plato, contending that punishment must have some other and
higher justification than the prevention of crime, makes use of this
argument--that if punishment were only for the sake of example, it would
be indifferent whether we punished the innocent or the guilty, since the
punishment, considered as an example, is equally efficacious in either
case. Now we must, in order to go along with this reasoning, suppose,
that the person who feels himself under temptation, observing somebody
punished, concludes himself to be in danger of being punished likewise,
and is terrified accordingly. But it is forgotten that if the person
punished is supposed to be innocent, or even if there be any doubt of
his guilt, the spectator will reflect that his own danger, whatever it
may be, is not contingent on his guiltiness, but threatens him equally
if he remains innocent, and how therefore is he deterred from guilt by
the apprehension of such punishment? M. Cousin supposes that people will
be dissuaded from guilt by whatever renders the condition of the guilty
more perilous, forgetting that the condition of the innocent (also one
of the elements in the calculation) is, in the case supposed, made
perilous in precisely an equal degree. This is a fallacy of overlooking;
or of non-observation, within the intent of our classification.

Fallacies of this description are the great stumbling-block to correct
thinking in political economy. The economical workings of society afford
numerous cases in which the effects of a cause consist of two sets of
phenomena: the one immediate, concentrated, obvious to all eyes, and
passing, in common apprehension, for the whole effect; the other widely
diffused, or lying deeper under the surface, and which is exactly
contrary to the former. Take, for instance, the common notion so
plausible at the first glance, of the encouragement given to industry by
lavish expenditure. A, who spends his whole income, and even his
capital, in expensive living, is supposed to give great employment to
labour. B, who lives on a small portion, and invests the remainder in
the funds, is thought to give little or no employment. For everybody
sees the gains which are made by A's tradesmen, servants, and others,
while his money is spending. B's savings, on the contrary, pass into the
hands of the person whose stock he purchased, who with it pays a debt he
owed to some banker, who lends it again to some merchant or
manufacturer; and the capital being laid out in hiring spinners and
weavers, or carriers and the crews of merchant vessels, not only gives
immediate employment to at least as much industry as A employs during
the whole of his career, but coming back with increase by the sale of
the goods which have been manufactured or imported, forms a fund for the
employment of the same and perhaps a greater quantity of labour in
perpetuity. But the observer does not see, and therefore does not
consider, what becomes of B's money; he does see what is done with A's:
he observes the amount of industry which A's profusion feeds; he
observes not the far greater quantity which it prevents from being fed;
and thence the prejudice, universal to the time of Adam Smith, that
prodigality encourages industry, and parsimony is a discouragement to

The common argument against free trade was a fallacy of the same nature.
The purchaser of British silk encourages British industry; the purchaser
of Lyons silk encourages only French; the former conduct is patriotic,
the latter ought to be interdicted by law. The circumstance is
overlooked, that the purchaser of any foreign commodity necessarily
causes, directly or indirectly, the export of an equivalent value of
some article of home production (beyond what would otherwise be
exported), either to the same foreign country or to some other; which
fact, though from the complication of the circumstances it cannot always
be verified by specific observation, no observation can possibly be
brought to contradict, while the evidence of reasoning on which it rests
is irrefragable. The fallacy is, therefore, the same as in the preceding
case, that of seeing a part only of the phenomena, and imagining that
part to be the whole: and may be ranked among Fallacies of

§ 5. To complete the examination of the second of our five classes, we
have now to speak of Mal-observation; in which the error does not lie in
the fact that something is unseen, but that something seen is seen

Perception being infallible evidence of whatever is really perceived,
the error now under consideration can be committed no otherwise than by
mistaking for conception what is in fact inference. We have formerly
shown how intimately the two are blended in almost everything which is
called observation, and still more in every Description.[26] What is
actually on any occasion perceived by our senses being so minute in
amount, and generally so unimportant a portion of the state of facts
which we wish to ascertain or to communicate; it would be absurd to say
that either in our observations, or in conveying their result to others,
we ought not to mingle inference with fact; all that can be said is,
that when we do so we ought to be aware of what we are doing, and to
know what part of the assertion rests on consciousness, and is therefore
indisputable, what part on inference, and is therefore questionable.

One of the most celebrated examples of an universal error produced by
mistaking an inference for the direct evidence of the senses, was the
resistance made, on the ground of common sense, to the Copernican
system. People fancied they _saw_ the sun rise and set, the stars
revolve in circles round the pole. We now know that they saw no such
thing; what they really saw was a set of appearances, equally
reconcileable with the theory they held and with a totally different
one. It seems strange that such an instance as this, of the testimony of
the senses pleaded with the most entire conviction in favour of
something which was a mere inference of the judgment, and, as it turned
out, a false inference, should not have opened the eyes of the bigots of
common sense, and inspired them with a more modest distrust of the
competency of mere ignorance to judge the conclusions of cultivated

In proportion to any person's deficiency of knowledge and mental
cultivation, is generally his inability to discriminate between his
inferences and the perceptions on which they were grounded. Many a
marvellous tale, many a scandalous anecdote, owes its origin to this
incapacity. The narrator relates, not what he saw or heard, but the
impression which he derived from what he saw or heard, and of which
perhaps the greater part consisted of inference, though the whole is
related not as inference but as matter-of-fact. The difficulty of
inducing witnesses to restrain within any moderate limits the
intermixture of their inferences with the narrative of their
perceptions, is well known to experienced cross-examiners; and still
more is this the case when ignorant persons attempt to describe any
natural phenomenon. "The simplest narrative," says Dugald Stewart,[27]
"of the most illiterate observer involves more or less of hypothesis;
nay, in general, it will be found that, in proportion to his ignorance,
the greater is the number of conjectural principles involved in his
statements. A village apothecary (and, if possible, in a still greater
degree, an experienced nurse) is seldom able to describe the plainest
case, without employing a phraseology of which every word is a theory:
whereas a simple and genuine specification of the phenomena which mark a
particular disease; a specification unsophisticated by fancy, or by
preconceived opinions, may be regarded as unequivocal evidence of a mind
trained by long and successful study to the most difficult of all arts,
that of the faithful _interpretation_ of nature."

The universality of the confusion between perceptions and the inferences
drawn from them, and the rarity of the power to discriminate the one
from the other, ceases to surprise us when we consider that in the far
greater number of instances the actual perceptions of our senses are of
no importance or interest to us except as marks from which we infer
something beyond them. It is not the colour and superficial extension
perceived by the eye that are important to us, but the object, of which
those visible appearances testify the presence; and where the sensation
itself is indifferent, as it generally is, we have no motive to attend
particularly to it, but acquire a habit of passing it over without
distinct consciousness, and going on at once to the inference. So that
to know what the sensation actually was, is a study in itself, to which
painters, for example, have to train themselves by special and
long-continued discipline and application. In things further removed
from the dominion of the outward senses, no one who has not great
experience in psychological analysis is competent to break this intense
association; and when such analytic habits do not exist in the requisite
degree, it is hardly possible to mention any of the habitual judgments
of mankind on subjects of a high degree of abstraction, from the being
of a God and the immortality of the soul down to the multiplication
table, which are not, or have not been, considered as matter of direct
intuition. So strong is the tendency to ascribe an intuitive character
to judgments which are mere inferences, and often false ones. No one can
doubt that many a deluded visionary has actually believed that he was
directly inspired from Heaven, and that the Almighty had conversed with
him face to face; which yet was only, on his part, a conclusion drawn
from appearances to his senses, or feelings in his internal
consciousness, which afforded no warrant for any such belief. A caution,
therefore, against this class of errors, is not only needful but
indispensable; though to determine whether, on any of the great
questions of metaphysics, such errors are actually committed, belongs
not to this place, but, as I have so often said, to a different science.



§ 1. The class of Fallacies of which we are now to speak, is the most
extensive of all; embracing a greater number and variety of unfounded
inferences than any of the other classes, and which it is even more
difficult to reduce to sub-classes or species. If the attempt made in
the preceding books to define the principles of well-grounded
generalization has been successful, all generalizations not conformable
to those principles might, in a certain sense, be brought under the
present class: when however the rules are known and kept in view, but a
casual lapse committed in the application of them, this is a blunder,
not a fallacy. To entitle an error of generalization to the latter
epithet, it must be committed on principle; there must lie in it some
erroneous general conception of the inductive process; the legitimate
mode of drawing conclusions from observation and experiment must be
fundamentally misconceived.

Without attempting anything so chimerical as an exhaustive
classification of all the misconceptions which can exist on the subject,
let us content ourselves with noting, among the cautions which might be
suggested, a few of the most useful and needful.

§ 2. In the first place, there are certain kinds of generalization
which, if the principles already laid down be correct, _must_ be
groundless: experience cannot afford the necessary conditions for
establishing them by a correct induction. Such, for instance, are all
inferences from the order of nature existing on the earth, or in the
solar system, to that which may exist in remote parts of the universe;
where the phenomena, for aught we know, may be entirely different, or
may succeed one another according to different laws, or even according
to no fixed law at all. Such, again, in matters dependent on causation,
are all universal negatives, all propositions that assert impossibility.
The non-existence of any given phenomenon, however uniformly experience
may as yet have testified to the fact, proves at most that no cause,
adequate to its production, has yet manifested itself; but that no such
causes exist in nature can only be inferred if we are so foolish as to
suppose that we know all the forces in nature. The supposition would at
least be premature while our acquaintance with some even of those which
we do know is so extremely recent. And however much our knowledge of
nature may hereafter be extended, it is not easy to see how that
knowledge could ever be complete, or how, if it were, we could ever be
assured of its being so.

The only laws of nature which afford sufficient warrant for attributing
impossibility (even with reference to the existing order of nature, and
to our own region of the universe), are first, those of number and
extension, which are paramount to the laws of the succession of
phenomena, and not exposed to the agency of counteracting causes; and
secondly, the universal law of causality itself. That no variation in
any effect or consequent will take place while the whole of the
antecedents remain the same, may be affirmed with full assurance. But,
that the addition of some new antecedent might not entirely alter and
subvert the accustomed consequent, or that antecedents competent to do
this do not exist in nature, we are in no case empowered positively to

§ 3. It is next to be remarked that all generalizations which profess,
like the theories of Thales, Democritus, and others of the early Greek
speculators, to resolve all things into some one element, or like many
modern theories, to resolve phenomena radically different into the same,
are necessarily false. By radically different phenomena I mean
impressions on our senses which differ in quality, and not merely in
degree. On this subject what appeared necessary was said in the chapter
on the Limits to the Explanation of Laws of Nature; but as the fallacy
is even in our own times a common one, I shall touch on it somewhat
further in this place.

When we say that the force which retains the planets in their orbits is
resolved into gravity, or that the force which makes substances combine
chemically is resolved into electricity, we assert in the one case what
is, and in the other case what might, and probably will ultimately, be a
legitimate result of induction. In both these cases, motion is resolved
into motion. The assertion is, that a case of motion, which was supposed
to be special, and to follow a distinct law of its own, conforms to and
is included in the general law which regulates another class of motions.
But, from these and similar generalizations, countenance and currency
have been given to attempts to resolve, not motion into motion, but heat
into motion, light into motion, sensation itself into motion; states of
consciousness into states of the nervous system, as in the ruder forms
of the materialist philosophy; vital phenomena into mechanical or
chemical processes, as in some schools of physiology.

Now I am far from pretending that it may not be capable of proof, or
that it will not be an important addition to our knowledge if proved,
that certain motions in the particles of bodies are among the
_conditions_ of the production of heat or light; that certain assignable
physical modifications of the nerves may be the _conditions_ not only of
our sensations or emotions, but even of our thoughts; that certain
mechanical and chemical conditions may, in the order of nature, be
sufficient to determine to action the physiological laws of life. All I
insist upon, in common with every thinker who entertains any clear idea
of the logic of science, is, that it shall not be supposed that by
proving these things one step would be made towards a real explanation
of heat, light, or sensation; or that the generic peculiarity of those
phenomena can be in the least degree evaded by any such discoveries,
however well established. Let it be shown, for instance, that the most
complex series of physical causes and effects succeed one another in the
eye and in the brain to produce a sensation of colour; rays falling on
the eye, refracted, converging, crossing one another, making an inverted
image on the retina, and after this a motion--let it be a vibration, or
a rush of nervous fluid, or whatever else you are pleased to suppose,
along the optic nerve--a propagation of this motion to the brain itself,
and as many more different motions as you choose; still, at the end of
these motions, there is something which is not motion, there is a
feeling or sensation of colour. Whatever number of motions we may be
able to interpolate, and whether they be real or imaginary, we shall
still find, at the end of the series, a motion antecedent and a colour
consequent. The mode in which any one of the motions produces the next,
might possibly be susceptible of explanation by some general law of
motion; but the mode in which the last motion produces the sensation of
colour, cannot be explained by any law of motion; it is the law of
colour: which is, and must always remain, a peculiar thing. Where our
consciousness recognises between two phenomena an inherent distinction;
where we are sensible of a difference which is not merely of degree, and
feel that no adding one of the phenomena to itself would produce the
other; any theory which attempts to bring either under the laws of the
other must be false; though a theory which merely treats the one as a
cause or condition of the other, may possibly be true.

§ 4. Among the remaining forms of erroneous generalization, several of
those most worthy of and most requiring notice have fallen under our
examination in former places, where, in investigating the rules of
correct induction, we have had occasion to advert to the distinction
between it and some common mode of the incorrect. In this number is what
I have formerly called the natural Induction of uninquiring minds, the
Induction of the ancients, which proceeds _per enumerationem
simplicem_: "This, that, and the other A are B, I cannot think of any A
which is not B, therefore every A is B." As a final condemnation of this
rude and slovenly mode of generalization, I will quote Bacon's emphatic
denunciation of it; the most important part, as I have more than once
ventured to assert, of the permanent service rendered by him to
philosophy. "Inductio quæ procedit per enumerationem simplicem, res
puerilis est, et precario concludit" (concludes only _by your leave_, or
provisionally,) "et periculo exponitur ab instantiâ contradictoriâ, et
plerumque secundum pauciora quam par est, et _ex his tantummodo quæ
præsto sunt pronunciat_. At Inductio quæ ad inventionem et
demonstrationem Scientiarum et Artium erit utilis, Naturam separare
debet, per rejectiones et exclusiones debitas; ac deinde post negativas
tot quot sufficiunt, super affirmativas concludere."

I have already said that the mode of Simple Enumeration is still the
common and received method of Induction in whatever relates to man and
society. Of this a very few instances, more by way of memento than of
instruction, may suffice. What, for example, is to be thought of all the
"common-sense" maxims for which the following may serve as the universal
formula, "Whatsoever has never been, will never be." As for example:
negroes have never been as civilized as whites sometimes are, therefore
it is impossible they should be so. Women, as a class, are supposed not
to have hitherto been equal in intellect to men, therefore they are
necessarily inferior. Society cannot prosper without this or the other
institution; _e.g._ in Aristotle's time, without slavery; in later
times, without an established priesthood, without artificial
distinctions of rank, &c. One poor person in a thousand, educated, while
the nine hundred and ninety-nine remain uneducated, has usually aimed at
raising himself out of his class, therefore education makes people
dissatisfied with the condition of a labourer. Bookish men, taken from
speculative pursuits and set to work on something they know nothing
about, have generally been found or thought to do it ill; therefore
philosophers are unfit for business, &c. &c. All these are inductions by
simple enumeration. Reasons having some reference to the canons of
scientific investigation have been attempted to be given, however
unsuccessfully, for some of these propositions; but to the multitude of
those who parrot them, the _enumeratio simplex, ex his tantummodo quæ
præsto sunt pronuncians_, is the sole evidence. Their fallacy consists
in this, that they are inductions without elimination: there has been no
real comparison of instances, nor even ascertainment of the material
facts in any given instance. There is also the further error, of
forgetting that such generalizations, even if well established, could
not be ultimate truths, but must be results of laws much more
elementary; and therefore, until deduced from such, could at most be
admitted as empirical laws, holding good within the limits of space and
time by which the particular observations that suggested the
generalization were bounded.

This error, of placing more empirical laws, and laws in which there is
no direct evidence of causation, on the same footing of certainty as
laws of cause and effect, an error which is at the root of perhaps the
greater number of bad inductions, is exemplified only in its grossest
form in the kind of generalizations to which we have now referred.
These, indeed, do not possess even the degree of evidence which pertains
to a well-ascertained empirical law; but admit of refutation on the
empirical ground itself, without ascending to causal laws. A little
reflection, indeed, will show that mere negations can only form the
ground of the lowest and least valuable kind of empirical law. A
phenomenon has never been noticed; this only proves that the conditions
of that phenomenon have not yet occurred in experience, but does not
prove that they may not occur hereafter. There is a better kind of
empirical law than this, namely, when a phenomenon which is observed
presents within the limits of observation a series of gradations, in
which a regularity, or something like a mathematical law, is
perceptible: from which, therefore, something may be rationally presumed
as to those terms of the series which are beyond the limits of
observation. But in negation there are no gradations, and no series: the
generalizations, therefore, which deny the possibility of any given
condition of man and society merely because it has never yet been
witnessed, cannot possess this higher degree of validity even as
empirical laws. What is more, the minuter examination which that higher
order of empirical laws presupposes, being applied to the subject-matter
of these, not only does not confirm but actually refutes them. For in
reality the past history of Man and Society, instead of exhibiting them
as immovable, unchangeable, incapable of ever presenting new phenomena,
shows them on the contrary to be, in many most important particulars,
not only changeable, but actually undergoing a progressive change. The
empirical law, therefore, best expressive, in most cases, of the genuine
result of observation, would be, not that such and such a phenomenon
will continue unchanged, but that it will continue to change in some
particular manner.

Accordingly, while almost all generalizations relating to Man and
Society, antecedent to the last fifty years, have erred in the gross way
which we have attempted to characterize, namely, by implicitly assuming
that human nature and society will for ever revolve in the same orbit,
and exhibit essentially the same phenomena; which is also the vulgar
error of the ostentatiously practical, the votaries of so-called common
sense, in our day, especially in Great Britain; the more thinking minds
of the present age, having applied a more minute analysis to the past
records of our race, have for the most part adopted a contrary opinion,
that the human species is in a state of necessary progression, and that
from the terms of the series which are past we may infer positively
those which are yet to come. Of this doctrine, considered as a
philosophical tenet, we shall have occasion to speak more fully in the
concluding Book. If not, in all its forms, free from error, it is at
least free from the gross and stupid error which we previously
exemplified. But, in all except the most eminently philosophical minds,
it is infected with precisely the same _kind_ of fallacy as that is. For
we must remember that even this other and better generalization, the
progressive change in the condition of the human species, is, after all,
but an empirical law: to which, too, it is not difficult to point out
exceedingly large exceptions; and even if these could be got rid of,
either by disputing the facts or by explaining and limiting the theory,
the general objection remains valid against the supposed law, as
applicable to any other than what, in our third book, were termed
Adjacent Cases. For not only is it no ultimate, but not even a causal
law. Changes do indeed take place in human affairs, but every one of
those changes depends on determinate causes; the "progressiveness of the
species" is not a cause, but a summary expression for the general result
of all the causes. So soon as, by a quite different sort of induction,
it shall be ascertained what causes have produced these successive
changes, from the beginning of history, in so far as they have really
taken place, and by what causes of a contrary tendency they have been
occasionally checked or entirely counteracted, we may then be prepared
to predict the future with reasonable foresight; we may be in possession
of the real _law_ of the future; and may be able to declare on what
circumstances the continuance of the same onward movement will
eventually depend. But this it is the error of many of the more advanced
thinkers, in the present age, to overlook; and to imagine that the
empirical law collected from a mere comparison of the condition of our
species at different past times, is a real law, is _the_ law of its
changes, not only past but also to come. The truth is, that the causes
on which the phenomena of the moral world depend, are in every age, and
almost in every country, combined in some different proportion; so that
it is scarcely to be expected that the general result of them all should
conform very closely, in its details at least, to any uniformly
progressive series. And all generalizations which affirm that mankind
have a tendency to grow better or worse, richer or poorer, more
cultivated or more barbarous, that population increases faster than
subsistence, or subsistence than population, that inequality of fortune
has a tendency to increase or to break down, and the like, propositions
of considerable value as empirical laws within certain (but generally
rather narrow) limits, are in reality true or false according to times
and circumstances.

What we have said of empirical generalizations from times past to times
still to come, holds equally true of similar generalizations from
present times to times past; when persons whose acquaintance with moral
and social facts is confined to their own age, take the men and the
things of that age for the type of men and things in general, and apply
without scruple to the interpretation of the events of history, the
empirical laws which represent sufficiently for daily guidance the
common phenomena of human nature at that time and in that particular
state of society. If examples are wanted, almost every historical work,
until a very recent period, abounded in them. The same may be said of
those who generalize empirically from the people of their own country to
the people of other countries, as if human beings felt, judged, and
acted, everywhere in the same manner.

§ 5. In the foregoing instances, the distinction is confounded between
empirical laws, which express merely the customary order of the
succession of effects, and the laws of causation on which the effects
depend. There may, however, be incorrect generalization when this
mistake is not committed; when the investigation takes its proper
direction, that of causes, and the result erroneously obtained purports
to be a really causal law.

The most vulgar form of this fallacy is that which is commonly called
_post hoc, ergo propter hoc_, or, _cum hoc, ergo propter hoc_. As when
it was inferred that England owed her industrial pre-eminence to her
restrictions on commerce: as when the old school of financiers, and some
speculative writers, maintained that the national debt was one of the
causes of national prosperity: as when the excellence of the Church, of
the Houses of Lords and Commons, of the procedure of the law courts,
&c., were inferred from the mere fact that the country had prospered
under them. In such cases as these, if it can be rendered probable by
other evidence that the supposed causes have some tendency to produce
the effect ascribed to them, the fact of its having been produced,
though only in one instance, is of some value as a verification by
specific experience: but in itself it goes scarcely any way at all
towards establishing such a tendency, since, admitting the effect, a
hundred other antecedents could show an equally strong title of _that_
kind to be considered as the cause.

In these examples we see bad generalization _à posteriori_, or
empiricism properly so called: causation inferred from casual
conjunction, without either due elimination, or any presumption arising
from known properties of the supposed agent. But bad generalization _à
priori_ is fully as common: which is properly called false theory;
conclusions drawn, by way of deduction, from properties of some one
agent which is known or supposed to be present, all other coexisting
agents being overlooked. As the former is the error of sheer ignorance,
so the latter is especially that of semi-instructed minds; and is mainly
committed in attempting to explain complicated phenomena by a simpler
theory than their nature admits of. As when one school of physicians
sought for the universal principle of all disease in "lentor and morbid
viscidity of the blood," and imputing most bodily derangements to
mechanical obstructions, thought to cure them by mechanical
remedies;[28] while another, the chemical school, "acknowledged no
source of disease but the presence of some hostile acid or alkali, or
some deranged condition in the chemical composition of the fluid or
solid parts," and conceived, therefore, that "all remedies must act by
producing chemical changes in the body. We find Tournefort busily
engaged in testing every vegetable juice, in order to discover in it
some traces of an acid or alkaline ingredient, which might confer upon
it medicinal activity. The fatal errors into which such an hypothesis
was liable to betray the practitioner, received an awful illustration in
the history of the memorable fever that raged at Leyden in the year
1699, and which consigned two-thirds of the population of that city to
an untimely grave; an event which in a great measure depended upon the
Professor Sylvius de la Boe, who having just embraced the chemical
doctrines of Van Helmont, assigned the origin of the distemper to a
prevailing acid, and declared that its cure could alone [only] be
effected by the copious administration of absorbent and testaceous

These aberrations in medical theory have their exact parallels in
politics. All the doctrines which ascribe absolute goodness to
particular forms of government, particular social arrangements, and even
to particular modes of education, without reference to the state of
civilization and the various distinguishing characters of the society
for which they are intended, are open to the same objection--that of
assuming one class of influencing circumstances to be the paramount
rulers of phenomena which depend in an equal or greater degree on many
others. But on these considerations it is the less necessary that we
should now dwell, as they will occupy our attention more largely in the
concluding Book.

§ 6. The last of the modes of erroneous generalization to which I shall
advert, is that to which we may give the name of False Analogies. This
Fallacy stands distinguished from those already treated of by the
peculiarity, that it does not even simulate a complete and conclusive
induction, but consists in the misapplication of an argument which is at
best only admissible as an inconclusive presumption, where real proof is

An argument from analogy, is an inference that what is true in a certain
case, is true in a case known to be somewhat similar, but not known to
be exactly parallel, that is, to be similar in all the material
circumstances. An object has the property B: another object is not known
to have that property, but resembles the first in a property A, not
known to be connected with B; and the conclusion to which the analogy
points, is that this object has the property B also. As, for example,
that the planets are inhabited, because the earth is so. The planets
resemble the earth in describing elliptical orbits round the sun, in
being attracted by it and by one another, in being nearly spherical,
revolving on their axes, &c.; but it is not known that any of these
properties, or all of them together, are the conditions on which the
possession of inhabitants is dependent, or are marks of those
conditions. Nevertheless, so long as we do not know what the conditions
are, they _may_ be connected by some law of nature with those common
properties; and to the extent of that possibility the planets are more
likely to be inhabited, than if they did not resemble the earth at all.
This non-assignable and generally small increase of probability, beyond
what would otherwise exist, is all the evidence which a conclusion can
derive from analogy. For if we have the slightest reason to suppose any
real connexion between the two properties A and B, the argument is no
longer one of analogy. If it had been ascertained (I purposely put an
absurd supposition) that there was a connexion by causation between the
fact of revolving on an axis and the existence of animated beings, or if
there were any reasonable ground for even suspecting such a connexion, a
probability would arise of the existence of inhabitants in the planets,
which might be of any degree of strength, up to a complete induction;
but we should then infer the fact from the ascertained or presumed law
of causation, and not from the analogy of the earth.

The name analogy, however, is sometimes employed by extension to denote
those arguments of an inductive character but not amounting to a real
induction, which are employed to strengthen the argument drawn from a
simple resemblance. Though A, the property common to the two cases,
cannot be shown to be the cause or effect of B, the analogical reasoner
will endeavour to show that there is some less close degree of connexion
between them; that A is one of a set of conditions from which, when all
united, B would result; or is an occasional effect of some cause which
has been known also to produce B; and the like. Any of which things, if
shown, would render the existence of B by so much more probable, than if
there had not been even that amount of known connexion between B and A.

Now an error or fallacy of analogy may occur in two ways. Sometimes it
consists in employing an argument of either of the above kinds with
correctness indeed, but overrating its probative force. This very common
aberration is sometimes supposed to be particularly incident to persons
distinguished for their imagination; but in reality it is the
characteristic intellectual vice of those whose imaginations are barren,
either from want of exercise, natural defect, or the narrowness of their
range of ideas. To such minds objects present themselves clothed in but
few properties; and as, therefore, few analogies between one object and
another occur to them, they almost invariably overrate the degree of
importance of those few: while one whose fancy takes a wider range,
perceives and remembers so many analogies tending to conflicting
conclusions, that he is much less likely to lay undue stress on any of
them. We always find that those are the greatest slaves to metaphorical
language, who have but one set of metaphors.

But this is only one of the modes of error in the employment of
arguments of analogy. There is another, more properly deserving the name
of fallacy; namely, when resemblance in one point is inferred from
resemblance in another point, though there is not only no evidence to
connect the two circumstances by way of causation, but the evidence
tends positively to disconnect them. This is properly the Fallacy of
False Analogies.

As a first instance, we may cite that favourite argument in defence of
absolute power, drawn from the analogy of paternal government in a
family, which government, however much in need of control, is not and
cannot be controlled by the children themselves, while they remain
children. Paternal government, says the argument, works well; therefore,
despotic government in a state will work well. I wave, as not pertinent
in this place, all that could be said in qualification of the alleged
excellence of paternal government. However this might be, the argument
from the family to the state would not the less proceed on a false
analogy; implying that the beneficial working of parental government
depends, in the family, on the only point which it has in common with
political despotism, namely, irresponsibility. Whereas it depends, when
real, not on that but on two other circumstances of the case, the
affection of the parent for the children, and the superiority of the
parent in wisdom and experience; neither of which properties can be
reckoned on, or are at all likely to exist, between a political despot
and his subjects; and when either of these circumstances fails even in
the family, and the influence of the irresponsibility is allowed to work
uncorrected, the result is anything but good government. This,
therefore, is a false analogy.

Another example is the not uncommon _dictum_, that bodies politic have
youth, maturity, old age, and death, like bodies natural: that after a
certain duration of prosperity, they tend spontaneously to decay. This
also is a false analogy, because the decay of the vital powers in an
animated body can be distinctly traced to the natural progress of those
very changes of structure which, in their earlier stages, constitute its
growth to maturity: while in the body politic the progress of those
changes cannot, generally speaking, have any effect but the still
further continuance of growth: it is the stoppage of that progress, and
the commencement of retrogression, that alone would constitute decay.
Bodies politic die, but it is of disease, or violent death: they have no
old age.

The following sentence from Hooker's _Ecclesiastical Polity_ is an
instance of a false analogy from physical bodies to what are called
bodies politic. "As there could be in natural bodies no motion of
anything unless there were some which moveth all things, and continueth
immovable: even so in politic societies there must be some unpunishable,
or else no man shall suffer punishment." There is a double fallacy here,
for not only the analogy, but the premise from which it is drawn, is
untenable. The notion that there must be something immovable which
moves all other things, is the old scholastic error of a _primum

The following instance I quote from Archbishop Whately's _Rhetoric_: "It
would be admitted that a great and permanent diminution in the quantity
of some useful commodity, such as corn, or coal, or iron, throughout the
world, would be a serious and lasting loss; and again, that if the
fields and coal mines yielded regularly double quantities, with the same
labour, we should be so much the richer; hence it might be inferred,
that if the quantity of gold and silver in the world were diminished
one-half, or were doubled, like results would follow; the utility of
these metals, for the purposes of coin, being very great. Now there are
many points of resemblance and many of difference, between the precious
metals on the one hand, and corn, coal, &c., on the other; but the
important circumstance to the supposed argument is, that the _utility_
of gold and silver (as coin, which is far the chief) _depends on their
value_, which is regulated by their scarcity; or rather, to speak
strictly, by the difficulty of obtaining them; whereas, if corn and coal
were ten times as abundant (_i.e._ more easily obtained), a bushel of
either would still be as useful as now. But if it were twice as easy to
procure gold as it is, a sovereign would be twice as large; if only half
as easy it would be of the size of a half-sovereign, and this (besides
the trifling circumstance of the cheapness or dearness of gold
ornaments) would be all the difference. The analogy, therefore, fails in
the point essential to the argument."

The same author notices, after Bishop Copleston, the case of False
Analogy which consists in inferring from the similarity in many respects
between the metropolis of a country and the heart of the animal body,
that the increased size of the metropolis is a disease.

Some of the false analogies on which systems of physics were confidently
grounded in the time of the Greek philosophers, are such as we now call
fanciful, not that the resemblances are not often real, but that it is
long since any one has been inclined to draw from them the inferences
which were then drawn. Such, for instance, are the curious speculations
of the Pythagoreans on the subject of numbers. Finding that the
distances of the planets bore or seemed to bear to one another a
proportion not varying much from that of the divisions of the monochord,
they inferred from it the existence of an inaudible music, that of the
spheres: as if the music of a harp had depended solely on the numerical
proportions, and not on the material, nor even on the existence of any
material, any strings at all. It has been similarly imagined that
certain combinations of numbers, which were found to prevail in some
natural phenomena, must run through the whole of nature: as that there
must be four elements, because there are four possible combinations of
hot and cold, wet and dry; that there must be seven planets, because
there were seven metals, and even because there were seven days of the
week. Kepler himself thought that there could be only six planets
because there were only five regular solids. With these we may class the
reasonings, so common in the speculations of the ancients, founded on a
supposed _perfection_ in nature: meaning by nature the customary order
of events as they take place of themselves without human interference.
This also is a rude guess at an analogy supposed to pervade all
phenomena, however dissimilar. Since what was thought to be perfection
appeared to obtain in some phenomena, it was inferred (in opposition to
the plainest evidence) to obtain in all. "We always suppose that which
is better to take place in nature, if it be possible," says Aristotle:
and the vaguest and most heterogeneous qualities being confounded
together under the notion of being _better_, there was no limit to the
wildness of the inferences. Thus, because the heavenly bodies were
"perfect," they must move in circles and uniformly. For "they" (the
Pythagoreans) "would not allow," says Geminus,[30] "of any such disorder
among divine and eternal things, as that they should sometimes move
quicker and sometimes slower, and sometimes stand still; for no one
would tolerate such anomaly in the movements even of a man, who was
decent and orderly. The occasions of life, however, are often reasons
for men going quicker or slower; but in the incorruptible nature of the
stars, it is not possible that any cause can be alleged of quickness or
slowness." It is seeking an argument of analogy very far, to suppose
that the stars must observe the rules of decorum in gait and carriage,
prescribed for themselves by the long-bearded philosophers satirized by

As late as the Copernican controversy it was urged as an argument in
favour of the true theory of the solar system, that it placed the fire,
the noblest element, in the centre of the universe. This was a remnant
of the notion that the order of nature must be perfect, and that
perfection consisted in conformity to rules of precedency in dignity,
either real or conventional. Again, reverting to numbers: certain
numbers were _perfect_, therefore those numbers must obtain in the great
phenomena of nature. Six was a perfect number, that is, equal to the sum
of all its factors; an additional reason why there must be exactly six
planets. The Pythagoreans, on the other hand, attributed perfection to
the number ten; but agreed in thinking that the perfect number must be
somehow realized in the heavens; and knowing only of nine heavenly
bodies, to make up the enumeration, they asserted "that there was an
_antichthon_ or counter-earth, on the other side of the sun, invisible
to us."[31] Even Huygens was persuaded that when the number of the
heavenly bodies had reached twelve, it could not admit of any further
increase. Creative power could not go beyond that sacred number.

Some curious instances of false analogy are to be found in the arguments
of the Stoics to prove the equality of all crimes, and the equal
wretchedness of all who had not realized their idea of perfect virtue.
Cicero, towards the end of his Fourth Book _De Finibus_, states some of
these as follows. "Ut, inquit, in fidibus plurimis, si nulla earum ita
contenta numeris sit, ut concentum servare possit, omnes æque incontentæ
sunt; sic peccata, quia discrepant, æque discrepant; paria sunt igitur."
To which Cicero himself aptly answers, "æque contingit omnibus fidibus,
ut incontentæ sint; illud non continuo, ut æque incontentæ." The Stoic
resumes: "Ut enim, inquit, gubernator æque peccat, si palcarum navem
evertit, et si auri; item æque peccat qui parentem, et qui servum,
injuriâ verberat;" assuming, that because the magnitude of the interest
at stake makes no difference in the mere defect of skill, it can make
none in the moral defect: a false analogy. Again, "Quis ignorat, si
plures ex alto emergere velint, propius fore eos quidem ad respirandum,
qui ad summam jam aquam appropinquant, sed nihilo magis respirare posse,
quam eos, qui sunt in profundo? Nihil ergo adjuvat procedere, et
progredi in virtute, quominus miserrimus sit, antequam ad eam
pervenerit, quoniam in aquâ nihil adjuvat: et quoniam catuli, qui jam
despecturi sunt, cæci æque, et ii qui modo nati; Platonem quoque necesse
est, quoniam nondum videbat sapientiam, æque cæcum animo, ac Phalarim
fuisse." Cicero, in his own person, combats these false analogies by
other analogies tending to an opposite conclusion. "Ista similia non
sunt, Cato.... Illa sunt similia; hebes acies est cuipiam oculorum:
corpore alius languescit: hi curatione adhibitâ levantur in dies: alter
valet plus quotidie: alter videt. Hi similes sunt omnibus, qui virtuti
student; levantur vitiis, levantur erroribus."

§ 7. In these and all other arguments drawn from remote analogies, and
from metaphors, which are cases of analogy, it is apparent (especially
when we consider the extreme facility of raising up contrary analogies
and conflicting metaphors) that so far from the metaphor or analogy
proving anything, the applicability of the metaphor is the very thing to
be made out. It has to be shown that in the two cases asserted to be
analogous, the same law is really operating; that between the known
resemblance and the inferred one there is some connexion by means of
causation. Cicero and Cato might have bandied opposite analogies for
ever; it rested with each of them to prove by just induction, or at
least to render probable, that the case resembled the one set of
analogous cases and not the other, in the circumstances on which the
disputed question really hinged. Metaphors, for the most part,
therefore, assume the proposition which they are brought to prove:
their use is, to aid the apprehension of it; to make clearly and vividly
comprehended what it is that the person who employs the metaphor is
proposing to make out; and sometimes also, by what media he proposes to
do so. For an apt metaphor, though it cannot prove, often suggests the

For instance, when D'Alembert (I believe) remarked that in certain
governments, only two creatures find their way to the highest places,
the eagle and the serpent; the metaphor not only conveys with great
vividness the assertion intended, but contributes towards substantiating
it, by suggesting, in a lively manner, the means by which the two
opposite characters thus typified effect their rise. When it is said
that a certain person misunderstands another because the lesser of two
objects cannot comprehend the greater, the application of what is true
in the literal sense of the word _comprehend_, to its metaphorical
sense, points to the fact which is the ground and justification of the
assertion, viz. that one mind cannot thoroughly understand another
unless it can contain it in itself, that is, unless it possesses all
that is contained in the other. When it is urged as an argument for
education, that if the soil is left uncultivated, weeds will spring up,
the metaphor, though no proof, but a statement of the thing to be
proved, states it in terms which, by suggesting a parallel case, put the
mind upon the track of the real proof. For, the reason why weeds grow in
an uncultivated soil, is that the seeds of worthless products exist
everywhere, and can germinate and grow in almost all circumstances,
while the reverse is the case with those which are valuable; and this
being equally true of mental products, this mode of conveying an
argument, independently of its rhetorical advantages, has a logical
value; since it not only suggests the grounds of the conclusion, but
points to another case in which those grounds have been found, or at
least deemed to be, sufficient.

On the other hand, when Bacon, who is equally conspicuous in the use and
abuse of figurative illustration, says that the stream of time has
brought down to us only the least valuable part of the writings of the
ancients, as a river carries froth and straws floating on its surface,
while more weighty objects sink to the bottom; this, even if the
assertion illustrated by it were true, would be no good illustration,
there being no parity of cause. The levity by which substances float on
a stream, and the levity which is synonymous with worthlessness, have
nothing in common except the name; and (to show how little value there
is in the metaphor) we need only change the word into _buoyancy_, to
turn the semblance of argument involved in Bacon's illustration against

A metaphor, then, is not to be considered as an argument, but as an
assertion that an argument exists; that a parity subsists between the
case from which the metaphor is drawn and that to which it is applied.
This parity may exist though the two cases be apparently very remote
from one another; the only resemblance existing between them may be a
resemblance of relations, an analogy in Ferguson's and Archbishop
Whately's sense: as in the preceding instance, in which an illustration
from agriculture was applied to mental cultivation.

§ 8. To terminate the subject of Fallacies of Generalization, it remains
to be said, that the most fertile source of them is bad classification:
bringing together in one group, and under one name, things which have no
common properties, or none but such as are too unimportant to allow
general propositions of any considerable value to be made respecting the
class. The misleading effect is greatest, when a word which in common
use expresses some definite fact, is extended by slight links of
connexion to cases in which that fact does not exist, but some other or
others, only slightly resembling it. Thus Bacon,[32] in speaking of the
_Idola_ or Fallacies arising from notions _temere et inæqualiter à rebus
abstractæ_, exemplifies them by the notion of Humidum or Wet, so
familiar in the physics of antiquity and of the middle ages. "Invenietur
verbum istud, Humidum, nihil aliud quam nota confusa diversarum
actionum, quæ nullam constantiam aut reductionem patiuntur. Significat
enim, et quod circa aliud corpus facile se circumfundit; et quod in se
est indeterminabile, nec consistere potest; et quod facile cedit
undique; et quod facile se dividit et dispergit; et quod facile se unit
et colligit; et quod facile fluit, et in motu ponitur; et quod alteri
corpori facile adhæret, idque madefacit; et quod facile reducitur in
liquidum, sive colliquatur, cum antea consisteret. Itaque quum ad hujus
nominis prædicationem et impositionem ventum sit; si alia accipias,
flamma humida est; si alia accipias, aer humidus non est; si alia,
pulvis minutus humidus est; si alia, vitrum humidum est: ut facile
appareat, istam notionem ex aquâ tantum, et communibus et vulgaribus
liquoribus, absque ullâ debitâ verificatione, temere abstractam esse."

Bacon himself is not exempt from a similar accusation when inquiring
into the nature of heat: where he occasionally proceeds like one who
seeking for the cause of hardness, after examining that quality in iron,
flint, and diamond, should expect to find that it is something which can
be traced also in hard water, a hard knot, and a hard heart.

The word _κίνησις_ in the Greek philosophy, and the words Generation and
Corruption both then and long afterwards, denoted such a multitude of
heterogeneous phenomena, that any attempt at philosophizing in which
those words were used was almost as necessarily abortive as if the word
_hard_ had been taken to denote a class including all the things
mentioned above. _Κίνησις_, for instance, which properly signified
motion, was taken to denote not only all motion but even all change:
_ἀλλοίωσις_ being recognised as one of the modes of _κίνησις_. The
effect was, to connect with every form of _ἀλλοίωσις_ or change, ideas
drawn from motion in the proper and literal sense, and which had no real
connexion with any other kind of _κίνησις_ than that. Aristotle and
Plato laboured under a continual embarrassment from this misuse of
terms. But if we proceed further in this direction we shall encroach
upon the Fallacy of Ambiguity, which belongs to a different class, the
last in order of our classification, Fallacies of Confusion.



§ 1. We have now, in our progress through the classes of Fallacies,
arrived at those to which, in the common books of logic, the appellation
is in general exclusively appropriated; those which have their seat in
the ratiocinative or deductive part of the investigation of truth. On
these fallacies it is the less necessary for us to insist at any length,
as they have been most satisfactorily treated in a work familiar to
almost all, in this country at least, who feel any interest in these
speculations, Archbishop Whately's _Logic_. Against the more obvious
forms of this class of fallacies, the rules of the syllogism are a
complete protection. Not (as we have so often said) that the
ratiocination cannot be good unless it be in the form of a syllogism;
but that, by showing it in that form, we are sure to discover if it be
bad, or at least if it contain any fallacy of this class.

§ 2. Among Fallacies of Ratiocination, we ought perhaps to include the
errors committed in processes which have the appearance only, not the
reality, of an inference from premises; the fallacies connected with the
conversion and æquipollency of propositions. I believe errors of this
description to be far more frequently committed than is generally
supposed, or than their extreme obviousness might seem to admit of. For
example, the simple conversion of an universal affirmative proposition,
All A are B, therefore all B are A, I take to be a very common form of
error: though committed, like many other fallacies, oftener in the
silence of thought than in express words, for it can scarcely be clearly
enunciated without being detected. And so with another form of fallacy,
not substantially different from the preceding: the erroneous
conversion of an hypothetical proposition. The proper converse of an
hypothetical proposition is this: If the consequent be false, the
antecedent is false; but this, If the consequent be true, the antecedent
is true, by no means holds good, but is an error corresponding to the
simple conversion of an universal affirmative. Yet hardly anything is
more common than for people, in their private thoughts, to draw this
inference. As when the conclusion is accepted, which it so often is, for
proof of the premises. That the premises cannot be true if the
conclusion is false, is the unexceptionable foundation of the legitimate
mode of reasoning called a _reductio ad absurdum_. But people
continually think and express themselves, as if they also believed that
the premises cannot be false if the conclusion is true. The truth, or
supposed truth, of the inferences which follow from a doctrine, often
enables it to find acceptance in spite of gross absurdities in it. How
many philosophical systems which had scarcely any intrinsic
recommendation, have been received by thoughtful men because they were
supposed to lend additional support to religion, morality, some
favourite view of politics, or some other cherished persuasion: not
merely because their wishes were thereby enlisted on its side, but
because its leading to what they deemed sound conclusions appeared to
them a strong presumption in favour of its truth: though the
presumption, when viewed in its true light, amounted only to the absence
of that particular evidence of falsehood, which would have resulted from
its leading by correct inference to something already known to be false.

Again, the very frequent error in conduct, of mistaking reverse of wrong
for right, is the practical form of a logical error with respect to the
Opposition of Propositions. It is committed for want of the habit of
distinguishing the _contrary_ of a proposition from the _contradictory_
of it, and of attending to the logical canon, that contrary
propositions, though they cannot both be true, may both be false. If the
error were to express itself in words, it would run distinctly counter
to this canon. It generally, however, does not so express itself, and
to compel it to do so is the most effectual method of detecting and
exposing it.

§ 3. Among Fallacies of Ratiocination are to be ranked in the first
place, all the cases of vicious syllogism laid down in the books. These
generally resolve themselves into having more than three terms to the
syllogism, either avowedly, or in the covert mode of an undistributed
middleterm, or an _illicit process_ of one of the two extremes. It is
not, indeed, very easy fully to convict an argument of falling under any
one of these vicious cases in particular; for the reason already more
than once referred to, that the premises are seldom formally set out: if
they were, the fallacy would impose upon nobody; and while they are not,
it is almost always to a certain degree optional in what manner the
suppressed link shall be filled up. The rules of the syllogism are rules
for compelling a person to be aware of the whole of what he must
undertake to defend if he persists in maintaining his conclusion. He has
it almost always in his power to make his syllogism good by introducing
a false premise; and hence it is scarcely ever possible decidedly to
affirm that any argument involves a bad syllogism: but this detracts
nothing from the value of the syllogistic rules, since it is by them
that a reasoner is compelled distinctly to make his election what
premises he is prepared to maintain. The election made, there is
generally so little difficulty in seeing whether the conclusion follows
from the premises set out, that we might without much logical
impropriety have merged this fourth class of fallacies in the fifth, or
Fallacies of Confusion.

§ 4. Perhaps, however, the commonest, and certainly the most dangerous
fallacies of this class, are those which do not lie in a single
syllogism, but slip in between one syllogism and another in a chain of
argument, and are committed by _changing the premises_. A proposition is
proved, or an acknowledged truth laid down, in the first part of an
argumentation, and in the second a further argument is founded not on
the same proposition, but on some other, resembling it sufficiently to
be mistaken for it. Instances of this fallacy will be found in almost
all the argumentative discourses of unprecise thinkers; and we need only
here advert to one of the obscurer forms of it, recognised by the
schoolmen as the fallacy _à dicto secundum quid ad dictum simpliciter_.
This is committed when, in the premises, a proposition is asserted with
a qualification, and the qualification lost sight of in the conclusion;
or oftener, when a limitation or condition, though not asserted, is
necessary to the truth of the proposition, but is forgotten when that
proposition comes to be employed as a premise. Many of the bad arguments
in vogue belong to this class of error. The premise is some admitted
truth, some common maxim, the reasons or evidence for which have been
forgotten, or are not thought of at the time, but if they had been
thought of would have shown the necessity of so limiting the premise
that it would no longer have supported the conclusion drawn from it.

Of this nature is the fallacy in what is called, by Adam Smith and
others, the Mercantile Theory in Political Economy. That theory sets out
from the common maxim, that whatever brings in money enriches; or that
every one is rich in proportion to the quantity of money he obtains.
From this it is concluded that the value of any branch of trade, or of
the trade of the country altogether, consists in the balance of money it
brings in; that any trade which carries more money out of the country
than it draws into it is a losing trade; that therefore money should be
attracted into the country and kept there, by prohibitions and bounties:
and a train of similar corollaries. All for want of reflecting that if
the riches of an individual are in proportion to the quantity of money
he can command, it is because that is the measure of his power of
purchasing money's worth; and is therefore subject to the proviso that
he is not debarred from employing his money in such purchases. The
premise, therefore, is only true _secundum quid_; but the theory assumes
it to be true absolutely, and infers that increase of money is increase
of riches, even when produced by means subversive of the condition under
which alone money can be riches.

A second instance is, the argument by which it used to be contended,
before the commutation of tithe, that tithes fell on the landlord, and
were a deduction from rent; because the rent of tithe-free land was
always higher than that of land of the same quality, and the same
advantages of situation, subject to tithe. Whether it be true or not
that a tithe falls on rent, a treatise on Logic is not the place to
examine; but it is certain that this is no proof of it. Whether the
proposition be true or false, tithe-free land must, by the necessity of
the case, pay a higher rent. For if tithes do not fall on rent, it must
be because they fall on the consumer; because they raise the price of
agricultural produce. But if the produce be raised in price, the farmer
of tithe-free as well as the farmer of tithed land gets the benefit. To
the latter the rise is but a compensation for the tithe he pays; to the
first, who pays none, it is clear gain, and therefore enables him, and
if there be freedom of competition forces him, to pay so much more rent
to his landlord. The question remains, to what class of fallacies this
belongs. The premise is, that the owner of tithed land receives less
rent than the owner of tithe-free land; the conclusion is, that
therefore he receives less than he himself would receive if tithe were
abolished. But the premise is only true conditionally; the owner of
tithed land receives less than what the owner of tithe-free land is
enabled to receive _when other lands are tithed_; while the conclusion
is applied to a state of circumstances in which that condition fails,
and in which, by consequence, the premise would not be true. The
fallacy, therefore, is _à dicto secundum quid ad dictum simpliciter_.

A third example is the opposition sometimes made to legitimate
interferences of government in the economical affairs of society,
grounded on a misapplication of the maxim, that an individual is a
better judge than the government, of what is for his own pecuniary
interest. This objection was urged to Mr. Wakefield's principle of
colonization; the concentration of the settlers, by fixing such a price
on unoccupied land as may preserve the most desirable proportion between
the quantity of land in culture, and the labouring population. Against
this it was argued, that if individuals found it for their advantage to
occupy extensive tracts of land, they, being better judges of their own
interest than the legislature (which can only proceed on general rules)
ought not to be restrained from doing so. But in this argument it was
forgotten that the fact of a person's taking a large tract of land is
evidence only that it is his interest to take as much as other people,
but not that it might not be for his interest to content himself with
less, if he could be assured that other people would do so too; an
assurance which nothing but a government regulation can give. If all
other people took much, and he only a little, he would reap none of the
advantages derived from the concentration of the population and the
consequent possibility of procuring labour for hire, but would have
placed himself, without equivalent, in a situation of voluntary
inferiority. The proposition, therefore, that the quantity of land which
people will take when left to themselves is that which is most for their
interest to take, is true only _secundum quid_: it is only their
interest while they have no guarantee for the conduct of one another.
But the arrangement disregards the limitation, and takes the proposition
for true _simpliciter_.

One of the conditions oftenest dropped, when what would otherwise be a
true proposition is employed as a premise for proving others, is the
condition of _time_. It is a principle of political economy that prices,
profits, wages, &c. "always find their level;" but this is often
interpreted as if it meant that they are always, or generally, _at_
their level; while the truth is, as Coleridge epigrammatically expresses
it, that they are always _finding_ their level, "which might be taken as
a paraphrase or ironical definition of a storm."

Under the same head of fallacy (_à dicto secundum quid ad dictum
simpliciter_) might be placed all the errors which are vulgarly called
misapplications of abstract truths: that is, where a principle, true (as
the common expression is) _in the abstract_, that is, all modifying
causes being supposed absent, is reasoned on as if it were true
absolutely, and no modifying circumstance could ever by possibility
exist. This very common form of error it is not requisite that we
should exemplify here, as it will be particularly treated of hereafter
in its application to the subjects on which it is most frequent and most
fatal, those of politics and society.[33]



§ 1. Under this fifth and last class it is convenient to arrange all
those fallacies, in which the source of error is not so much a false
estimate of the probative force of known evidence, as an indistinct,
indefinite, and fluctuating conception of what the evidence is.

At the head of these stands that multitudinous body of fallacious
reasonings, in which the source of error is the ambiguity of terms: when
something which is true if a word be used in a particular sense, is
reasoned on as if it were true in another sense. In such a case there is
not a mal-estimation of evidence, because there is not properly any
evidence to the point at all; there is evidence, but to a different
point, which from a confused apprehension of the meaning of the terms
used, is supposed to be the same. This error will naturally be oftener
committed in our ratiocinations than in our direct inductions, because
in the former we are deciphering our own or other people's notes, while
in the latter we have the things themselves present, either to the
senses or to the memory. Except, indeed, when the induction is not from
individual cases to a generality, but from generalities to a still
higher generalization; in that case the fallacy of ambiguity may affect
the inductive process as well as the ratiocinative. It occurs in
ratiocination in two ways: when the middleterm is ambiguous, or when one
of the terms of the syllogism is taken in one sense in the premises, and
in another sense in the conclusion.

Some good exemplifications of this fallacy are given by Archbishop
Whately. "One case," says he, "which may be regarded as coming under the
head of Ambiguous Middle, is (what I believe logical writers mean by
'_Fallacia Figuræ Dictionis_,') the fallacy built on the grammatical
structure of language, from men's usually taking for granted that
_paronymous_ (or _conjugate_) words, _i.e._ those belonging to each
other, as the substantive, adjective, verb, &c. of the same root, have a
precisely corresponding meaning; which is by no means universally the
case. Such a fallacy could not indeed be even exhibited in strict
logical form, which would preclude even the attempt at it, since it has
two middleterms in sound as well as sense. But nothing is more common in
practice than to vary continually the terms employed, with a view to
grammatical convenience; nor is there anything unfair in such a
practice, as long as the _meaning_ is preserved unaltered; _e.g._
'murder should be punished with death; this man is a murderer, therefore
he deserves to die,' &c. Here we proceed on the assumption (in this case
just) that to commit murder, and to be a murderer,--to deserve death,
and to be one who ought to die, are, respectively, equivalent
expressions; and it would frequently prove a heavy inconvenience to be
debarred this kind of liberty; but the abuse of it gives rise to the
Fallacy in question: _e.g._ _projectors_ are unfit to be trusted; this
man has formed a _project_, therefore he is unfit to be trusted: here
the sophist proceeds on the hypothesis that he who forms a _project_
must be a _projector_: whereas the bad sense that commonly attaches to
the latter word, is not at all implied in the former. This fallacy may
often be considered as lying not in the Middle, but in one of the terms
of the Conclusion; so that the conclusion drawn shall not be, in
reality, at all warranted by the premises, though it will appear to be
so, by means of the grammatical affinity of the words: _e.g._ to be
acquainted with the guilty is a _presumption_ of guilt; this man is so
acquainted, therefore we may _presume_ that he is guilty: this argument
proceeds on the supposition of an exact correspondence between _presume_
and _presumption_, which, however, does not really exist; for
'presumption' is commonly used to express a kind of _slight suspicion_;
whereas, 'to presume' amounts to actual belief. There are innumerable
instances of a non-correspondence in paronymous words, similar to that
above instanced; as between _art_ and _artful_, _design_ and
_designing_, _faith_ and _faithful_, &c.; and the more slight the
variation of the meaning, the more likely is the fallacy to be
successful; for when the words have become so widely removed in sense as
'pity' and 'pitiful,' every one would perceive such a fallacy, nor could
it be employed but in jest.[34]

"The present Fallacy is nearly allied to, or rather, perhaps, may be
regarded as a branch of, that founded on _etymology_; viz. when a term
is used, at one time in its customary, and at another in its
etymological sense. Perhaps no example of this can be found that is more
extensively and mischievously employed than in the case of the word
_representative_: assuming that its right meaning must correspond
exactly with the strict and original sense of the verb 'represent,' the
sophist persuades the multitude, that a member of the House of Commons
is bound to be guided in all points by the opinion of his constituents;
and, in short, to be merely their _spokesman_; whereas law and custom,
which in this case may be considered as fixing the meaning of the term,
require no such thing, but enjoin the representative to act according to
the best of his _own_ judgment, and on his own responsibility."

The following are instances of great practical importance, in which
arguments are habitually founded on a verbal ambiguity.

The mercantile public are frequently led into this fallacy by the
phrase, "scarcity of money." In the language of commerce "money" has two
meanings: _currency_, or the circulating medium; and _capital seeking
investment_, especially investment on loan. In this last sense the word
is used when the "money market" is spoken of, and when the "value of
money" is said to be high or low, the rate of interest being meant. The
consequence of this ambiguity is, that as soon as scarcity of money in
the latter of these senses begins to be felt,--as soon as there is
difficulty of obtaining loans, and the rate of interest is high,--it is
concluded that this must arise from causes acting upon the quantity of
money in the other and more popular sense; that the circulating medium
must have diminished in quantity, or ought to be increased. I am aware
that, independently of the double meaning of the term, there are in
facts themselves some peculiarities, giving an apparent support to this
error; but the ambiguity of the language stands on the very threshold of
the subject, and intercepts all attempts to throw light upon it.

Another ambiguous expression which continually meets us in the political
controversies of the present time, especially in those which relate to
organic changes, is the phrase "influence of property:" which is
sometimes used for the influence of respect for superior intelligence,
or gratitude for the kind offices which persons of large property have
it so much in their power to bestow; at other times for the influence of
fear; fear of the worst sort of power, which large property also gives
to its possessor, the power of doing mischief to dependents. To confound
these two, is the standing fallacy of ambiguity brought against those
who seek to purify the electoral system from corruption and
intimidation. Persuasive influence, acting through the conscience of the
voter, and carrying his heart and mind with it, is beneficial--therefore
(it is pretended) coercive influence, which compels him to forget that
he is a moral agent, or to act in opposition to his moral convictions,
ought not to be placed under restraint.

Another word which is often turned into an instrument of the fallacy of
ambiguity, is Theory. In its most proper acceptation, theory means the
completed result of philosophical induction from experience. In that
sense, there are erroneous as well as true theories, for induction may
be incorrectly performed, but theory of some sort is the necessary
result of knowing anything of a subject, and having put one's knowledge
into the form of general propositions for the guidance of practice. In
this, the proper sense of the word, Theory is the explanation of
practice. In another and a more vulgar sense, theory means any mere
fiction of the imagination, endeavouring to conceive how a thing may
possibly have been produced, instead of examining how it was produced.
In this sense only are theory, and theorists, unsafe guides; but because
of this, ridicule or discredit is attempted to be attached to theory in
its proper sense, that is, to legitimate generalization, the end and aim
of all philosophy; and a conclusion is represented as worthless, just
because that has been done, which if done correctly, constitutes the
highest worth that a principle for the guidance of practice can possess,
namely, to comprehend in a few words the real law on which a phenomenon
depends, or some property or relation which is universally true of it.

"The Church" is sometimes understood to mean the clergy alone, sometimes
the whole body of believers, or at least of communicants. The
declamations respecting the inviolability of church property are
indebted for the greater part of their apparent force to this ambiguity.
The clergy, being called the church, are supposed to be the real owners
of what is called church property; whereas they are in truth only the
managing members of a much larger body of proprietors, and enjoy on
their own part a mere usufruct, not extending beyond a life interest.

The following is a Stoical argument taken from Cicero _De Finibus_, book
the third: "Quod est bonum, omne laudabile est. Quod autem laudabile
est, omne honestum est. Bonum igitur quod est, honestum est." Here the
ambiguous word is _laudabile_, which in the minor premise means anything
which mankind are accustomed, on good grounds, to admire or value; as
beauty, for instance, or good fortune: but in the major, it denotes
exclusively moral qualities. In much the same manner the Stoics
endeavoured logically to justify as philosophical truths, their
figurative and rhetorical expressions of ethical sentiment: as that the
virtuous man is alone free, alone beautiful, alone a king, &c. Whoever
has virtue has Good (because it has been previously determined not to
call anything else good); but, again, Good necessarily includes
freedom, beauty, and even kingship, all these being good things;
therefore whoever has virtue has all these.

The following is an argument of Descartes to prove, in his _à priori_
manner, the being of a God. The conception, says he, of an infinite
Being proves the real existence of such a being. For if there is not
really any such being, _I_ must have made the conception; but if I could
make it, I can also unmake it; which evidently is not true; therefore
there must be, externally to myself, an archetype, from which the
conception was derived. In this argument (which, it may be observed,
would equally prove the real existence of ghosts and of witches) the
ambiguity is in the pronoun _I_, by which, in one place, is to be
understood my _will_, in another the _laws of my nature_. If the
conception, existing as it does in my mind, had no original without, the
conclusion would unquestionably follow that _I_ made it; that is, the
laws of my nature must have somehow evolved it: but that my _will_ made
it, would not follow. Now when Descartes afterwards adds that I cannot
unmake the conception, he means that I cannot get rid of it by an act of
my will: which is true, but is not the proposition required. I can as
much unmake this conception as I can any other: no conception which I
have once had, can I ever dismiss by mere volition: but what some of the
laws of my nature have produced, other laws, or those same laws in other
circumstances, may, and often do, subsequently efface.

Analogous to this are some of the ambiguities in the free-will
controversy; which, as they will come under special consideration in the
concluding Book, I only mention _memoriæ causâ_. In that discussion,
too, the word _I_ is often shifted from one meaning to another, at one
time standing for my volitions, at another time for the actions which
are the consequences of them, or the mental dispositions from which they
proceed. The latter ambiguity is exemplified in an argument of Coleridge
(in his _Aids to Reflection_), in support of the freedom of the will. It
is not true, he says, that a man is governed by motives; "the man makes
the motive, not the motive the man;" the proof being that "what is a
strong motive to one man is no motive at all to another." The premise is
true, but only amounts to this, that different persons have different
degrees of susceptibility to the same motive; as they have also to the
same intoxicating liquid, which however does not prove that they are
free to be drunk or not drunk, whatever quantity of the fluid they may
drink. What is proved is, that certain mental conditions in the person
himself, must co-operate, in the production of the act, with the
external inducement: but those mental conditions also are the effect of
causes; and there is nothing in the argument to prove that they can
arise without a cause--that a spontaneous determination of the will,
without any cause at all, ever takes place, as the free-will doctrine

The double use, in the free-will controversy, of the word Necessity,
which sometimes stands only for Certainty, at other times for
Compulsion; sometimes for what _cannot_ be prevented, at other times
only for what we have reason to be assured _will_ not; we shall have
occasion hereafter to pursue to some of its ulterior consequences.

A most important ambiguity, both in common and in metaphysical language,
is thus pointed out by Archbishop Whately in the Appendix to his Logic:
"_Same_ (as well as _One_, _Identical_, and other words derived from
them,) is used frequently in a sense very different from its primary
one, as applicable to a _single_ object; being employed to denote great
_similarity_. When several objects are undistinguishably alike, _one
single description_ will apply equally to any of them; and thence they
are said to be all of _one and the same_ nature, appearance, &c. As,
_e.g._ when we say 'this house is built of the _same_ stone with such
another,' we only mean that the stones are undistinguishable in their
qualities; not that the one building was pulled down, and the other
constructed with the materials. Whereas _sameness_, in the primary
sense, does not even necessarily imply similarity; for if we say of any
man that he is greatly altered since such a time, we understand, and
indeed imply by the very expression, that he is _one person_, though
different in several qualities. It is worth observing also, that Same,
in the secondary sense, admits, according to popular usage, of degrees:
we speak of two things being _nearly_ the same, but not entirely:
personal identity does not admit of degrees. Nothing, perhaps, has
contributed more to the error of Realism than inattention to this
ambiguity. When several persons are said to have _one and the same_
opinion, thought, or idea, many men, overlooking the true simple
statement of the case, which is, that they are _all thinking alike_,
look for something more abstruse and mystical, and imagine there must be
some _One Thing_, in the primary sense, though not an individual, which
is present at once in the mind of each of these persons; and thence
readily sprung Plato's theory of Ideas, each of which was, according to
him, one real, eternal object, existing entire and complete in each of
the individual objects that are known by one name."

It is, indeed, not a matter of inference but of authentic history, that
Plato's doctrine of Ideas, and the Aristotelian doctrine (in this
respect similar to the Platonic) of substantial forms and second
substances, grew up in the precise way here pointed out; from the
supposed necessity of finding, in things which were said to have the
_same_ nature, or the _same_ qualities, something which was the _same_
in the very sense in which a man is the same as himself. All the idle
speculations respecting _τὸ ὄν_, _τὸ ἕν_, _τὸ ὅμοίον_, and similar
abstractions, so common in the ancient and in some modern schools of
thought, sprang from the same source. The Aristotelian logicians saw,
however, one case of the ambiguity, and provided against it with their
peculiar felicity in the invention of technical language, when they
distinguished things which differed both _specie_ and _numero_, from
those which differed _numero tantum_, that is, which were exactly alike
(in some particular respect at least) but were distinct individuals. An
extension of this distinction to the two meanings of the word Same,
namely, things which are the same _specie tantum_, and a thing which is
the same _numero_ as well as _specie_, would have prevented the
confusion which has been a source of so much darkness and such an
abundance of positive error in metaphysical philosophy.

One of the most singular examples of the length to which a thinker of
eminence may be led away by an ambiguity of language, is afforded by
this very case. I refer to the famous argument by which Bishop Berkeley
flattered himself that he had for ever put an end to "scepticism,
atheism, and irreligion." It is briefly as follows. I thought of a thing
yesterday; I ceased to think of it; I think of it again to-day. I had,
therefore, in my mind yesterday an _idea_ of the object; I have also an
idea of it to-day; this idea is evidently not another, but the very same
idea. Yet an intervening time elapsed in which I had it not. Where was
the idea during this interval? It must have been somewhere; it did not
cease to exist; otherwise the idea I had yesterday could not be the
_same_ idea; no more than the man I see alive to-day can be the same
whom I saw yesterday, if the man has died in the meanwhile. Now an idea
cannot be conceived to exist anywhere except in a mind; and hence there
must exist an Universal Mind, in which all ideas have their permanent
residence, during the intervals of their conscious presence in our own

It is evident that Berkeley here confounded sameness _numero_ with
sameness _specie_, that is, with exact resemblance, and assumed the
former where there was only the latter; not perceiving that when we say
we have the same thought to-day which we had yesterday, we do not mean
the same individual thought, but a thought exactly similar: as we say
that we have the same illness which we had last year, meaning only the
same sort of illness.

In one remarkable instance the scientific world was divided into two
furiously hostile parties by an ambiguity of language affecting a branch
of science which, more completely than most others, enjoys the advantage
of a precise and well-defined terminology. I refer to the famous dispute
respecting the _vis viva_, the history of which is given at large in
Professor Playfair's Dissertation. The question was, whether the _force_
of a moving body was proportional (its mass being given) to its velocity
simply, or to the square of its velocity: and the ambiguity was in the
word Force. "One of the effects," says Playfair, "produced by a moving
body is proportional to the square of the velocity, while another is
proportional to the velocity simply:" from whence clearer thinkers were
subsequently led to establish a double measure of the efficiency of a
moving power, one being called _vis viva_, and the other _momentum_.
About the facts, both parties were from the first agreed: the only
question was, with which of the two effects the term _force_ should be,
or could most conveniently be, associated. But the disputants were by no
means aware that this was all; they thought that force was one thing,
the production of effects another; and the question, by which set of
effects the force which produced both the one and the other should be
measured, was supposed to be a question not of terminology but of fact.

The ambiguity of the word Infinite is the real fallacy in the amusing
logical puzzle of Achilles and the Tortoise, a puzzle which has been too
hard for the ingenuity or patience of many philosophers, and which no
less a thinker than Sir William Hamilton considered as insoluble; as a
sound argument, though leading to a palpable falsehood. The fallacy, as
Hobbes hinted, lies in the tacit assumption that whatever is infinitely
divisible is infinite; but the following solution, (to the invention of
which I have no claim,) is more precise and satisfactory.

The argument is, let Achilles run ten times as fast as the tortoise, yet
if the tortoise has the start, Achilles will never overtake him. For
suppose them to be at first separated by an interval of a thousand feet:
when Achilles has run these thousand feet, the tortoise will have got on
a hundred; when Achilles has run those hundred, the tortoise will have
run ten, and so on for ever: therefore Achilles may run for ever without
overtaking the tortoise.

Now, the "for ever," in the conclusion, means, for any length of time
that can be supposed; but in the premises "ever" does not mean any
_length_ of time: it means any _number of subdivisions_ of time. It
means that we may divide a thousand feet by ten, and that quotient again
by ten, and so on as often as we please; that there never needs be an
end to the subdivisions of the distance, nor consequently to those of
the time in which it is performed. But an unlimited number of
subdivisions may be made of that which is itself limited. The argument
proves no other infinity of duration than may be embraced within five
minutes. As long as the five minutes are not expired, what remains of
them may be divided by ten, and again by ten, as often as we like, which
is perfectly compatible with their being only five minutes altogether.
It proves, in short, that to pass through this finite space requires a
time which is infinitely divisible, but not an infinite time: the
confounding of which distinction Hobbes had already seen to be the gist
of the fallacy.

The following ambiguities of the word _right_ (in addition to the
obvious and familiar one of _a_ right and the _adjective_ right) are
extracted from a forgotten paper of my own, in a periodical:--

"Speaking morally, you are said to have a right to do a thing, if all
persons are morally bound not to hinder you from doing it. But, in
another sense, to have a right to do a thing is the opposite of having
_no_ right to do it, _i.e._ of being under a moral obligation to forbear
doing it. In this sense, to say that you have a right to do a thing,
means that you may do it without any breach of duty on your part; that
other persons not only ought not to hinder you, but have no cause to
think worse of you for doing it. This is a perfectly distinct
proposition from the preceding. The right which you have by virtue of a
duty incumbent upon other persons, is obviously quite a different thing
from a right consisting in the absence of any duty incumbent upon
yourself. Yet the two things are perpetually confounded. Thus a man will
say he has a right to publish his opinions; which may be true in this
sense, that it would be a breach of duty in any other person to
interfere and prevent the publication: but he assumes thereupon, that in
publishing his opinions, he himself violates no duty; which may either
be true or false, depending, as it does, on his having taken due pains
to satisfy himself, first, that the opinions are true, and next, that
their publication in this manner, and at this particular juncture, will
probably be beneficial to the interests of truth on the whole.

"The second ambiguity is that of confounding a right of any kind, with a
right to enforce that right by resisting or punishing a violation of it.
People will say, for example, that they have a right to good government,
which is undeniably true, it being the moral duty of their governors to
govern them well. But in granting this, you are supposed to have
admitted their right or liberty to turn out their governors, and perhaps
to punish them, for having failed in the performance of this duty;
which, far from being the same thing, is by no means universally true,
but depends on an immense number of varying circumstances," requiring to
be conscientiously weighed before adopting or acting on such a
resolution. This last example is (like others which have been cited) a
case of fallacy within fallacy; it involves not only the second of the
two ambiguities pointed out, but the first likewise.

One not unusual form of the Fallacy of Ambiguous Terms, is known
technically as the Fallacy of Composition and Division: when the same
term is collective in the premises, distributive in the conclusion, or
_vice versâ_: or when the middle term is collective in one premise,
distributive in the other. As if one were to say (I quote from
Archbishop Whately) "All the angles of a triangle are equal to two right
angles: ABC is an angle of a triangle; therefore ABC is equal to two
right angles.... There is no fallacy more common, or more likely to
deceive, than the one now before us. The form in which it is most
usually employed is to establish some truth, separately, concerning
_each single_ member of a certain class, and thence to infer the same of
the _whole collectively_." As in the argument one sometimes hears, to
prove that the world could do without great men. If Columbus (it is
said) had never lived, America would still have been discovered, at most
only a few years later; if Newton had never lived, some other person
would have discovered the law of gravitation; and so forth. Most true:
these things would have been done, but in all probability not until
some one had again been found with the qualities of Columbus or Newton.
Because any one great man might have had his place supplied by other
great men, the argument concludes that all great men could have been
dispensed with. The term "great men" is distributive in the premises and
collective in the conclusion.

"Such also is the fallacy which probably operates on most adventurers in
lotteries; _e.g._ 'the gaining of a high prize is no uncommon
occurrence; and what is no uncommon occurrence may reasonably be
expected; therefore the gaining of a high prize may reasonably be
expected:' the conclusion when applied to the individual (as in practice
it is) must be understood in the sense of 'reasonably expected _by a
certain individual_;' therefore for the major premise to be true, the
middle term must be understood to mean, 'no uncommon occurrence to some
one _particular_ person;' whereas for the minor (which has been placed
first) to be true, you must understand it of 'no uncommon occurrence to
_some one or other_;' and thus you will have the Fallacy of Composition.

"This is a Fallacy with which men are extremely apt to deceive
_themselves_; for when a multitude of particulars are presented to the
mind, many are too weak or too indolent to take a comprehensive view of
them, but confine their attention to each single point, by turns; and
then decide, infer, and act, accordingly: _e.g._ the imprudent
spendthrift, finding that he is able to afford this, _or_ that, _or_ the
other expense, forgets that _all of them together_ will ruin him." The
debauchee destroys his health by successive acts of intemperance,
because no _one_ of those acts would be of itself sufficient to do him
any serious harm. A sick person reasons with himself, "one, and another,
and another, of my symptoms, do not prove that I have a fatal disease;"
and practically concludes that all taken together do not prove it.

§ 2. We have now sufficiently exemplified one of the principal Genera in
this Order of Fallacies; where, the source of error being the ambiguity
of terms, the premises are verbally what is required to support the
conclusion, but not really so. In the second great Fallacy of Confusion
they are neither verbally nor really sufficient, though, from their
multiplicity and confused arrangement, and still oftener from defect of
memory, they are not seen to be what they are. The fallacy I mean is
that of Petitio Principii, or begging the question; including the more
complex and not uncommon variety of it, which is termed Reasoning in a

_Petitio Principii_, as defined by Archbishop Whately, is the fallacy
"in which the premise either appears manifestly to be the same as the
conclusion, or is actually proved from the conclusion, or is such as
would naturally and properly so be proved." By the last clause I presume
is meant, that it is not susceptible of any other proof; for otherwise,
there would be no fallacy. To deduce from a proposition, propositions
from which it would itself more naturally be deduced, is often an
allowable deviation from the usual didactic order; or at most, what, by
an adaptation of a phrase familiar to mathematicians, may be called a
logical _inelegance_.[35]

The employment of a proposition to prove that on which it is itself
dependent for proof, by no means implies the degree of mental imbecility
which might at first be supposed. The difficulty of comprehending how
this fallacy could possibly be committed, disappears when we reflect
that all persons, even the instructed, hold a great number of opinions
without exactly recollecting how they came by them. Believing that they
have at some former time verified them by sufficient evidence, but
having forgotten what the evidence was, they may easily be betrayed into
deducing from them the very propositions which are alone capable of
serving as premises for their establishment. "As if," says Archbishop
Whately, "one should attempt to prove the being of a God from the
authority of Holy Writ;" which might easily happen to one with whom both
doctrines, as fundamental tenets of his religious creed, stand on the
same ground of familiar and traditional belief.

Arguing in a circle, however, is a stronger case of the fallacy, and
implies more than the mere passive reception of a premise by one who
does not remember how it is to be proved. It implies an actual attempt
to prove two propositions reciprocally from one another; and is seldom
resorted to, at least in express terms, by any person in his own
speculations, but is committed by those who, being hard pressed by an
adversary, are forced into giving reasons for an opinion of which, when
they began to argue, they had not sufficiently considered the grounds.
As in the following example from Archbishop Whately: "Some mechanicians
attempt to prove (what they ought to lay down as a probable but doubtful
hypothesis[36]) that every particle of matter gravitates equally: 'why?'
'because those bodies which contain more particles ever gravitate more
strongly, _i.e._ are heavier:' 'but, (it may be urged,) those which are
heaviest are not always more bulky;' 'no, but they contain more
particles, though more closely condensed:' 'how do you know that?'
'because they are heavier:' 'how does that prove it?' 'because all
particles of matter gravitating equally, that mass which is specifically
the heavier must needs have the more of them in the same space.'" It
appears to me that the fallacious reasoner, in his private thoughts,
would not be likely to proceed beyond the first step. He would acquiesce
in the sufficiency of the reason first given, "bodies which contain more
particles are heavier." It is when he finds this questioned, and is
called upon to prove it, without knowing how, that he tries to
establish his premise by supposing proved what he is attempting to prove
by it. The most effectual way, in fact, of exposing a Petitio Principii,
when circumstances allow of it, is by challenging the reasoner to prove
his premises; which if he attempts to do, he is necessarily driven into
arguing in a circle.

It is not uncommon, however, for thinkers, and those not of the lowest
description, to be led, even in their own thoughts, not indeed into
formally proving each of two propositions from the other, but into
admitting propositions which can only be so proved. In the preceding
example the two together form a complete and consistent, though
hypothetical, explanation of the facts concerned. And the tendency to
mistake mutual coherency for truth; to trust one's safety to a strong
chain though it has no point of support; is at the bottom of much which,
when reduced to the strict forms of argumentation, can exhibit itself no
otherwise than as reasoning in a circle. All experience bears testimony
to the enthralling effect of neat concatenation in a system of
doctrines, and the difficulty with which people admit the persuasion
that anything which holds so well together can possibly fall.

Since every case where a conclusion which can only be proved from
certain premises is used for the proof of those premises, is a case of
_petitio principii_, that fallacy includes a very great proportion of
all incorrect reasoning. It is necessary, for completing our view of the
fallacy, to exemplify some of the disguises under which it is accustomed
to mask itself, and to escape exposure.

A proposition would not be admitted by any person in his senses as a
corollary from itself, unless it were expressed in language which made
it seem different. One of the commonest modes of so expressing it, is to
present the proposition itself in abstract terms, as a proof of the same
proposition expressed in concrete language. This is a very frequent
mode, not only of pretended proof, but of pretended explanation; and is
parodied when Molière makes one of his absurd physicians say, "l'opium
endormit parcequ'il a une vertu soporifique," or, in the equivalent

       Mihi à docto doctore,
       Domandatur causam et rationem quare
     Opium facit dormire.
       A quoi respondeo,
       Quia est in eo
       Virtus dormitiva,
     Cujus est natura
       Sensus assoupire.

The words Nature and Essence are grand instruments of this mode of
begging the question. As in the well-known argument of the scholastic
theologians, that the mind thinks always, because the _essence_ of the
mind is to think. Locke had to point out, that if by essence is here
meant some property which must manifest itself by actual exercise at all
times, the premise is a direct assumption of the conclusion; while if it
only means that to think is the distinctive property of a mind, there is
no connexion between the premise and the conclusion, since it is not
necessary that a distinctive property should be perpetually in action.

The following is one of the modes in which these abstract terms, Nature
and Essence, are used as instruments of this fallacy. Some particular
properties of a thing are selected, more or less arbitrarily, to be
termed its nature or essence; and when this has been done, these
properties are supposed to be invested with a kind of indefeasibleness;
to have become paramount to all the other properties of the thing, and
incapable of being prevailed over or counteracted by them. As when
Aristotle, in a passage already cited, "decides that there is no void on
such arguments as this: in a void there could be no difference of up and
down; for as in nothing there are no differences, so there are none in a
privation or negation; but a void is merely a privation or negation of
matter; therefore, in a void, bodies could not move up and down, which
it is in their _nature_ to do."[37] In other words; it is in the
_nature_ of bodies to move up and down, _ergo_ any physical fact which
supposes them not so to move, cannot be authentic. This mode of
reasoning, by which a bad generalization is made to overrule all facts
which contradict it, is _petitio principii_ in one of its most palpable

None of the modes of assuming what should be proved are in more frequent
use than what are termed by Bentham "question-begging appellatives;"
names which beg the question under the disguise of stating it. The most
potent of these are such as have a laudatory or vituperative character.
For instance, in politics, the word Innovation. The dictionary meaning
of this term being merely "a change to something new," it is difficult
for the defenders even of the most salutary improvement to deny that it
is an innovation; yet the word having acquired in common usage a
vituperative connotation in addition to its dictionary meaning, the
admission is always construed as a large concession to the disadvantage
of the thing proposed.

The following passage from the argument in refutation of the Epicureans,
in the second book of Cicero _de Finibus_, affords a fine example of
this sort of fallacy. "Et quidem illud ipsum non nimium probo (et tantum
patior) philosophum loqui de cupiditatibus finiendis. An potest
cupiditas finiri? tollenda est, atque extrahenda radicitus. Quis est
enim, in quo sit cupiditas, quin recte cupidus dici possit? Ergo et
avarus erit, sed finite: adulter, verum habebit modum: et luxuriosus
eodem modo. Qualis ista philosophia est, quæ non interitum afferat
pravitatis, sed sit contenta mediocritate vitiorum?" The question was,
whether certain desires, when kept within bounds, are vices or not; and
the argument decides the point by applying to them a word (_cupiditas_)
which _implies_ vice. It is shown, however, in the remarks which follow,
that Cicero did not intend this as a serious argument, but as a
criticism on what he deemed an inappropriate expression. "Rem ipsam
prorsus probo: elegantiam desidero. Appellet hæc _desideria naturæ_;
cupiditatis nomen servet alio," &c. But many persons, both ancient and
modern, have employed this, or something equivalent to it, as a real and
conclusive argument. We may remark that the passage respecting
_cupiditas_ and _cupidus_ is also an example of another fallacy already
noticed, that of Paronymous Terms.

Many more of the arguments of the ancient moralists, and especially of
the Stoics, fall within the definition of Petitio Principii. In the _De
Finibus_, for example, which I continue to quote as being probably the
best extant exemplification at once of the doctrines and the methods of
the schools of philosophy existing at that time; of what value as
arguments are such pleas as those of Cato in the third book: That if
virtue were not happiness, it could not be a thing to _boast_ of: That
if death or pain were evils, it would be impossible not to fear them,
and it could not, therefore, be laudable to despise them, &c. In one way
of viewing these arguments, they may be regarded as appeals to the
authority of the general sentiment of mankind, which had stamped its
approval upon certain actions and characters by the phrases referred to;
but that such could have been the meaning intended is very unlikely,
considering the contempt of the ancient philosophers for vulgar opinion.
In any other sense they are clear cases of Petitio Principii, since the
word laudable, and the idea of boasting, imply principles of conduct;
and practical maxims can only be proved from speculative truths, namely
from the properties of the subject matter, and cannot, therefore, be
employed to prove those properties. As well might it be argued that a
government is good because we ought to support it, or that there is a
God because it is our duty to pray to him.

It is assumed by all the disputants in the _De Finibus_ as the
foundation of the inquiry into the _summum bonum_, that "sapiens semper
beatus est." Not simply that wisdom gives the best chance of happiness,
or that wisdom consists in knowing what happiness is, and by what things
it is promoted; these propositions would not have been enough for
them:--but that the sage always is, and must of necessity be, happy. The
idea that wisdom could be consistent with unhappiness, was always
rejected as inadmissible: the reason assigned by one of the
interlocutors, near the beginning of the third book, being, that if the
wise could be unhappy, there was little use in pursuing wisdom. But by
unhappiness they did not mean pain or suffering; to that, it was granted
that the wisest person was liable in common with others: he was happy,
because in possessing wisdom he had the most valuable of all
possessions, the most to be sought and prized of all things, and to
possess the most valuable thing was to be the most happy. By laying it
down, therefore, at the commencement of the inquiry, that the sage must
be happy, the disputed question respecting the _summum bonum_ was in
fact begged; with the further assumption, that pain and suffering, so
far as they can coexist with wisdom, are not unhappiness, and are no

The following are additional instances of Petitio Principii, under more
or less of disguise.

Plato, in the _Sophistes_, attempts to prove that things may exist which
are incorporeal, by the argument that justice and wisdom are
incorporeal, and justice and wisdom must be something. Here, if by
_something_ be meant, as Plato did in fact mean, a thing capable of
existing in and by itself, and not as a quality of some other thing, he
begs the question in asserting that justice and wisdom must be
something: if he means anything else, his conclusion is not proved. This
fallacy might also be classed under ambiguous middleterm: _something_,
in the one premise, meaning some substance, in the other merely some
object of thought, whether substance or attribute.

It was formerly an argument employed in proof of what is now no longer a
popular doctrine, the infinite divisibility of matter, that every
portion of matter, however small, must at least have an upper and an
under surface. Those who used this argument did not see that it assumed
the very point in dispute, the impossibility of arriving at a minimum of
thickness; for if there be a minimum, its upper and under surface will
of course be one: it will be itself a surface, and no more. The argument
owes its very considerable plausibility to this, that the premise does
actually seem more obvious than the conclusion, though really identical
with it. As expressed in the premise, the proposition appeals directly
and in concrete language to the incapacity of the human imagination for
conceiving a minimum. Viewed in this light, it becomes a case of the _à
priori_ fallacy or natural prejudice, that whatever cannot be conceived
cannot exist. Every fallacy of Confusion (it is almost unnecessary to
repeat) will, if cleared up, become a fallacy of some other sort; and it
will be found of deductive or ratiocinative fallacies generally, that
when they mislead, there is mostly, as in this case, a fallacy of some
other description lurking under them, by virtue of which chiefly it is
that the verbal juggle, which is the outside or body of this kind of
fallacy, passes undetected.

Euler's Algebra, a book otherwise of great merit, but full, to
overflowing, of logical errors in respect to the foundation of the
science, contains the following argument to prove that _minus_
multiplied by _minus_ gives _plus_, a doctrine the opprobrium of all
mere mathematicians, and which Euler had not a glimpse of the true
method of proving. He says, _minus_ multiplied by _minus_ cannot give
_minus_; for _minus_ multiplied by _plus_ gives _minus_, and _minus_
multiplied by _minus_ cannot give the same product as _minus_ multiplied
by _plus_. Now one is obliged to ask, why minus multiplied by minus must
give any product at all? and if it does, why its product cannot be the
same as that of minus multiplied by plus? for this would seem, at the
first glance, not more absurd than that minus by minus should give the
same as plus by plus, the proposition which Euler prefers to it. The
premise requires proof, as much as the conclusion: nor can it be proved,
except by that more comprehensive view of the nature of multiplication,
and of algebraic processes in general, which would also supply a far
better proof of the mysterious doctrine which Euler is here endeavouring
to demonstrate.

A striking instance of reasoning in a circle is that of some ethical
writers, who first take for their standard of moral truth what, being
the general, they deem to be the natural or instinctive sentiments and
perceptions of mankind, and then explain away the numerous instances of
divergence from their assumed standard, by representing them as cases in
which the perceptions are unhealthy. Some particular mode of conduct or
feeling is affirmed to be _unnatural_; why? because it is abhorrent to
the universal and natural sentiments of mankind. Finding no such
sentiment in yourself, you question the fact; and the answer is (if your
antagonist is polite), that you are an exception, a peculiar case. But
neither (say you) do I find in the people of some other country, or of
some former age, any such feeling of abhorrence; "ay, but their feelings
were sophisticated and unhealthy."

One of the most notable specimens of reasoning in a circle is the
doctrine of Hobbes, Rousseau, and others, which rests the obligations by
which human beings are bound as members of society, on a supposed social
compact. I wave the consideration of the fictitious nature of the
compact itself; but when Hobbes, through the whole Leviathan,
elaborately deduces the obligation of obeying the sovereign, not from
the necessity or utility of doing so, but from a promise supposed to
have been made by our ancestors, on renouncing savage life and agreeing
to establish political society, it is impossible not to retort by the
question, why are we bound to keep a promise made for us by others? or
why bound to keep a promise at all? No satisfactory ground can be
assigned for the obligation, except the mischievous consequences of the
absence of faith and mutual confidence among mankind. We are, therefore,
brought round to the interests of society, as the ultimate ground of the
obligation of a promise; and yet those interests are not admitted to be
a sufficient justification for the existence of government and law.
Without a promise it is thought that we should not be bound to that
which is implied in all modes of living in society, namely, to yield a
general obedience to the laws therein established; and so necessary is
the promise deemed, that if none has actually been made, some additional
safety is supposed to be given to the foundations of society by feigning

§ 3. Two principal subdivisions of the class of Fallacies of Confusion
having been disposed of; there remains a third, in which the confusion
is not, as in the Fallacy of Ambiguity, in misconceiving the import of
the premises, nor, as in _Petitio Principii_, in forgetting what the
premises are, but in mistaking the conclusion which is to be proved.
This is the fallacy of _Ignoratio Elenchi_, in the widest sense of the
phrase; also called by Archbishop Whately the Fallacy of Irrelevant
Conclusion. His examples and remarks are highly worthy of citation.

"Various kinds of propositions are, according to the occasion,
substituted for the one of which proof is required: sometimes the
particular for the universal; sometimes a proposition with different
terms; and various are the contrivances employed to effect and to
conceal this substitution, and to make the conclusion which the sophist
has drawn, answer practically the same purpose as the one he ought to
have established. We say, 'practically the same purpose,' because it
will very often happen that some _emotion_ will be excited, some
sentiment impressed on the mind, (by a dexterous employment of this
fallacy), such as shall bring men into the _disposition_ requisite for
your purpose; though they may not have assented to, or even stated
distinctly in their own minds, the _proposition_ which it was your
business to establish. Thus if a sophist has to defend one who has been
guilty of some _serious_ offence, which he wishes to extenuate, though
he is unable distinctly to prove that it is not such, yet if he can
succeed in _making the audience laugh_ at some casual matter, he has
gained practically the same point. So also if any one has pointed out
the extenuating circumstances in some particular case of offence, so as
to show that it differs widely from the generality of the same class,
the sophist if he find himself unable to disprove these circumstances,
may do away the force of them, by simply _referring the action to that
very class_, which no one can deny that it belongs to, and the very name
of which will excite a feeling of disgust sufficient to counteract the
extenuation; _e.g._ let it be a case of peculation, and that many
_mitigating_ circumstances have been brought forward which cannot be
denied; the sophistical opponent will reply, 'Well, but after all, the
man is a _rogue_, and there is an end of it;' now in reality this was
(by hypothesis) never the question; and the mere assertion of what was
never denied, _ought_ not, in fairness, to be regarded as decisive: but,
practically, the odiousness of the word, arising in great measure from
the association of those very circumstances which belong to most of the
class, but which we have supposed to be _absent_ in _this particular_
instance, excites precisely that feeling of disgust, which in effect
destroys the force of the defence. In like manner we may refer to this
head all cases of improper appeal to the passions, and everything else
which is mentioned by Aristotle as extraneous to the matter in hand
(_ἔξω τοῦ πράγματος_)."

Again, "instead of proving that 'this prisoner has committed an
atrocious fraud,' you prove that the fraud he is accused of is
atrocious: instead of proving (as in the well-known tale of Cyrus and
the two coats) that the taller boy had a right to force the other boy to
exchange coats with him, you prove that the exchange would have been
advantageous to both: instead of proving that the poor ought to be
relieved in this way rather than in that, you prove that the poor ought
to be relieved: instead of proving that the irrational agent--whether a
brute or a madman--can never be deterred from any act by apprehension of
punishment (as for instance a dog from sheep-biting, by fear of being
beaten), you prove that the beating of one dog does not operate as an
_example_ to _other_ dogs, &c.

"It is evident that _ignoratio elenchi_ may be employed as well for the
apparent refutation of your opponent's proposition, as for the apparent
establishment of your own; for it is substantially the same thing, to
prove what was not denied or to disprove what was not asserted. The
latter practice is not less common, and it is more offensive, because it
frequently amounts to a personal affront, in attributing to a person,
opinions, &c., which he perhaps holds in abhorrence. Thus, when in a
discussion one party vindicates, on the ground of general expediency, a
particular instance of resistance to government in a case of intolerable
oppression, the opponent may gravely maintain, 'that we ought not to do
evil that good may come;' a proposition which of course had never been
denied, the point in dispute being, 'whether resistance in this
particular case _were_ doing evil or not.' Or again, by way of
disproving the assertion of the right of private judgment in religion,
one may hear a grave argument to prove that 'it is impossible every one
can be _right in his judgment_.'"

The works of controversial writers are seldom free from this fallacy.
The attempts, for instance, to disprove the population doctrines of
Malthus, have been mostly cases of _ignoratio elenchi_. Malthus has been
supposed to be refuted if it could be shown that in some countries or
ages population has been nearly stationary; as if he had asserted that
population always increases in a given ratio, or had not expressly
declared that it increases only in so far as it is not restrained by
prudence, or kept down by poverty and disease. Or, perhaps, a collection
of facts is produced to prove that in some one country the people are
better off with a dense population than they are in another country with
a thin one; or that the people have become more numerous and better off
at the same time. As if the assertion were that a dense population could
not possibly be well off: as if it were not part of the very doctrine,
and essential to it, that where there is a more abundant capital there
may be a greater population without any increase of poverty, or even
with a diminution of it.

The favourite argument against Berkeley's theory of the non-existence of
matter, and the most popularly effective, next to a "grin"[38]--an
argument, moreover, which is not confined to "coxcombs," nor to men like
Samuel Johnson, whose greatly overrated ability certainly did not lie in
the direction of metaphysical speculation, but is the stock argument of
the Scotch school of metaphysicians--is a palpable _ignoratio elenchi_.
The argument is perhaps as frequently expressed by gesture as by words,
and one of its commonest forms consists in knocking a stick against the
ground. This short and easy confutation overlooks the fact, that in
denying matter, Berkeley did not deny anything to which our senses bear
witness, and therefore cannot be answered by any appeal to them. His
scepticism related to the supposed substratum, or hidden cause of the
appearances perceived by our senses: the evidence of which, whatever may
be thought of its conclusiveness, is certainly not the evidence of
sense. And it will always remain a signal proof of the want of
metaphysical profundity of Reid, Stewart, and, I am sorry to add, of
Brown, that they should have persisted in asserting that Berkeley, if he
believed his own doctrine, was bound to walk into the kennel, or run his
head against a post. As if persons who do not recognise an occult cause
of their sensations, could not possibly believe that a fixed order
subsists among the sensations themselves. Such a want of comprehension
of the distinction between a thing and its sensible manifestation, or,
in metaphysical language, between the noumenon and the phenomenon, would
be impossible to even the dullest disciple of Kant or Coleridge.

It would be easy to add a greater number of examples of this fallacy, as
well as of the others which I have attempted to characterize. But a more
copious exemplification does not seem to be necessary; and the
intelligent reader will have little difficulty in adding to the
catalogue from his own reading and experience. We shall therefore here
close our exposition of the general principles of logic, and proceed to
the supplementary inquiry which is necessary to complete our design.


[1] Supra, p. 204.

[2] _Vulgar Errors_, book v. chap. 21.

[3] _Pharmacologia_, Historical Introduction, p. 16.

[4] The author of one of the Bridgewater Treatises has fallen, as it
seems to me, into a similar fallacy when, after arguing in rather a
curious way to prove that matter may exist without any of the known
properties of matter, and may therefore be changeable, he concludes that
it cannot be eternal, because "eternal (passive) existence necessarily
involves incapability of change." I believe it would be difficult to
point out any other connexion between the facts of eternity and
unchangeableness, than a strong association between the two ideas. Most
of the _à priori_ arguments, both religious and anti-religious, on the
origin of things, are fallacies drawn from the same source.

[5] Supra, book ii. chap. v. § 6, and ch. vii. § 1, 2, 3. See also
_Examination of Sir William Hamilton's Philosophy_, chap. vi. and

[6] I quote this passage from Playfair's celebrated _Dissertations on
the Progress of Mathematical and Physical Science_.

[7] This statement I must now correct, as too unqualified. The maxim in
question was maintained with full conviction by no less an authority
than Sir William Hamilton. See my _Examination_, chap. xxiv.

[8] _Nouveaux Essais sur l'Entendement Humain--Avant-propos_.
(Œuvres, Paris ed. 1842, vol. i. p. 19.)

[9] This doctrine also was accepted as true, and conclusions were
grounded on it, by Sir William Hamilton. See _Examination_, chap. xxiv.

[10] Not that of Leibnitz, but the principle commonly appealed to under
that name by mathematicians.

[11] _Dissertation_, ut supra, p. 27.

[12] _Hist. Ind. Sc._ Book i. chap. i.

[13] _Novum Organum_, Aph. 75.

[14] Supra, book iii. ch. vii. § 4.

[15] It is hardly needful to remark that nothing is here intended to be
said against the possibility at some future period of making gold; by
first discovering it to be a compound, and putting together its
different elements or ingredients. But this is a totally different idea
from that of the seekers of the grand arcanum.

[16] _Pharmacologia_, pp. 43-5.

[17] Vol. i. chap. 8.

[18] _Nov. Org._, Aph. 46.

[19] Playfair's _Dissertation_, sect. 4.

[20] _Nov. Org. Renov._, p. 61.

[21] _Pharmacologia_, p. 21.

[22] _Pharmacologia_, pp. 23-4.

[23] Ibid. p. 28.

[24] Ibid. p. 62.

[25] _Pharmacologia_, pp. 61-2.

[26] Supra, p. 182.

[27] _Elements of the Philosophy of the Mind_, vol. ii. ch. 4, sect. 5.

[28] "Thus Fourcroy," says Dr. Paris, "explained the operation of
mercury by its specific gravity, and the advocates of this doctrine
favoured the general introduction of the preparations of iron,
especially in scirrhus of the spleen or liver, upon the same
hypothetical principle; for, say they, whatever is most forcible in
removing the obstruction must be the most proper instrument of cure;
such is steel, which, besides the attenuating power with which it is
furnished, has still a greater force in this case from the gravity of
its particles, which, being seven times specifically heavier than any
vegetable, acts in proportion with a stronger impulse, and therefore is
a more powerful deobstruent. This may be taken as a specimen of the
style in which these mechanical physicians reasoned and
practised."--_Pharmacologia_, pp. 38-9.

[29] _Pharmacologia_, pp. 39, 40.

[30] I quote from Dr. Whewell's _Hist. Ind. Sc._ 3rd ed. i. 129.

[31] _Hist. Ind. Sc._ i. 52.

[32] _Nov. Org._ Aph. 60.

[33] "An advocate," says Mr. De Morgan (_Formal Logic_, p. 270), "is
sometimes guilty of the argument _à dicto secundum quid ad dictum
simpliciter_: it is his business to do for his client all that his
client might _honestly_ do for himself. Is not the word in italics
frequently omitted? _Might_ any man honestly try to do for himself all
that counsel frequently try to do for him? We are often reminded of the
two men who stole the leg of mutton; one could swear he had not got it,
the other that he had not taken it. The counsel is doing his duty by his
client, the client has left the matter to his counsel. Between the
unexecuted intention of the client, and the unintended execution of the
counsel, there may be a wrong done, and, if we are to believe the usual
maxims, no wrong-doer."

The same writer justly remarks (p. 251) that there is a converse
fallacy, _à dicto simpliciter ad dictum secundum quid_, called by the
scholastic logicians, _fallacia accidentis_; and another which may be
called _à dicto secundum quid ad dictum secundum alterum quid_ (p. 265).
For apt instances of both, I must refer the reader to Mr. De Morgan's
able chapter on Fallacies.

[34] An example of this fallacy is the popular error that _strong_ drink
must be a cause of _strength_. There is here fallacy within fallacy; for
granting that the words "strong" and "strength" were not (as they are)
applied in a totally different sense to fermented liquors and to the
human body, there would still be involved the error of supposing that an
effect must be like its cause; that the conditions of a phenomenon are
likely to resemble the phenomenon itself; which we have already treated
of as an _à priori_ fallacy of the first rank. As well might it be
supposed that a strong poison will make the person who takes it, strong.

[35] In his later editions, Archbishop Whately confines the name of
Petitio Principii "to those cases in which one of the premises either is
manifestly the same in sense with the conclusion, or is actually proved
from it, or is such as the persons you are addressing are not likely to
know, or to admit, except as an inference from the conclusion: as,
_e.g._ if any one should infer the authenticity of a certain history,
from its recording such and such facts, the reality of which rests on
the evidence of that history."

[36] No longer even a probable hypothesis, since the establishment of
the atomic theory; it being now certain that the integral particles of
different substances gravitate unequally. It is true that these
particles, though real _minima_ for the purposes of chemical
combination, may not be the ultimate particles of the substance; and
this doubt alone renders the hypothesis admissible, even as an

[37] _Hist. Ind. Sc._ i. 34.

[38] "And coxcombs vanquish Berkeley with a grin."



"Si l'homme peut prédire, avec une assurance presque entière, les
phénomènes dont il connaît les lois; si lors même qu'elles lui sont
inconnues, il peut, d'après l'expérience, prévoir avec une grande
probabilité les événemens de l'avenir; pourquoi regarderait-on comme une
entreprise chimérique, celle de tracer avec quelque vraisemblance le
tableau des destinées futures de l'espèce humaine, d'après les résultats
de son histoire? Le seul fondement de croyance dans les sciences
naturelles, est cette idée, que les lois générales, connues ou ignorées,
qui règlent les phénomènes de l'univers, sont nécessaires et constantes;
et par quelle raison ce principe serait-il moins vrai pour le
développement des facultés intellectuelles et morales de l'homme, que
pour les autres opérations de la nature? Enfin, puisque des opinions
formées d'après l'expérience ... sont la seule règle de la conduite des
hommes les plus sages, pourquoi interdirait-on au philosophe d'appuyer
ses conjectures sur cette même base, pourvu qu'il ne leur attribue pas
une certitude supérieure à celle qui peut naître du nombre, de la
constance, de l'exactitude des observations?"--CONDORCET, _Esquisse d'un
Tableau Historique des Progrès de l'Esprit Humain_.



§ 1. Principles of Evidence and Theories of Method are not to be
constructed _à priori_. The laws of our rational faculty, like those of
every other natural agency, are only learnt by seeing the agent at work.
The earlier achievements of science were made without the conscious
observance of any Scientific Method; and we should never have known by
what process truth is to be ascertained, if we had not previously
ascertained many truths. But it was only the easier problems which could
be thus resolved: natural sagacity, when it tried its strength against
the more difficult ones, either failed altogether, or if it succeeded
here and there in obtaining a solution, had no sure means of convincing
others that its solution was correct. In scientific investigation, as in
all other works of human skill, the way of obtaining the end is seen as
it were instinctively by superior minds in some comparatively simple
case, and is then, by judicious generalization, adapted to the variety
of complex cases. We learn to do a thing in difficult circumstances, by
attending to the manner in which we have spontaneously done the same
thing in easier ones.

This truth is exemplified by the history of the various branches of
knowledge which have successively, in the ascending order of their
complication, assumed the character of sciences; and will doubtless
receive fresh confirmation from those, of which the final scientific
constitution is yet to come, and which are still abandoned to the
uncertainties of vague and popular discussion. Although several other
sciences have emerged from this state at a comparatively recent date,
none now remain in it except those which relate to man himself, the
most complex and most difficult subject of study on which the human mind
can be engaged.

Concerning the physical nature of man, as an organized being,--though
there is still much uncertainty and much controversy, which can only be
terminated by the general acknowledgment and employment of stricter
rules of induction than are commonly recognised,--there is, however, a
considerable body of truths which all who have attended to the subject
consider to be fully established; nor is there now any radical
imperfection in the method observed in this department of science by its
most distinguished modern teachers. But the laws of Mind, and, in even a
greater degree, those of Society, are so far from having attained a
similar state of even partial recognition, that it is still a
controversy whether they are capable of becoming subjects of science in
the strict sense of the term: and among those who are agreed on this
point, there reigns the most irreconcileable diversity on almost every
other. Here, therefore, if anywhere, the principles laid down in the
preceding Books may be expected to be useful.

If, on matters so much the most important with which human intellect can
occupy itself, a more general agreement is ever to exist among thinkers;
if what has been pronounced "the proper study of mankind" is not
destined to remain the only subject which Philosophy cannot succeed in
rescuing from Empiricism; the same process through which the laws of
many simpler phenomena have by general acknowledgment been placed beyond
dispute, must be consciously and deliberately applied to those more
difficult inquiries. If there are some subjects on which the results
obtained have finally received the unanimous assent of all who have
attended to the proof, and others on which mankind have not yet been
equally successful; on which the most sagacious minds have occupied
themselves from the earliest date, and have never succeeded in
establishing any considerable body of truths, so as to be beyond denial
or doubt; it is by generalizing the methods successfully followed in the
former inquiries, and adapting them to the latter, that we may hope to
remove this blot on the face of science. The remaining chapters are an
endeavour to facilitate this most desirable object.

§ 2. In attempting this, I am not unmindful how little can be done
towards it in a mere treatise on Logic, or how vague and unsatisfactory
all precepts of Method must necessarily appear, when not practically
exemplified in the establishment of a body of doctrine. Doubtless, the
most effectual mode of showing how the sciences of Ethics and Politics
may be constructed, would be to construct them: a task which, it needs
scarcely be said, I am not about to undertake. But even if there were no
other examples, the memorable one of Bacon would be sufficient to
demonstrate, that it is sometimes both possible and useful to point out
the way, though without being oneself prepared to adventure far into it.
And if more were to be attempted, this at least is not a proper place
for the attempt.

In substance, whatever can be done in a work like this for the Logic of
the Moral Sciences, has been or ought to have been accomplished in the
five preceding Books; to which the present can be only a kind of
supplement or appendix, since the methods of investigation applicable to
moral and social science must have been already described, if I have
succeeded in enumerating and characterizing those of science in general.
It remains, however, to examine which of those methods are more
especially suited to the various branches of moral inquiry; under what
peculiar facilities or difficulties they are there employed; how far the
unsatisfactory state of those inquiries is owing to a wrong choice of
methods, how far to want of skill in the application of right ones; and
what degree of ultimate success may be attained or hoped for, by a
better choice or more careful employment of logical processes
appropriate to the case. In other words, whether moral sciences exist,
or can exist; to what degree of perfection they are susceptible of being
carried; and by what selection or adaptation of the methods brought to
view in the previous part of this work, that degree of perfection is

At the threshold of this inquiry we are met by an objection, which, if
not removed, would be fatal to the attempt to treat human conduct as a
subject of science. Are the actions of human beings, like all other
natural events, subject to invariable laws? Does that constancy of
causation, which is the foundation of every scientific theory of
successive phenomena, really obtain among them? This is often denied;
and for the sake of systematic completeness, if not from any very urgent
practical necessity, the question should receive a deliberate answer in
this place. We shall devote to the subject a chapter apart.



§ 1. The question, whether the law of causality applies in the same
strict sense to human actions as to other phenomena, is the celebrated
controversy concerning the freedom of the will: which, from at least as
far back as the time of Pelagius, has divided both the philosophical and
the religious world. The affirmative opinion is commonly called the
doctrine of Necessity, as asserting human volitions and actions to be
necessary and inevitable. The negative maintains that the will is not
determined, like other phenomena, by antecedents, but determines itself;
that our volitions are not, properly speaking, the effects of causes, or
at least have no causes which they uniformly and implicitly obey.

I have already made it sufficiently apparent that the former of these
opinions is that which I consider the true one; but the misleading terms
in which it is often expressed, and the indistinct manner in which it is
usually apprehended, have both obstructed its reception, and perverted
its influence when received. The metaphysical theory of free will, as
held by philosophers, (for the practical feeling of it, common in a
greater or less degree to all mankind, is in no way inconsistent with
the contrary theory,) was invented because the supposed alternative of
admitting human actions to be _necessary_, was deemed inconsistent with
every one's instinctive consciousness, as well as humiliating to the
pride and even degrading to the moral nature of man. Nor do I deny that
the doctrine, as sometimes held, is open to these imputations; for the
misapprehension in which I shall be able to show that they originate,
unfortunately is not confined to the opponents of the doctrine, but
participated in by many, perhaps we might say by most, of its

§ 2. Correctly conceived, the doctrine called Philosophical Necessity
is simply this: that, given the motives which are present to an
individual's mind, and given likewise the character and disposition of
the individual, the manner in which he will act might be unerringly
inferred: that if we knew the person thoroughly, and knew all the
inducements which are acting upon him, we could foretell his conduct
with as much certainty as we can predict any physical event. This
proposition I take to be a mere interpretation of universal experience,
a statement in words of what every one is internally convinced of. No
one who believed that he knew thoroughly the circumstances of any case,
and the characters of the different persons concerned, would hesitate to
foretell how all of them would act. Whatever degree of doubt he may in
fact feel, arises from the uncertainty whether he really knows the
circumstances, or the character of some one or other of the persons,
with the degree of accuracy required: but by no means from thinking that
if he did know these things, there could be any uncertainty what the
conduct would be. Nor does this full assurance conflict in the smallest
degree with what is called our feeling of freedom. We do not feel
ourselves the less free, because those to whom we are intimately known
are well assured how we shall will to act in a particular case. We
often, on the contrary, regard the doubt what our conduct will be, as a
mark of ignorance of our character, and sometimes even resent it as an
imputation. The religious metaphysicians who have asserted the freedom
of the will, have always maintained it to be consistent with divine
foreknowledge of our actions: and if with divine, then with any other
foreknowledge. We may be free, and yet another may have reason to be
perfectly certain what use we shall make of our freedom. It is not,
therefore, the doctrine that our volitions and actions are invariable
consequents of our antecedent states of mind, that is either
contradicted by our consciousness, or felt to be degrading.

But the doctrine of causation, when considered as obtaining between our
volitions and their antecedents, is almost universally conceived as
involving more than this. Many do not believe, and very few practically
feel, that there is nothing in causation but invariable, certain, and
unconditional sequence. There are few to whom mere constancy of
succession appears a sufficiently stringent bond of union for so
peculiar a relation as that of cause and effect. Even if the reason
repudiates, the imagination retains, the feeling of some more intimate
connexion, of some peculiar tie, or mysterious constraint exercised by
the antecedent over the consequent. Now this it is which, considered as
applying to the human will, conflicts with our consciousness, and
revolts our feelings. We are certain that, in the case of our volitions,
there is not this mysterious constraint. We know that we are not
compelled, as by a magical spell, to obey any particular motive. We
feel, that if we wished to prove that we have the power of resisting the
motive, we could do so, (that wish being, it needs scarcely be observed,
a _new antecedent_;) and it would be humiliating to our pride, and (what
is of more importance) paralysing to our desire of excellence if we
thought otherwise. But neither is any such mysterious compulsion now
supposed, by the best philosophical authorities, to be exercised by any
other cause over its effect. Those who think that causes draw their
effects after them by a mystical tie, are right in believing that the
relation between volitions and their antecedents is of another nature.
But they should go farther, and admit that this is also true of all
other effects and their antecedents. If such a tie is considered to be
involved in the word necessity, the doctrine is not true of human
actions; but neither is it then true of inanimate objects. It would be
more correct to say that matter is not bound by necessity than that mind
is so.

That the free-will metaphysicians, being mostly of the school which
rejects Hume's and Brown's analysis of Cause and Effect, should miss
their way for want of the light which that analysis affords, cannot
surprise us. The wonder is, that the necessarians, who usually admit
that philosophical theory, should in practice equally lose sight of it.
The very same misconception of the doctrine called Philosophical
Necessity, which prevents the opposite party from recognising its truth,
I believe to exist more or less obscurely in the minds of most
necessarians, however they may in words disavow it. I am much mistaken
if they habitually feel that the necessity which they recognise in
actions is but uniformity of order, and capability of being predicted.
They have a feeling as if there were at bottom a stronger tie between
the volitions and their causes: as if, when they asserted that the will
is governed by the balance of motives, they meant something more cogent
than if they had only said, that whoever knew the motives, and our
habitual susceptibilities to them, could predict how we should will to
act. They commit, in opposition to their own scientific system, the very
same mistake which their adversaries commit in obedience to theirs; and
in consequence do really in some instances suffer those depressing
consequences, which their opponents erroneously impute to the doctrine

§ 3. I am inclined to think that this error is almost wholly an effect
of the associations with a word; and that it would be prevented, by
forbearing to employ, for the expression of the simple fact of
causation, so extremely inappropriate a term as Necessity. That word, in
its other acceptations, involves much more than mere uniformity of
sequence: it implies irresistibleness. Applied to the will, it only
means that the given cause will be followed by the effect, subject to
all possibilities of counteraction by other causes: but in common use it
stands for the operation of those causes exclusively, which are supposed
too powerful to be counteracted at all. When we say that all human
actions take place of necessity, we only mean that they will certainly
happen if nothing prevents:--when we say that dying of want, to those
who cannot get food, is a necessity, we mean that it will certainly
happen whatever may be done to prevent it. The application of the same
term to the agencies on which human actions depend, as is used to
express those agencies of nature which are really uncontrollable, cannot
fail, when habitual, to create a feeling of uncontrollableness in the
former also. This however is a mere illusion. There are physical
sequences which we call necessary, as death for want of food or air;
there are others which, though as much cases of causation as the
former, are not said to be necessary, as death from poison, which an
antidote, or the use of the stomach-pump, will sometimes avert. It is
apt to be forgotten by people's feelings, even if remembered by their
understandings, that human actions are in this last predicament: they
are never (except in some cases of mania) ruled by any one motive with
such absolute sway, that there is no room for the influence of any
other. The causes, therefore, on which action depends, are never
uncontrollable; and any given effect is only necessary provided that the
causes tending to produce it are not controlled. That whatever happens,
could not have happened otherwise unless something had taken place which
was capable of preventing it, no one surely needs hesitate to admit. But
to call this by the name necessity is to use the term in a sense so
different from its primitive and familiar meaning, from that which it
bears in the common occasions of life, as to amount almost to a play
upon words. The associations derived from the ordinary sense of the term
will adhere to it in spite of all we can do: and though the doctrine of
Necessity, as stated by most who hold it, is very remote from fatalism,
it is probable that most necessarians are fatalists, more or less, in
their feelings.

A fatalist believes, or half believes (for nobody is a consistent
fatalist), not only that whatever is about to happen, will be the
infallible result of the causes which produce it, (which is the true
necessarian doctrine,) but moreover that there is no use in struggling
against it; that it will happen however we may strive to prevent it.
Now, a necessarian, believing that our actions follow from our
characters, and that our characters follow from our organization, our
education, and our circumstances, is apt to be, with more or less of
consciousness on his part, a fatalist as to his own actions, and to
believe that his nature is such, or that his education and circumstances
have so moulded his character, that nothing can now prevent him from
feeling and acting in a particular way, or at least that no effort of
his own can hinder it. In the words of the sect which in our own day has
most perseveringly inculcated and most perversely misunderstood this
great doctrine, his character is formed _for_ him, and not _by_ him;
therefore his wishing that it had been formed differently is of no use;
he has no power to alter it. But this is a grand error. He has, to a
certain extent, a power to alter his character. Its being, in the
ultimate resort, formed for him, is not inconsistent with its being, in
part, formed _by_ him as one of the intermediate agents. His character
is formed by his circumstances (including among these his particular
organization); but his own desire to mould it in a particular way, is
one of those circumstances, and by no means one of the least
influential. We cannot, indeed, directly will to be different from what
we are. But neither did those who are supposed to have formed our
characters, directly will that we should be what we are. Their will had
no direct power except over their own actions. They made us what they
did make us, by willing, not the end, but the requisite means; and we,
when our habits are not too inveterate, can, by similarly willing the
requisite means, make ourselves different. If they could place us under
the influence of certain circumstances, we, in like manner, can place
ourselves under the influence of other circumstances. We are exactly as
capable of making our own character, _if we will_, as others are of
making it for us.

Yes (answers the Owenite), but these words, "if we will," surrender the
whole point: since the will to alter our own character is given us, not
by any efforts of ours, but by circumstances which we cannot help; it
comes to us either from external causes, or not at all. Most true: if
the Owenite stops here, he is in a position from which nothing can expel
him. Our character is formed by us as well as for us; but the wish which
induces us to attempt to form it is formed for us; and how? Not, in
general, by our organization, nor wholly by our education, but by our
experience; experience of the painful consequences of the character we
previously had: or by some strong feeling of admiration or aspiration,
accidentally aroused. But to think that we have no power of altering our
character, and to think that we shall not use our power unless we desire
to use it, are very different things, and have a very different effect
on the mind. A person who does not wish to alter his character, cannot
be the person who is supposed to feel discouraged or paralysed by
thinking himself unable to do it. The depressing effect of the fatalist
doctrine can only be felt where there _is_ a wish to do what that
doctrine represents as impossible. It is of no consequence what we think
forms our character, when we have no desire of our own about forming it;
but it is of great consequence that we should not be prevented from
forming such a desire by thinking the attainment impracticable, and that
if we have the desire, we should know that the work is not so
irrevocably done as to be incapable of being altered.

And indeed, if we examine closely, we shall find that this feeling, of
our being able to modify our own character _if we wish_, is itself the
feeling of moral freedom which we are conscious of. A person feels
morally free who feels that his habits or his temptations are not his
masters, but he theirs: who even in yielding to them knows that he could
resist; that were he desirous of altogether throwing them off, there
would not be required for that purpose a stronger desire than he knows
himself to be capable of feeling. It is of course necessary, to render
our consciousness of freedom complete, that we should have succeeded in
making our character all we have hitherto attempted to make it; for if
we have wished and not attained, we have, to that extent, not power over
our own character, we are not free. Or at least, we must feel that our
wish, if not strong enough to alter our character, is strong enough to
conquer our character when the two are brought into conflict in any
particular case of conduct. And hence it is said with truth, that none
but a person of confirmed virtue is completely free.

The application of so improper a term as Necessity to the doctrine of
cause and effect in the matter of human character, seems to me one of
the most signal instances in philosophy of the abuse of terms, and its
practical consequences one of the most striking examples of the power of
language over our associations. The subject will never be generally
understood, until that objectionable term is dropped. The free-will
doctrine, by keeping in view precisely that portion of the truth which
the word Necessity puts out of sight, namely the power of the mind to
co-operate in the formation of its own character, has given to its
adherents a practical feeling much nearer to the truth than has
generally (I believe) existed in the minds of necessarians. The latter
may have had a stronger sense of the importance of what human beings can
do to shape the characters of one another; but the free-will doctrine
has, I believe, fostered in its supporters a much stronger spirit of

§ 4. There is still one fact which requires to be noticed (in addition
to the existence of a power of self-formation) before the doctrine of
the causation of human actions can be freed from the confusion and
misapprehensions which surround it in many minds. When the will is said
to be determined by motives, a motive does not mean always, or solely,
the anticipation of a pleasure or of a pain. I shall not here inquire
whether it be true that, in the commencement, all our voluntary actions
are mere means consciously employed to obtain some pleasure, or avoid
some pain. It is at least certain that we gradually, through the
influence of association, come to desire the means without thinking of
the end: the action itself becomes an object of desire, and is performed
without reference to any motive beyond itself. Thus far, it may still be
objected, that, the action having through association become
pleasurable, we are, as much as before, moved to act by the anticipation
of a pleasure, namely the pleasure of the action itself. But granting
this, the matter does not end here. As we proceed in the formation of
habits, and become accustomed to will a particular act or a particular
course of conduct because it is pleasurable, we at last continue to will
it without any reference to its being pleasurable. Although, from some
change in us or in our circumstances, we have ceased to find any
pleasure in the action, or perhaps to anticipate any pleasure as the
consequence of it, we still continue to desire the action, and
consequently to do it. In this manner it is that habits of hurtful
excess continue to be practised although they have ceased to be
pleasurable; and in this manner also it is that the habit of willing to
persevere in the course which he has chosen, does not desert the moral
hero, even when the reward, however real, which he doubtless receives
from the consciousness of well-doing, is anything but an equivalent for
the sufferings he undergoes, or the wishes which he may have to

A habit of willing is commonly called a purpose; and among the causes of
our volitions, and of the actions which flow from them, must be reckoned
not only likings and aversions, but also purposes. It is only when our
purposes have become independent of the feelings of pain or pleasure
from which they originally took their rise, that we are said to have a
confirmed character. "A character," says Novalis, "is a completely
fashioned will:" and the will, once so fashioned, may be steady and
constant, when the passive susceptibilities of pleasure and pain are
greatly weakened, or materially changed.

With the corrections and explanations now given, the doctrine of the
causation of our volitions by motives, and of motives by the desirable
objects offered to us, combined with our particular susceptibilities of
desire, may be considered, I hope, as sufficiently established for the
purposes of this treatise.[1]



§ 1. It is a common notion, or at least it is implied in many common
modes of speech, that the thoughts, feelings, and actions of sentient
beings are not a subject of science, in the same strict sense in which
this is true of the objects of outward nature. This notion seems to
involve some confusion of ideas, which it is necessary to begin by
clearing up.

Any facts are fitted, in themselves, to be a subject of science, which
follow one another according to constant laws; although those laws may
not have been discovered, nor even be discoverable by our existing
resources. Take, for instance, the most familiar class of meteorological
phenomena, those of rain and sunshine. Scientific inquiry has not yet
succeeded in ascertaining the order of antecedence and consequence among
these phenomena, so as to be able, at least in our regions of the earth,
to predict them with certainty, or even with any high degree of
probability. Yet no one doubts that the phenomena depend on laws, and
that these must be derivative laws resulting from known ultimate laws,
those of heat, electricity, vaporization, and elastic fluids. Nor can it
be doubted that if we were acquainted with all the antecedent
circumstances, we could, even from those more general laws, predict
(saving difficulties of calculation) the state of the weather at any
future time. Meteorology, therefore, not only has in itself every
natural requisite for being, but actually is, a science; though, from
the difficulty of observing the facts on which the phenomena depend (a
difficulty inherent in the peculiar nature of those phenomena) the
science is extremely imperfect; and were it perfect, might probably be
of little avail in practice, since the data requisite for applying its
principles to particular instances would rarely be procurable.

A case may be conceived, of an intermediate character between the
perfection of science, and this its extreme imperfection. It may happen
that the greater causes, those on which the principal part of the
phenomena depends, are within the reach of observation and measurement;
so that if no other causes intervened, a complete explanation could be
given not only of the phenomenon in general, but of all the variations
and modifications which it admits of. But inasmuch as other, perhaps
many other causes, separately insignificant in their effects, co-operate
or conflict in many or in all cases with those greater causes; the
effect, accordingly, presents more or less of aberration from what would
be produced by the greater causes alone. Now if these minor causes are
not so constantly accessible, or not accessible at all, to accurate
observation; the principal mass of the effect may still, as before, be
accounted for, and even predicted; but there will be variations and
modifications which we shall not be competent to explain thoroughly, and
our predictions will not be fulfilled accurately, but only

It is thus, for example, with the theory of the tides. No one doubts
that Tidology (as Dr. Whewell proposes to call it) is really a science.
As much of the phenomena as depends on the attraction of the sun and
moon is completely understood, and may in any, even unknown, part of the
earth's surface, be foretold with certainty; and the far greater part of
the phenomena depends on those causes. But circumstances of a local or
casual nature, such as the configuration of the bottom of the ocean, the
degree of confinement from shores, the direction of the wind, &c.,
influence, in many or in all places, the height and time of the tide;
and a portion of these circumstances being either not accurately
knowable, not precisely measurable, or not capable of being certainly
foreseen, the tide in known places commonly varies from the calculated
result of general principles by some difference that we cannot explain,
and in unknown ones may vary from it by a difference that we are not
able to foresee or conjecture. Nevertheless, not only is it certain
that these variations depend on causes, and follow their causes by laws
of unerring uniformity; not only, therefore, is tidology a science, like
meteorology, but it is, what hitherto at least meteorology is not, a
science largely available in practice. General laws may be laid down
respecting the tides, predictions may be founded on those laws, and the
result will in the main, though often not with complete accuracy,
correspond to the predictions.

And this is what is or ought to be meant by those who speak of sciences
which are not _exact_ sciences. Astronomy was once a science, without
being an exact science. It could not become exact until not only the
general course of the planetary motions, but the perturbations also,
were accounted for, and referred to their causes. It has become an exact
science, because its phenomena have been brought under laws
comprehending the whole of the causes by which the phenomena are
influenced, whether in a great or only in a trifling degree, whether in
all or only in some cases, and assigning to each of those causes the
share of effect which really belongs to it. But in the theory of the
tides the only laws as yet accurately ascertained, are those of the
causes which affect the phenomenon in all cases, and in a considerable
degree; while others which affect it in some cases only, or, if in all,
only in a slight degree, have not been sufficiently ascertained and
studied to enable us to lay down their laws; still less to deduce the
completed law of the phenomenon, by compounding the effects of the
greater with those of the minor causes. Tidology, therefore, is not yet
an exact science; not from any inherent incapacity of being so, but from
the difficulty of ascertaining with complete precision the real
derivative uniformities. By combining, however, the exact laws of the
greater causes, and of such of the minor ones as are sufficiently known,
with such empirical laws or such approximate generalizations respecting
the miscellaneous variations as can be obtained by specific observation,
we can lay down general propositions which will be true in the main, and
on which, with allowance for the degree of their probable inaccuracy, we
may safely ground our expectations and our conduct.

§ 2. The science of human nature is of this description. It falls far
short of the standard of exactness now realized in Astronomy; but there
is no reason that it should not be as much a science as Tidology is, or
as Astronomy was when its calculations had only mastered the main
phenomena, but not the perturbations.

The phenomena with which this science is conversant being the thoughts,
feelings, and actions of human beings, it would have attained the ideal
perfection of a science if it enabled us to foretell how an individual
would think, feel, or act, throughout life, with the same certainty with
which astronomy enables us to predict the places and the occultations of
the heavenly bodies. It needs scarcely be stated that nothing
approaching to this can be done. The actions of individuals could not be
predicted with scientific accuracy, were it only because we cannot
foresee the whole of the circumstances in which those individuals will
be placed. But further, even in any given combination of (present)
circumstances, no assertion, which is both precise and universally true,
can be made respecting the manner in which human beings will think,
feel, or act. This is not, however, because every person's modes of
thinking, feeling, and acting, do not depend on causes; nor can we doubt
that if, in the case of any individual, our data could be complete, we
even now know enough of the ultimate laws by which mental phenomena are
determined, to enable us in many cases to predict, with tolerable
certainty, what, in the greater number of supposable combinations of
circumstances, his conduct or sentiments would be. But the impressions
and actions of human beings are not solely the result of their present
circumstances, but the joint result of those circumstances and of the
characters of the individuals: and the agencies which determine human
character are so numerous and diversified, (nothing which has happened
to the person throughout life being without its portion of influence,)
that in the aggregate they are never in any two cases exactly similar.
Hence, even if our science of human nature were theoretically perfect,
that is, if we could calculate any character as we can calculate the
orbit of any planet, _from given data_; still, as the data are never
all given, nor ever precisely alike in different cases, we could neither
make positive predictions, nor lay down universal propositions.

Inasmuch, however, as many of those effects which it is of most
importance to render amenable to human foresight and control are
determined, like the tides, in an incomparably greater degree by general
causes, than by all partial causes taken together; depending in the main
on those circumstances and qualities which are common to all mankind, or
at least to large bodies of them, and only in a small degree on the
idiosyncrasies of organization or the peculiar history of individuals;
it is evidently possible with regard to all such effects, to make
predictions which will _almost_ always be verified, and general
propositions which are almost always true. And whenever it is sufficient
to know how the great majority of the human race, or of some nation or
class of persons, will think, feel, and act, these propositions are
equivalent to universal ones. For the purposes of political and social
science this _is_ sufficient. As we formerly remarked,[2] an approximate
generalization is, in social inquiries, for most practical purposes
equivalent to an exact one; that which is only probable when asserted of
individual human beings indiscriminately selected, being certain when
affirmed of the character and collective conduct of masses.

It is no disparagement, therefore, to the science of Human Nature, that
those of its general propositions which descend sufficiently into detail
to serve as a foundation for predicting phenomena in the concrete, are
for the most part only approximately true. But in order to give a
genuinely scientific character to the study, it is indispensable that
these approximate generalizations, which in themselves would amount only
to the lowest kind of empirical laws, should be connected deductively
with the laws of nature from which they result; should be resolved into
the properties of the causes on which the phenomena depend. In other
words, the science of Human Nature may be said to exist, in proportion
as the approximate truths, which compose a practical knowledge of
mankind, can be exhibited as corollaries from the universal laws of
human nature on which they rest; whereby the proper limits of those
approximate truths would be shown, and we should be enabled to deduce
others for any new state of circumstances, in anticipation of specific

The proposition now stated is the text on which the two succeeding
chapters will furnish the comment.



§ 1. What the Mind is, as well as what Matter is, or any other question
respecting Things in themselves, as distinguished from their sensible
manifestations, it would be foreign to the purposes of this treatise to
consider. Here, as throughout our inquiry, we shall keep clear of all
speculations respecting the mind's own nature, and shall understand by
the laws of mind, those of mental Phenomena; of the various feelings or
states of consciousness of sentient beings. These, according to the
classification we have uniformly followed, consist of Thoughts,
Emotions, Volitions, and Sensations; the last being as truly states of
Mind as the three former. It is usual indeed to speak of sensations as
states of body, not of mind. But this is the common confusion, of giving
one and the same name to a phenomenon and to the proximate cause or
conditions of the phenomenon. The immediate antecedent of a sensation is
a state of body, but the sensation itself is a state of mind. If the
word mind means anything, it means that which feels. Whatever opinion we
hold respecting the fundamental identity or diversity of matter and
mind, in any case the distinction between mental and physical facts,
between the internal and the external world, will always remain, as a
matter of classification: and in that classification, sensations, like
all other feelings, must be ranked as mental phenomena. The mechanism of
their production, both in the body itself and in what is called outward
nature, is all that can with any propriety be classed as physical.

The phenomena of mind, then, are the various feelings of our nature,
both those improperly called physical, and those peculiarly designated
as mental: and by the laws of mind, I mean the laws according to which
those feelings generate one another.

§ 2. All states of mind are immediately caused either by other states of
mind, or by states of body. When a state of mind is produced by a state
of mind, I call the law concerned in the case, a law of Mind. When a
state of mind is produced directly by a state of body, the law is a law
of Body, and belongs to physical science.

With regard to those states of mind which are called sensations, all are
agreed that these have for their immediate antecedents, states of body.
Every sensation has for its proximate cause some affection of the
portion of our frame called the nervous system; whether this affection
originate in the action of some external object, or in some pathological
condition of the nervous organization itself. The laws of this portion
of our nature--the varieties of our sensations, and the physical
conditions on which they proximately depend--manifestly belong to the
province of Physiology.

Whether the remainder of our mental states are similarly dependent on
physical conditions, is one of the _vexatæ questiones_ in the science of
human nature. It is still disputed whether our thoughts, emotions, and
volitions are generated through the intervention of material mechanism;
whether we have organs of thought and of emotion, in the same sense in
which we have organs of sensation. Many eminent physiologists hold the
affirmative. These contend, that a thought (for example) is as much the
result of nervous agency, as a sensation: that some particular state of
our nervous system, in particular of that central portion of it called
the brain, invariably precedes, and is presupposed by, every state of
our consciousness. According to this theory, one state of mind is never
really produced by another: all are produced by states of body. When one
thought seems to call up another by association, it is not really a
thought which recals a thought; the association did not exist between
the two thoughts, but between the two states of the brain or nerves
which preceded the thoughts: one of those states recals the other, each
being attended, in its passage, by the particular state of consciousness
which is consequent on it. On this theory the uniformities of succession
among states of mind would be mere derivative uniformities, resulting
from the laws of succession of the bodily states which cause them. There
would be no original mental laws, no Laws of Mind in the sense in which
I use the term, at all: and mental science would be a mere branch,
though the highest and most recondite branch, of the science of
physiology. M. Comte, accordingly, claims the scientific cognizance of
moral and intellectual phenomena exclusively for physiologists; and not
only denies to Psychology, or Mental Philosophy properly so called, the
character of a science, but places it, in the chimerical nature of its
objects and pretensions, almost on a par with astrology.

But, after all has been said which can be said, it remains incontestible
that there exist uniformities of succession among states of mind, and
that these can be ascertained by observation and experiment. Further,
that every mental state has a nervous state for its immediate antecedent
and proximate cause, though extremely probable, cannot hitherto be said
to be proved, in the conclusive manner in which this can be proved of
sensations; and even were it certain, yet every one must admit that we
are wholly ignorant of the characteristics of these nervous states; we
know not, and at present have no means of knowing, in what respect one
of them differs from another; and our only mode of studying their
successions or coexistences must be by observing the successions and
coexistences of the mental states, of which they are supposed to be the
generators or causes. The successions, therefore, which obtain among
mental phenomena, do not admit of being deduced from the physiological
laws of our nervous organization: and all real knowledge of them must
continue, for a long time at least, if not always, to be sought in the
direct study, by observation and experiment, of the mental successions
themselves. Since therefore the order of our mental phenomena must be
studied in those phenomena, and not inferred from the laws of any
phenomena more general, there is a distinct and separate Science of

The relations, indeed, of that science to the science of physiology must
never be overlooked or undervalued. It must by no means be forgotten
that the laws of mind may be derivative laws resulting from laws of
animal life, and that their truth therefore may ultimately depend on
physical conditions; and the influence of physiological states or
physiological changes in altering or counteracting the mental
successions, is one of the most important departments of psychological
study. But, on the other hand, to reject the resource of psychological
analysis, and construct the theory of the mind solely on such data as
physiology at present affords, seems to me as great an error in
principle, and an even more serious one in practice. Imperfect as is the
science of mind, I do not scruple to affirm, that it is in a
considerably more advanced state than the portion of physiology which
corresponds to it; and to discard the former for the latter appears to
me an infringement of the true canons of inductive philosophy, which
must produce, and which does produce, erroneous conclusions in some very
important departments of the science of human nature.

§ 3. The subject, then, of Psychology, is the uniformities of
succession, the laws, whether ultimate or derivative, according to which
one mental state succeeds another; is caused by, or at least, is caused
to follow, another. Of these laws, some are general, others more
special. The following are examples of the most general laws.

First: Whenever any state of consciousness has once been excited in us,
no matter by what cause; an inferior degree of the same state of
consciousness, a state of consciousness resembling the former, but
inferior in intensity, is capable of being reproduced in us, without the
presence of any such cause as excited it at first. Thus, if we have once
seen or touched an object, we can afterwards think of the object though
it be absent from our sight or from our touch. If we have been joyful or
grieved at some event, we can think of, or remember our past joy or
grief, though no new event of a happy or painful nature has taken place.
When a poet has put together a mental picture of an imaginary object, a
Castle of Indolence, a Una, or a Hamlet, he can afterwards think of the
ideal object he has created, without any fresh act of intellectual
combination. This law is expressed by saying, in the language of Hume,
that every mental _impression_ has its _idea_.

Secondly: These ideas, or secondary mental states, are excited by our
impressions, or by other ideas, according to certain laws which are
called Laws of Association. Of these laws the first is, that similar
ideas tend to excite one another. The second is, that when two
impressions have been frequently experienced (or even thought of) either
simultaneously or in immediate succession, then whenever one of these
impressions, or the idea of it, recurs, it tends to excite the idea of
the other. The third law is, that greater intensity in either or both of
the impressions, is equivalent, in rendering them excitable by one
another, to a greater frequency of conjunction. These are the laws of
ideas: on which I shall not enlarge in this place, but refer the reader
to works professedly psychological, in particular to Mr. James Mill's
_Analysis of the Phenomena of the Human Mind_, where the principal laws
of association, along with many of their applications, are copiously
exemplified, and with a masterly hand.[3]

These simple or elementary Laws of Mind have been ascertained by the
ordinary methods of experimental inquiry; nor could they have been
ascertained in any other manner. But a certain number of elementary
laws having thus been obtained, it is a fair subject of scientific
inquiry how far those laws can be made to go in explaining the actual
phenomena. It is obvious that complex laws of thought and feeling not
only may, but must, be generated from these simple laws. And it is to be
remarked, that the case is not always one of Composition of Causes: the
effect of concurring causes is not always precisely the sum of the
effects of those causes when separate, nor even always an effect of the
same kind with them. Reverting to the distinction which occupies so
prominent a place in the theory of induction; the laws of the phenomena
of mind are sometimes analogous to mechanical, but sometimes also to
chemical laws. When many impressions or ideas are operating in the mind
together, there sometimes takes place a process, of a similar kind to
chemical combination. When impressions have been so often experienced in
conjunction, that each of them calls up readily and instantaneously the
ideas of the whole group, those ideas sometimes melt and coalesce into
one another, and appear not several ideas, but one; in the same manner
as, when the seven prismatic colours are presented to the eye in rapid
succession, the sensation produced is that of white. But as in this last
case it is correct to say that the seven colours when they rapidly
follow one another _generate_ white, but not that they actually _are_
white; so it appears to me that the Complex Idea, formed by the blending
together of several simpler ones, should, when it really appears simple,
(that is, when the separate elements are not consciously distinguishable
in it,) be said to _result from_, or _be generated by_, the simple
ideas, not to _consist_ of them. Our idea of an orange really _consists_
of the simple ideas of a certain colour, a certain form, a certain taste
and smell, &c., because we can, by interrogating our consciousness,
perceive all these elements in the idea. But we cannot perceive, in so
apparently simple a feeling as our perception of the shape of an object
by the eye, all that multitude of ideas derived from other senses,
without which it is well ascertained that no such visual perception
would ever have had existence; nor, in our idea of Extension, can we
discover those elementary ideas of resistance, derived from our
muscular frame, in which it has been conclusively shown that the idea
originates. These therefore are cases of mental chemistry: in which it
is proper to say that the simple ideas generate, rather than that they
compose, the complex ones.

With respect to all the other constituents of the mind, its beliefs, its
abstruser conceptions, its sentiments, emotions, and volitions; there
are some (among whom are Hartley, and the author of the _Analysis_) who
think that the whole of these are generated from simple ideas of
sensation, by a chemistry similar to that which we have just
exemplified. These philosophers have made out a great part of their
case, but I am not satisfied that they have established the whole of it.
They have shown that there is such a thing as mental chemistry; that the
heterogeneous nature of a feeling A, considered in relation to B and C,
is no conclusive argument against its being generated from B and C.
Having proved this, they proceed to show, that where A is found, B and C
were or may have been present, and why therefore, they ask, should not A
have been generated from B and C? But even if this evidence were carried
to the highest degree of completeness which it admits of; if it were
shown (which hitherto it has not, in all cases, been) that certain
groups of associated ideas not only might have been, but actually were,
present whenever the more recondite mental feeling was experienced; this
would amount only to the Method of Agreement, and could not prove
causation until confirmed by the more conclusive evidence of the Method
of Difference. If the question be whether Belief is a mere case of close
association of ideas, it would be necessary to examine experimentally if
it be true that any ideas whatever, provided they are associated with
the required degree of closeness, give rise to belief. If the inquiry be
into the origin of moral feelings, the feeling for example of moral
reprobation, it is necessary to compare all the varieties of actions or
states of mind which are ever morally disapproved, and see whether in
all these cases it can be shown, or reasonably surmised, that the action
or state of mind had become connected by association, in the
disapproving mind, with some particular class of hateful or disgusting
ideas; and the method employed is, thus far, that of Agreement. But
this is not enough. Supposing this proved, we must try further by the
Method of Difference, whether this particular kind of hateful or
disgusting ideas, when it becomes associated with an action previously
indifferent, will render that action a subject of moral disapproval. If
this question can be answered in the affirmative, it is shown to be a
law of the human mind, that an association of that particular
description is the generating cause of moral reprobation. That all this
is the case has been rendered extremely probable, but the experiments
have not been tried with the degree of precision necessary for a
complete and absolutely conclusive induction.[4]

It is further to be remembered, that even if all which this theory of
mental phenomena contends for could be proved, we should not be the more
enabled to resolve the laws of the more complex feelings into those of
the simpler ones. The generation of one class of mental phenomena from
another, whenever it can be made out, is a highly interesting fact in
psychological chemistry; but it no more supersedes the necessity of an
experimental study of the generated phenomenon, than a knowledge of the
properties of oxygen and sulphur enables us to deduce those of sulphuric
acid without specific observation and experiment. Whatever, therefore,
may be the final issue of the attempt to account for the origin of our
judgments, our desires, or our volitions, from simpler mental phenomena,
it is not the less imperative to ascertain the sequences of the complex
phenomena themselves, by special study in conformity to the canons of
Induction. Thus, in respect to Belief, psychologists will always have to
inquire, what beliefs we have by direct consciousness, and according to
what laws one belief produces another; what are the laws, in virtue of
which one thing is recognised by the mind, either rightly or
erroneously, as evidence of another thing. In regard to Desire, they
will have to examine what objects we desire naturally, and by what
causes we are made to desire things originally indifferent, or even
disagreeable to us; and so forth. It may be remarked, that the general
laws of association prevail among these more intricate states of mind,
in the same manner as among the simpler ones. A desire, an emotion, an
idea of the higher order of abstraction, even our judgments and
volitions when they have become habitual, are called up by association,
according to precisely the same laws as our simple ideas.

§ 4. In the course of these inquiries it will be natural and necessary
to examine, how far the production of one state of mind by another is
influenced by any assignable state of body. The commonest observation
shows that different minds are susceptible in very different degrees, to
the action of the same psychological causes. The idea, for example, of a
given desirable object, will excite in different minds very different
degrees of intensity of desire. The same subject of meditation,
presented to different minds, will excite in them very unequal degrees
of intellectual action. These differences of mental susceptibility in
different individuals may be, first, original and ultimate facts, or,
secondly, they may be consequences of the previous mental history of
those individuals, or thirdly and lastly, they may depend on varieties
of physical organization. That the previous mental history of the
individuals must have some share in producing or in modifying the whole
of their mental character, is an inevitable consequence of the laws of
mind; but that differences of bodily structure also co-operate, is the
opinion of all physiologists, confirmed by common experience. It is to
be regretted that hitherto this experience, being accepted in the gross,
without due analysis, has been made the groundwork of empirical
generalizations most detrimental to the progress of real knowledge.

It is certain that the natural differences which really exist in the
mental predispositions or susceptibilities of different persons, are
often not unconnected with diversities in their organic constitution.
But it does not therefore follow that these organic differences must in
all cases influence the mental phenomena directly and immediately. They
often affect them through the medium of their psychological causes. For
example, the idea of some particular pleasure may excite in different
persons, even independently of habit or education, very different
strengths of desire, and this may be the effect of their different
degrees or kinds of nervous susceptibility; but these organic
differences, we must remember, will render the pleasurable sensation
itself more intense in one of these persons than in the other; so that
the idea of the pleasure will also be an intenser feeling, and will, by
the operation of mere mental laws, excite an intenser desire, without
its being necessary to suppose that the desire itself is directly
influenced by the physical peculiarity. As in this, so in many cases,
such differences in the kind or in the intensity of the physical
sensations as must necessarily result from differences of bodily
organization, will of themselves account for many differences not only
in the degree, but even in the kind, of the other mental phenomena. So
true is this, that even different _qualities_ of mind, different types
of mental character, will naturally be produced by mere differences of
intensity in the sensations generally: as is well pointed out in an able
essay on Dr. Priestley, mentioned in a former chapter:--

"The sensations which form the elements of all knowledge are received
either simultaneously or successively; when several are received
simultaneously, as the smell, the taste, the colour, the form, &c. of a
fruit, their association together constitutes our idea of an _object_;
when received successively, their association makes up the idea of an
_event_. Anything, then, which favours the associations of synchronous
ideas, will tend to produce a knowledge of objects, a perception of
qualities; while anything which favours association in the successive
order, will tend to produce a knowledge of events, of the order of
occurrences, and of the connexion of cause and effect: in other words,
in the one case a perceptive mind, with a discriminate feeling of the
pleasurable and painful properties of things, a sense of the grand and
the beautiful, will be the result: in the other, a mind attentive to the
movements and phenomena, a ratiocinative and philosophic intellect. Now
it is an acknowledged principle, that all sensations experienced during
the presence of any vivid impression, become strongly associated with
it, and with each other; and does it not follow, that the synchronous
feelings of a sensitive constitution, (_i.e._ the one which has vivid
impressions,) will be more intimately blended than in a differently
formed mind? If this suggestion has any foundation in truth, it leads to
an inference not unimportant; that where nature has endowed an
individual with great original susceptibility, he will probably be
distinguished by fondness for natural history, a relish for the
beautiful and great, and moral enthusiasm; where there is but a
mediocrity of sensibility, a love of science, of abstract truth, with a
deficiency of taste and of fervour, is likely to be the result."

We see from this example, that when the general laws of mind are more
accurately known, and above all, more skilfully applied to the detailed
explanation of mental peculiarities, they will account for many more of
those peculiarities than is ordinarily supposed. Unfortunately the
reaction of the last and present generation against the philosophy of
the eighteenth century has produced a very general neglect of this great
department of analytical inquiry; of which, consequently, the recent
progress has been by no means proportional to its early promise. The
majority of those who speculate on human nature, prefer dogmatically to
assume that the mental differences which they perceive, or think they
perceive, among human beings, are ultimate facts, incapable of being
either explained or altered, rather than take the trouble of fitting
themselves, by the requisite processes of thought, for referring those
mental differences to the outward causes by which they are for the most
part produced, and on the removal of which they would cease to exist.
The German school of metaphysical speculation, which has not yet lost
its temporary predominance in European thought, has had this among many
other injurious influences: and at the opposite extreme of the
psychological scale, no writer, either of early or of recent date, is
chargeable in a higher degree with this aberration from the true
scientific spirit, than M. Comte.

It is certain that, in human beings at least, differences in education
and in outward circumstances are capable of affording an adequate
explanation of by far the greatest portion of character; and that the
remainder may be in great part accounted for by physical differences in
the sensations produced in different individuals by the same external or
internal cause. There are, however, some mental facts which do not seem
to admit of these modes of explanation. Such, to take the strongest
case, are the various instincts of animals, and the portion of human
nature which corresponds to those instincts. No mode has been suggested,
even by way of hypothesis, in which these can receive any satisfactory,
or even plausible, explanation from psychological causes alone; and
there is great reason to think that they have as positive, and even as
direct and immediate, a connexion with physical conditions of the brain
and nerves, as any of our mere sensations have. A supposition which (it
is perhaps not superfluous to add) in no way conflicts with the
indisputable fact, that these instincts may be modified to any extent,
or entirely conquered, in human beings at least, by other mental
influences, and by education.

Whether organic causes exercise a direct influence over any other
classes of mental phenomena, is hitherto as far from being ascertained,
as is the precise nature of the organic conditions even in the case of
instincts. The physiology, however, of the brain and nervous system is
in a state of such rapid advance, and is continually bringing forth such
new and interesting results, that if there be really a connexion between
mental peculiarities and any varieties cognizable by our senses in the
structure of the cerebral and nervous apparatus, the nature of that
connexion is now in a fair way of being found out. The latest
discoveries in cerebral physiology appear to have proved, that any such
connexion which may exist is of a radically different character from
that contended for by Gall and his followers, and that whatever may
hereafter be found to be the true theory of the subject, phrenology at
least is untenable.



§ 1. The laws of mind as characterized in the preceding chapter, compose
the universal or abstract portion of the philosophy of human nature; and
all the truths of common experience, constituting a practical knowledge
of mankind, must, to the extent to which they are truths, be results or
consequences of these. Such familiar maxims, when collected _à
posteriori_ from observation of life, occupy among the truths of the
science the place of what, in our analysis of Induction, have so often
been spoken of under the title of Empirical Laws.

An Empirical Law (it will be remembered) is an uniformity, whether of
succession or of coexistence, which holds true in all instances within
our limits of observation, but is not of a nature to afford any
assurance that it would hold beyond those limits; either because the
consequent is not really the effect of the antecedent, but forms part
along with it of a chain of effects, flowing from prior causes not yet
ascertained; or because there is ground to believe that the sequence
(though a case of causation) is resolvable into simpler sequences, and,
depending therefore on a concurrence of several natural agencies, is
exposed to an unknown multitude of possibilities of counteraction. In
other words, an empirical law is a generalization, of which, not content
with finding it true, we are obliged to ask, why is it true? knowing
that its truth is not absolute, but dependent on some more general
conditions, and that it can only be relied on in so far as there is
ground of assurance that those conditions are realized.

Now, the observations concerning human affairs collected from common
experience, are precisely of this nature. Even if they were universally
and exactly true within the bounds of experience, which they never are,
still they are not the ultimate laws of human action; they are not the
principles of human nature, but results of those principles under the
circumstances in which mankind have happened to be placed. When the
Psalmist said in his haste that "all men are liars," he enunciated what
in some ages and countries is borne out by ample experience; but it is
not a law of man's nature to lie; though it is one of the consequences
of the laws of human nature, that lying is nearly universal when certain
external circumstances exist universally, especially circumstances
productive of habitual distrust and fear. When the character of the old
is asserted to be cautious, and of the young impetuous, this, again, is
but an empirical law; for it is not because of their youth that the
young are impetuous, nor because of their age that the old are cautious.
It is chiefly, if not wholly, because the old, during their many years
of life, have generally had much experience of its various evils, and
having suffered or seen others suffer much from incautious exposure to
them, have acquired associations favourable to circumspection: while the
young, as well from the absence of similar experience as from the
greater strength of the inclinations which urge them to enterprise,
engage themselves in it more readily. Here, then, is the _explanation_
of the empirical law; here are the conditions which ultimately determine
whether the law holds good or not. If an old man has not been oftener
than most young men in contact with danger and difficulty, he will be
equally incautious: if a youth has not stronger inclinations than an old
man, he probably will be as little enterprising. The empirical law
derives whatever truth it has, from the causal laws of which it is a
consequence. If we know those laws, we know what are the limits to the
derivative law: while, if we have not yet accounted for the empirical
law--if it rest only on observation--there is no safety in applying it
far beyond the limits of time, place, and circumstance, in which the
observations were made.

The really scientific truths, then, are not these empirical laws, but
the causal laws which explain them. The empirical laws of those
phenomena which depend on known causes, and of which a general theory
can therefore be constructed, have, whatever may be their value in
practice, no other function in science than that of verifying the
conclusions of theory. Still more must this be the case when most of the
empirical laws amount, even within the limits of observation, only to
approximate generalizations.

§ 2. This however is not, so much as is sometimes supposed, a
peculiarity of the sciences called moral. It is only in the simplest
branches of science that empirical laws are ever exactly true; and not
always in those. Astronomy, for example, is the simplest of all the
sciences which explain, in the concrete, the actual course of natural
events. The causes or forces, on which astronomical phenomena depend,
are fewer in number than those which determine any other of the great
phenomena of nature. Accordingly, as each effect results from the
conflict of but few causes, a great degree of regularity and uniformity
might be expected to exist among the effects; and such is really the
case: they have a fixed order, and return in cycles. But propositions
which should express, with absolute correctness, all the successive
positions of a planet until the cycle is completed, would be of almost
unmanageable complexity, and could be obtained from theory alone. The
generalizations which can be collected on the subject from direct
observation, even such as Kepler's law, are mere approximations: the
planets, owing to their perturbations by one another, do not move in
exact ellipses. Thus even in astronomy, perfect exactness in the mere
empirical laws is not to be looked for; much less, then, in more complex
subjects of inquiry.

The same example shows how little can be inferred against the
universality or even the simplicity of the ultimate laws, from the
impossibility of establishing any but approximate empirical laws of the
effects. The laws of causation according to which a class of phenomena
are produced may be very few and simple, and yet the effects themselves
may be so various and complicated that it shall be impossible to trace
any regularity whatever completely through them. For the phenomena in
question may be of an eminently modifiable character; insomuch that
innumerable circumstances are capable of influencing the effect,
although they may all do it according to a very small number of laws.
Suppose that all which passes in the mind of man is determined by a few
simple laws: still, if those laws be such that there is not one of the
facts surrounding a human being, or of the events which happen to him,
that does not influence in some mode or degree his subsequent mental
history, and if the circumstances of different human beings are
extremely different, it will be no wonder if very few propositions can
be made respecting the details of their conduct or feelings, which will
be true of all mankind.

Now, without deciding whether the ultimate laws of our mental nature are
few or many, it is at least certain that they are of the above
description. It is certain that our mental states, and our mental
capacities and susceptibilities, are modified, either for a time or
permanently, by everything which happens to us in life. Considering
therefore how much these modifying causes differ in the case of any two
individuals, it would be unreasonable to expect that the empirical laws
of the human mind, the generalizations which can be made respecting the
feelings or actions of mankind without reference to the causes that
determine them, should be anything but approximate generalizations. They
are the common wisdom of common life, and as such are invaluable;
especially as they are mostly to be applied to cases not very dissimilar
to those from which they were collected. But when maxims of this sort,
collected from Englishmen, come to be applied to Frenchmen, or when
those collected from the present day are applied to past or future
generations, they are apt to be very much at fault. Unless we have
resolved the empirical law into the laws of the causes on which it
depends, and ascertained that those causes extend to the case which we
have in view, there can be no reliance placed in our inferences. For
every individual is surrounded by circumstances different from those of
every other individual; every nation or generation of mankind from every
other nation or generation: and none of these differences are without
their influence in forming a different type of character. There is,
indeed, also a certain general resemblance; but peculiarities of
circumstances are continually constituting exceptions even to the
propositions which are true in the great majority of cases.

Although, however, there is scarcely any mode of feeling or conduct
which is, in the absolute sense, common to all mankind; and though the
generalizations which assert that any given variety of conduct or
feeling will be found universally, (however nearly they may approximate
to truth within given limits of observation,) will be considered as
scientific propositions by no one who is at all familiar with scientific
investigation; yet all modes of feeling and conduct met with among
mankind have causes which produce them; and in the propositions which
assign those causes, will be found the explanation of the empirical
laws, and the limiting principle of our reliance on them. Human beings
do not all feel and act alike in the same circumstances; but it is
possible to determine what makes one person, in a given position, feel
or act in one way, another in another; how any given mode of feeling and
conduct, compatible with the general laws (physical and mental) of human
nature, has been, or may be, formed. In other words, mankind have not
one universal character, but there exist universal laws of the Formation
of Character. And since it is by these laws, combined with the facts of
each particular case, that the whole of the phenomena of human action
and feeling are produced, it is on these that every rational attempt to
construct the science of human nature in the concrete, and for practical
purposes, must proceed.

§ 3. The laws, then, of the formation of character being the principal
object of scientific inquiry into human nature; it remains to determine
the method of investigation best fitted for ascertaining them. And the
logical principles according to which this question is to be decided,
must be those which preside over every other attempt to investigate the
laws of very complex phenomena. For it is evident that both the
character of any human being, and the aggregate of the circumstances by
which that character has been formed, are facts of a high order of
complexity. Now to such cases we have seen that the Deductive Method,
setting out from general laws, and verifying their consequences by
specific experience, is alone applicable. The grounds of this great
logical doctrine have formerly been stated: and its truth will derive
additional support from a brief examination of the specialities of the
present case.

There are only two modes in which laws of nature can be ascertained:
deductively, and experimentally: including under the denomination of
experimental inquiry, observation as well as artificial experiment. Are
the laws of the formation of character susceptible of a satisfactory
investigation by the method of experimentation? Evidently not; because,
even if we suppose unlimited power of varying the experiment, (which is
abstractedly possible, though no one but an oriental despot has that
power, or if he had, would probably be disposed to exercise it,) a still
more essential condition is wanting; the power of performing any of the
experiments with scientific accuracy.

The instances requisite for the prosecution of a directly experimental
inquiry into the formation of character, would be a number of human
beings to bring up and educate, from infancy to mature age. And to
perform any one of these experiments with scientific propriety, it would
be necessary to know and record every sensation or impression received
by the young pupil from a period long before it could speak; including
its own notions respecting the sources of all those sensations and
impressions. It is not only impossible to do this completely, but even
to do so much of it as should constitute a tolerable approximation. One
apparently trivial circumstance which eluded our vigilance, might let in
a train of impressions and associations sufficient to vitiate the
experiment as an authentic exhibition of the effects flowing from given
causes. No one who has sufficiently reflected on education is ignorant
of this truth: and whoever has not, will find it most instructively
illustrated in the writings of Rousseau and Helvetius on that great

Under this impossibility of studying the laws of the formation of
character by experiments purposely contrived to elucidate them, there
remains the resource of simple observation. But if it be impossible to
ascertain the influencing circumstances with any approach to
completeness even when we have the shaping of them ourselves, much more
impossible is it when the cases are further removed from our
observation, and altogether out of our control. Consider the difficulty
of the very first step--of ascertaining what actually is the character
of the individual, in each particular case that we examine. There is
hardly any person living, concerning some essential part of whose
character there are not differences of opinion even among his intimate
acquaintances: and a single action, or conduct continued only for a
short time, goes a very little way towards ascertaining it. We can only
make our observations in a rough way, and _en masse_; not attempting to
ascertain completely in any given instance, what character has been
formed, and still less by what causes; but only observing in what state
of previous circumstances it is found that certain marked mental
qualities or deficiencies _oftenest_ exist. These conclusions, besides
that they are mere approximate generalizations, deserve no reliance even
as such, unless the instances are sufficiently numerous to eliminate not
only chance, but every assignable circumstance in which a number of the
cases examined may happen to have resembled one another. So numerous and
various, too, are the circumstances which form individual character,
that the consequence of any particular combination is hardly ever some
definite and strongly marked character, always found where that
combination exists, and not otherwise. What is obtained, even after the
most extensive and accurate observation, is merely a comparative result;
as for example, that in a given number of Frenchmen, taken
indiscriminately, there will be found more persons of a particular
mental tendency, and fewer of the contrary tendency, than among an
equal number of Italians or English, similarly taken; or thus: of a
hundred Frenchmen and an equal number of Englishmen, fairly selected,
and arranged according to the degree in which they possess a particular
mental characteristic, each number, 1, 2, 3, &c., of the one series,
will be found to possess more of that characteristic than the
corresponding number of the other. Since, therefore, the comparison is
not one of kinds, but of ratios and degrees; and since in proportion as
the differences are slight, it requires a greater number of instances to
eliminate chance; it cannot often happen to any one to know a sufficient
number of cases with the accuracy requisite for making the sort of
comparison last mentioned; less than which, however, would not
constitute a real induction. Accordingly there is hardly one current
opinion respecting the characters of nations, classes, or descriptions
of persons, which is universally acknowledged as indisputable.[5]

And finally, if we could even obtain by way of experiment a much more
satisfactory assurance of these generalizations than is really possible,
they would still be only empirical laws. They would show, indeed, that
there was some connexion between the type of character formed, and the
circumstances existing in the case; but not what the precise connexion
was, nor to which of the peculiarities of those circumstances the effect
was really owing. They could only, therefore, be received as results of
causation, requiring to be resolved into the general laws of the causes:
until the determination of which, we could not judge within what limits
the derivative laws might serve as presumptions in cases yet unknown, or
even be depended on as permanent in the very cases from which they were
collected. The French people had, or were supposed to have, a certain
national character: but they drive out their royal family and
aristocracy, alter their institutions, pass through a series of
extraordinary events for half a century, and at the end of that time are
found to be, in many respects, greatly altered. A long list of mental
and moral differences are observed, or supposed, to exist between men
and women: but at some future, and, it may be hoped, not distant period,
equal freedom and an equally independent social position come to be
possessed by both, and their differences of character are either removed
or totally altered.

But if the differences which we think we observe between French and
English, or between men and women, can be connected with more general
laws; if they be such as might be expected to be produced by the
differences of government, former customs, and physical peculiarities in
the two nations, and by the diversities of education, occupations,
personal independence, and social privileges, and whatever original
differences there may be in bodily strength and nervous sensibility,
between the two sexes; then, indeed, the coincidence of the two kinds of
evidence justifies us in believing that we have both reasoned rightly
and observed rightly. Our observation, though not sufficient as proof,
is ample as verification. And having ascertained not only the empirical
laws, but the causes, of the peculiarities, we need be under no
difficulty in judging how far they may be expected to be permanent, or
by what circumstances they would be modified or destroyed.

§ 4. Since, then, it is impossible to obtain really accurate
propositions respecting the formation of character from observation and
experiment alone, we are driven perforce to that which, even if it had
not been the indispensable, would have been the most perfect, mode of
investigation, and which it is one of the principal aims of philosophy
to extend; namely, that which tries its experiments not on the complex
facts, but on the simple ones of which they are compounded; and after
ascertaining the laws of the causes, the composition of which gives rise
to the complex phenomena, then considers whether these will not explain
and account for the approximate generalizations which have been framed
empirically respecting the sequences of those complex phenomena. The
laws of the formation of character are, in short, derivative laws,
resulting from the general laws of mind; and are to be obtained by
deducing them from those general laws; by supposing any given set of
circumstances, and then considering what, according to the laws of mind,
will be the influence of those circumstances on the formation of

A science is thus formed, to which I would propose to give the name of
Ethology, or the Science of Character; from _ἦθος_, a word more nearly
corresponding to the term "character" as I here use it, than any other
word in the same language. The name is perhaps etymologically applicable
to the entire science of our mental and moral nature; but if, as is
usual and convenient, we employ the name Psychology for the science of
the elementary laws of mind, Ethology will serve for the ulterior
science which determines the kind of character produced, in conformity
to those general laws, by any set of circumstances, physical and moral.
According to this definition, Ethology is the science which corresponds
to the art of education; in the widest sense of the term, including the
formation of national or collective character as well as individual. It
would indeed be vain to expect (however completely the laws of the
formation of character might be ascertained) that we could know so
accurately the circumstances of any given case as to be able positively
to predict the character that would be produced in that case. But we
must remember that a degree of knowledge far short of the power of
actual prediction, is often of much practical value. There may be great
power of influencing phenomena, with a very imperfect knowledge of the
causes by which they are in any given instance determined. It is enough
that we know that certain means have a _tendency_ to produce a given
effect, and that others have a tendency to frustrate it. When the
circumstances of an individual or of a nation are in any considerable
degree under our control, we may, by our knowledge of tendencies, be
enabled to shape those circumstances in a manner much more favourable to
the ends we desire, than the shape which they would of themselves
assume. This is the limit of our power; but within this limit the power
is a most important one.

This science of Ethology may be called the Exact Science of Human
Nature; for its truths are not, like the empirical laws which depend on
them, approximate generalizations, but real laws. It is, however, (as in
all cases of complex phenomena) necessary to the exactness of the
propositions, that they should be hypothetical only, and affirm
tendencies, not facts. They must not assert that something will always,
or certainly, happen; but only that such and such will be the effect of
a given cause, so far as it operates uncounteracted. It is a scientific
proposition, that bodily strength tends to make men courageous; not that
it always makes them so: that an interest on one side of a question
tends to bias the judgment; not that it invariably does so: that
experience tends to give wisdom; not that such is always its effect.
These propositions, being assertive only of tendencies, are not the less
universally true because the tendencies may be frustrated.

§ 5. While on the one hand Psychology is altogether, or principally, a
science of observation and experiment, Ethology, as I have conceived it,
is, as I have already remarked, altogether deductive. The one ascertains
the simple laws of Mind in general, the other traces their operation in
complex combinations of circumstances. Ethology stands to Psychology in
a relation very similar to that in which the various branches of natural
philosophy stand to mechanics. The principles of Ethology are properly
the middle principles, the _axiomata media_ (as Bacon would have said)
of the science of mind: as distinguished, on the one hand from the
empirical laws resulting from simple observation, and on the other from
the highest generalizations.

And this seems a suitable place for a logical remark, which, though of
general application, is of peculiar importance in reference to the
present subject. Bacon has judiciously observed that the _axiomata
media_ of every science principally constitute its value. The lowest
generalizations, until explained by and resolved into the middle
principles of which they are the consequences, have only the imperfect
accuracy of empirical laws; while the most general laws are _too_
general, and include too few circumstances, to give sufficient
indication of what happens in individual cases, where the circumstances
are almost always immensely numerous. In the importance, therefore,
which Bacon assigns, in every science, to the middle principles, it is
impossible not to agree with him. But I conceive him to have been
radically wrong in his doctrine respecting the mode in which these
_axiomata media_ should be arrived at; though there is no one
proposition laid down in his works for which he has been more
extravagantly eulogized. He enunciates as an universal rule, that
induction should proceed from the lowest to the middle principles, and
from those to the highest, never reversing that order, and consequently
leaving no room for the discovery of new principles by way of deduction
at all. It is not to be conceived that a man of his sagacity could have
fallen into this mistake, if there had existed in his time, among the
sciences which treat of successive phenomena, one single instance of a
deductive science, such as mechanics, astronomy, optics, acoustics, &c.
now are. In those sciences it is evident that the higher and middle
principles are by no means derived from the lowest, but the reverse. In
some of them the very highest generalizations were those earliest
ascertained with any scientific exactness; as, for example (in
mechanics), the laws of motion. Those general laws had not indeed at
first the acknowledged universality which they acquired after having
been successfully employed to explain many classes of phenomena to which
they were not originally seen to be applicable; as when the laws of
motion were employed, in conjunction with other laws, to explain
deductively the celestial phenomena. Still, the fact remains, that the
propositions which were afterwards recognised as the most general truths
of the science, were, of all its accurate generalizations, those
earliest arrived at. Bacon's greatest merit cannot therefore consist, as
we are so often told that it did, in exploding the vicious method
pursued by the ancients of flying to the highest generalizations first,
and deducing the middle principles from them; since this is neither a
vicious nor an exploded, but the universally accredited method of modern
science, and that to which it owes its greatest triumphs. The error of
ancient speculation did not consist in making the largest
generalizations first, but in making them without the aid or warrant of
rigorous inductive methods, and applying them deductively without the
needful use of that important part of the Deductive Method termed

The order in which truths of the various degrees of generality should be
ascertained, cannot, I apprehend, be prescribed by any unbending rule. I
know of no maxim which can be laid down on the subject, but to obtain
those first, in respect to which the conditions of a real induction can
be first and most completely realized. Now, wherever our means of
investigation can reach causes, without stopping at the empirical laws
of the effects, the simplest cases, being those in which fewest causes
are simultaneously concerned, will be most amenable to the inductive
process; and these are the cases which elicit laws of the greatest
comprehensiveness. In every science, therefore, which has reached the
stage at which it becomes a science of causes, it will be usual as well
as desirable first to obtain the highest generalizations, and then
deduce the more special ones from them. Nor can I discover any
foundation for the Baconian maxim, so much extolled by subsequent
writers, except this: That before we attempt to explain deductively
from more general laws any new class of phenomena, it is desirable to
have gone as far as is practicable in ascertaining the empirical laws of
those phenomena; so as to compare the results of deduction, not with one
individual instance after another, but with general propositions
expressive of the points of agreement which have been found among many
instances. For if Newton had been obliged to verify the theory of
gravitation, not by deducing from it Kepler's laws, but by deducing all
the observed planetary positions which had served Kepler to establish
those laws, the Newtonian theory would probably never have emerged from
the state of an hypothesis.[6]

The applicability of these remarks to the special case under
consideration, cannot admit of question. The science of the formation of
character is a science of causes. The subject is one to which those
among the canons of induction, by which laws of causation are
ascertained, can be rigorously applied. It is, therefore, both natural
and advisable to ascertain the simplest, which are necessarily the most
general, laws of causation first, and to deduce the middle principles
from them. In other words, Ethology, the deductive science, is a system
of corollaries from Psychology, the experimental science.

§ 6. Of these, the earlier alone has been, as yet, really conceived or
studied as a science; the other, Ethology, is still to be created. But
its creation has at length become practicable. The empirical laws,
destined to verify its deductions, have been formed in abundance by
every successive age of humanity; and the premises for the deductions
are now sufficiently complete. Excepting the degree of uncertainty which
still exists as to the extent of the natural differences of individual
minds, and the physical circumstances on which these may be dependent,
(considerations which are of secondary importance when we are
considering mankind in the average, or _en masse_,) I believe most
competent judges will agree that the general laws of the different
constituent elements of human nature are even now sufficiently
understood, to render it possible for a competent thinker to deduce from
those laws with a considerable approach to certainty, the particular
type of character which would be formed, in mankind generally, by any
assumed set of circumstances. A science of Ethology, founded on the laws
of Psychology, is therefore possible; though little has yet been done,
and that little not at all systematically, towards forming it. The
progress of this important but most imperfect science will depend on a
double process: first, that of deducing theoretically the ethological
consequences of particular circumstances of position, and comparing them
with the recognised results of common experience; and secondly, the
reverse operation; increased study of the various types of human nature
that are to be found in the world; conducted by persons not only capable
of analysing and recording the circumstances in which these types
severally prevail, but also sufficiently acquainted with psychological
laws, to be able to explain and account for the characteristics of the
type, by the peculiarities of the circumstances: the residuum alone,
when there proves to be any, being set down to the account of congenital

For the experimental or _à posteriori_ part of this process, the
materials are continually accumulating by the observation of mankind. So
far as thought is concerned, the great problem of Ethology is to deduce
the requisite middle principles from the general laws of Psychology.
The subject to be studied is, the origin and sources of all those
qualities in human beings which are interesting to us, either as facts
to be produced, to be avoided, or merely to be understood: and the
object is, to determine, from the general laws of mind, combined with
the general position of our species in the universe, what actual or
possible combinations of circumstances are capable of promoting or of
preventing the production of those qualities. A science which possesses
middle principles of this kind, arranged in the order, not of causes,
but of the effects which it is desirable to produce or to prevent, is
duly prepared to be the foundation of the corresponding Art. And when
Ethology shall be thus prepared, practical education will be the mere
transformation of those principles into a parallel system of precepts,
and the adaptation of these to the sum total of the individual
circumstances which exist in each particular case.

It is hardly necessary again to repeat, that, as in every other
deductive science, verification _à posteriori_ must proceed _pari passu_
with deduction _à priori_. The inference given by theory as to the type
of character which would be formed by any given circumstances, must be
tested by specific experience of those circumstances whenever
obtainable; and the conclusions of the science as a whole, must undergo
a perpetual verification and correction from the general remarks
afforded by common experience respecting human nature in our own age,
and by history respecting times gone by. The conclusions of theory
cannot be trusted, unless confirmed by observation; nor those of
observation, unless they can be affiliated to theory, by deducing them
from the laws of human nature, and from a close analysis of the
circumstances of the particular situation. It is the accordance of these
two kinds of evidence separately taken--the consilience of _à priori_
reasoning and specific experience--which forms the only sufficient
ground for the principles of any science so "immersed in matter,"
dealing with such complex and concrete phenomena, as Ethology.



§ 1. Next after the science of individual man, comes the science of man
in society: of the actions of collective masses of mankind, and the
various phenomena which constitute social life.

If the formation of individual character is already a complex subject of
study, this subject must be, in appearance at least, still more complex;
because the number of concurrent causes, all exercising more or less
influence on the total effect, is greater, in the proportion in which a
nation, or the species at large, exposes a larger surface to the
operation of agents, psychological and physical, than any single
individual. If it was necessary to prove, in opposition to an existing
prejudice, that the simpler of the two is capable of being a subject of
science; the prejudice is likely to be yet stronger against the
possibility of giving a scientific character to the study of Politics,
and of the phenomena of Society. It is, accordingly, but of yesterday
that the conception of a political or social science has existed,
anywhere but in the mind of here and there an insulated thinker,
generally very ill prepared for its realization: though the subject
itself has of all others engaged the most general attention, and been a
theme of interested and earnest discussions, almost from the beginning
of recorded time.

The condition indeed of politics, as a branch of knowledge, was until
very lately, and has scarcely even yet ceased to be, that which Bacon
animadverted on, as the natural state of the sciences while their
cultivation is abandoned to practitioners; not being carried on as a
branch of speculative inquiry, but only with a view to the exigencies of
daily practice, and the _fructifera experimenta_, therefore, being
aimed at, almost to the exclusion of the _lucifera_. Such was medical
investigation, before physiology and natural history began to be
cultivated as branches of general knowledge. The only questions examined
were, what diet is wholesome, or what medicine will cure some given
disease; without any previous systematic inquiry into the laws of
nutrition, and of the healthy and morbid action of the different organs,
on which laws the effect of any diet or medicine must evidently depend.
And in politics, the questions which engaged general attention were
similar:--Is such an enactment, or such a form of government, beneficial
or the reverse--either universally, or to some particular community?
without any previous inquiry into the general conditions by which the
operation of legislative measures, or the effects produced by forms of
government, are determined. Students in politics thus attempted to study
the pathology and therapeutics of the social body, before they had laid
the necessary foundation in its physiology; to cure disease, without
understanding the laws of health. And the result was such as it must
always be when persons, even of ability, attempt to deal with the
complex questions of a science before its simpler and more elementary
truths have been established.

No wonder that when the phenomena of society have so rarely been
contemplated in the point of view characteristic of science, the
philosophy of society should have made little progress; should contain
few general propositions sufficiently precise and certain, for common
inquirers to recognise in them a scientific character. The vulgar notion
accordingly is, that all pretension to lay down general truths on
politics and society is quackery; that no universality and no certainty
are attainable in such matters. What partly excuses this common notion
is, that it is really not without foundation in one particular sense. A
large proportion of those who have laid claim to the character of
philosophic politicians, have attempted, not to ascertain universal
sequences, but to frame universal precepts. They have imagined some one
form of government, or system of laws, to fit all cases; a pretension
well meriting the ridicule with which it is treated by practitioners,
and wholly unsupported by the analogy of the art to which, from the
nature of its subject, that of politics must be the most nearly allied.
No one now supposes it possible that one remedy can cure all diseases,
or even the same disease in all constitutions and habits of body.

It is not necessary even to the perfection of a science, that the
corresponding art should possess universal, or even general, rules. The
phenomena of society might not only be completely dependent on known
causes, but the mode of action of all those causes might be reducible to
laws of considerable simplicity, and yet no two cases might admit of
being treated in precisely the same manner. So great might be the
variety of circumstances on which the results in different cases depend,
that the art might not have a single general precept to give, except
that of watching the circumstances of the particular case, and adapting
our measures to the effects which, according to the principles of the
science, result from those circumstances. But although, in so
complicated a class of subjects, it is impossible to lay down practical
maxims of universal application, it does not follow that the phenomena
do not conform to universal laws.

§ 2. All phenomena of society are phenomena of human nature, generated
by the action of outward circumstances upon masses of human beings: and
if, therefore, the phenomena of human thought, feeling, and action, are
subject to fixed laws, the phenomena of society cannot but conform to
fixed laws, the consequence of the preceding. There is, indeed, no hope
that these laws, though our knowledge of them were as certain and as
complete as it is in astronomy, would enable us to predict the history
of society, like that of the celestial appearances, for thousands of
years to come. But the difference of certainty is not in the laws
themselves, it is in the data to which these laws are to be applied. In
astronomy the causes influencing the result are few, and change little,
and that little according to known laws; we can ascertain what they are
now, and thence determine what they will be at any epoch of a distant
future. The data, therefore, in astronomy, are as certain as the laws
themselves. The circumstances, on the contrary, which influence the
condition and progress of society, are innumerable, and perpetually
changing; and though they all change in obedience to causes, and
therefore to laws, the multitude of the causes is so great as to defy
our limited powers of calculation. Not to say that the impossibility of
applying precise numbers to facts of such a description, would set an
impassable limit to the possibility of calculating them beforehand, even
if the powers of the human intellect were otherwise adequate to the

But, as before remarked, an amount of knowledge quite insufficient for
prediction, may be most valuable for guidance. The science of society
would have attained a very high point of perfection, if it enabled us,
in any given condition of social affairs, in the condition for instance
of Europe or any European country at the present time, to understand by
what causes it had, in any and every particular, been made what it was;
whether it was tending to any, and to what, changes; what effects each
feature of its existing state was likely to produce in the future; and
by what means any of those effects might be prevented, modified, or
accelerated, or a different class of effects superinduced. There is
nothing chimerical in the hope that general laws, sufficient to enable
us to answer these various questions for any country or time with the
individual circumstances of which we are well acquainted, do really
admit of being ascertained; and that the other branches of human
knowledge, which this undertaking presupposes, are so far advanced that
the time is ripe for its commencement. Such is the object of the Social

That the nature of what I consider the true method of the science may be
made more palpable, by first showing what that method is not; it will be
expedient to characterize briefly two radical misconceptions of the
proper mode of philosophizing on society and government, one or other of
which is, either explicitly or more often unconsciously, entertained by
almost all who have meditated or argued respecting the logic of
politics since the notion of treating it by strict rules, and on
Baconian principles, has been current among the more advanced thinkers.
These erroneous methods, if the word method can be applied to erroneous
tendencies arising from the absence of any sufficiently distinct
conception of method, may be termed the Experimental, or Chemical, mode
of investigation, and the Abstract, or Geometrical, mode. We shall begin
with the former.



§ 1. The laws of the phenomena of society are, and can be, nothing but
the laws of the actions and passions of human beings united together in
the social state. Men, however, in a state of society, are still men;
their actions and passions are obedient to the laws of individual human
nature. Men are not, when brought together, converted into another kind
of substance, with different properties; as hydrogen and oxygen are
different from water, or as hydrogen, oxygen, carbon, and azote, are
different from nerves, muscles, and tendons. Human beings in society
have no properties but those which are derived from, and may be resolved
into, the laws of the nature of individual man. In social phenomena the
Composition of Causes is the universal law.

Now, the method of philosophizing which may be termed chemical overlooks
this fact, and proceeds as if the nature of man as an individual were
not concerned at all, or were concerned in a very inferior degree, in
the operations of human beings in society. All reasoning in political or
social affairs, grounded on principles of human nature, is objected to
by reasoners of this sort, under such names as "abstract theory." For
the direction of their opinions and conduct, they profess to demand, in
all cases without exception, specific experience.

This mode of thinking is not only general with practitioners in
politics, and with that very numerous class who (on a subject which no
one, however ignorant, thinks himself incompetent to discuss) profess to
guide themselves by common sense rather than by science; but is often
countenanced by persons with greater pretensions to instruction; persons
who, having sufficient acquaintance with books and with the current
ideas to have heard that Bacon taught mankind to follow experience, and
to ground their conclusions on facts instead of metaphysical
dogmas--think that, by treating political facts in as directly
experimental a method as chemical facts, they are showing themselves
true Baconians, and proving their adversaries to be mere syllogizers and
schoolmen. As, however, the notion of the applicability of experimental
methods to political philosophy cannot coexist with any just conception
of these methods themselves, the kind of arguments from experience which
the chemical theory brings forth as its fruits (and which form the
staple, in this country especially, of parliamentary and hustings
oratory,) are such as, at no time since Bacon, would have been admitted
to be valid in chemistry itself, or in any other branch of experimental
science. They are such as these; that the prohibition of foreign
commodities must conduce to national wealth, because England has
flourished under it, or because countries in general which have adopted
it have flourished; that our laws, or our internal administration, or
our constitution, are excellent for a similar reason: and the eternal
arguments from historical examples, from Athens or Rome, from the fires
in Smithfield or the French Revolution.

I will not waste time in contending against modes of argumentation which
no person, with the smallest practice in estimating evidence, could
possibly be betrayed into; which draw conclusions of general application
from a single unanalysed instance, or arbitrarily refer an effect to
some one among its antecedents, without any process of elimination or
comparison of instances. It is a rule both of justice and of good sense
to grapple not with the absurdest, but with, the most reasonable form of
a wrong opinion. We shall suppose our inquirer acquainted with the true
conditions of experimental investigation, and competent in point of
acquirements for realizing them, so far as they can be realized. He
shall know as much of the facts of history as mere erudition can
teach--as much as can be proved by testimony, without the assistance of
any theory; and if those mere facts, properly collated, can fulfil the
conditions of a real induction, he shall be qualified for the task.

But, that no such attempt can have the smallest chance of success, has
been abundantly shown in the tenth chapter of the Third Book.[7] We
there examined whether effects which depend on a complication of causes
can be made the subject of a true induction by observation and
experiment; and concluded, on the most convincing grounds, that they
cannot. Since, of all effects, none depend on so great a complication of
causes as social phenomena, we might leave our case to rest in safety on
that previous showing. But a logical principle as yet so little familiar
to the ordinary run of thinkers, requires to be insisted on more than
once, in order to make the due impression; and the present being the
case which of all others exemplifies it the most strongly, there will be
advantage in re-stating the grounds of the general maxim, as applied to
the specialities of the class of inquiries now under consideration.

§ 2. The first difficulty which meets us in the attempt to apply
experimental methods for ascertaining the laws of social phenomena, is
that we are without the means of making artificial experiments. Even if
we could contrive experiments at leisure, and try them without limit, we
should do so under immense disadvantage; both from the impossibility of
ascertaining and taking note of all the facts of each case, and because
(those facts being in a perpetual state of change) before sufficient
time had elapsed to ascertain the result of the experiment, some
material circumstances would always have ceased to be the same. But it
is unnecessary to consider the logical objections which would exist to
the conclusiveness of our experiments, since we palpably never have the
power of trying any. We can only watch those which nature produces, or
which are produced for other reasons. We cannot adapt our logical means
to our wants, by varying the circumstances as the exigencies of
elimination may require. If the spontaneous instances, formed by
cotemporary events and by the successions of phenomena recorded in
history, afford a sufficient variation of circumstances, an induction
from specific experience is attainable; otherwise not. The question to
be resolved is, therefore, whether the requisites for induction
respecting the causes of political effects or the properties of
political agents, are to be met with in history? including under the
term, cotemporary history. And in order to give fixity to our
conceptions, it will be advisable to suppose this question asked in
reference to some special subject of political inquiry or controversy;
such as that frequent topic of debate in the present century, the
operation of restrictive and prohibitory commercial legislation upon
national wealth. Let this, then, be the scientific question to be
investigated by specific experience.

§ 3. In order to apply to the case the most perfect of the methods of
experimental inquiry, the Method of Difference, we require to find two
instances, which tally in every particular except the one which is the
subject of inquiry. If two nations can be found which are alike in all
natural advantages and disadvantages; whose people resemble each other
in every quality, physical and moral, spontaneous and acquired; whose
habits, usages, opinions, laws and institutions are the same in all
respects, except that one of them has a more protective tariff, or in
other respects interferes more with the freedom of industry; if one of
these nations is found to be rich, and the other poor, or one richer
than the other, this will be an _experimentum crucis_: a real proof by
experience, which of the two systems is most favourable to national
riches. But the supposition that two such instances can be met with is
manifestly absurd. Nor is such a concurrence even abstractly possible.
Two nations which agreed in everything except their commercial policy,
would agree also in that. Differences of legislation are not inherent
and ultimate diversities; are not properties of Kinds. They are effects
of pre-existing causes. If the two nations differ in this portion of
their institutions, it is from some difference in their position, and
thence in their apparent interests, or in some portion or other of their
opinions, habits, and tendencies; which opens a view of further
differences without any assignable limit, capable of operating on their
industrial prosperity, as well as on every other feature of their
condition, in more ways than can be enumerated or imagined. There is
thus a demonstrated impossibility of obtaining, in the investigations of
the social science, the conditions required for the most conclusive form
of inquiry by specific experience.

In the absence of the direct, we may next try, as in other cases, the
supplementary resource, called in a former place the Indirect Method of
Difference: which, instead of two instances differing in nothing but the
presence or absence of a given circumstance, compares two _classes_ of
instances respectively agreeing in nothing but the presence of a
circumstance on the one side and its absence on the other. To choose the
most advantageous case conceivable, (a case far too advantageous to be
ever obtained,) suppose that we compare one nation which has a
restrictive policy, with two or more nations agreeing in nothing but in
permitting free trade. We need not now suppose that either of these
nations agrees with the first in all its circumstances; one may agree
with it in some of its circumstances, and another in the remainder. And
it may be argued, that if these nations remain poorer than the
restrictive nation, it cannot be for want either of the first or of the
second set of circumstances, but it must be for want of the protective
system. If (we might say) the restrictive nation had prospered from the
one set of causes, the first of the free-trade nations would have
prospered equally; if by reason of the other, the second would: but
neither has: therefore the prosperity was owing to the restrictions.
This will be allowed to be a very favourable specimen of an argument
from specific experience in politics, and if this be inconclusive, it
would not be easy to find another preferable to it.

Yet, that it is inconclusive, scarcely requires to be pointed out. Why
must the prosperous nation have prospered from one cause exclusively?
National prosperity is always the collective result of a multitude of
favourable circumstances; and of these, the restrictive nation may unite
a greater number than either of the others, though it may have all of
those circumstances in common with either one or the other of them. Its
prosperity may be partly owing to circumstances common to it with one of
those nations, and partly with the other, while they, having each of
them only half the number of favourable circumstances, have remained
inferior. So that the closest imitation which can be made, in the social
science, of a legitimate induction from direct experience, gives but a
specious semblance of conclusiveness, without any real value.

§ 4. The Method of Difference in either of its forms being thus
completely out of the question, there remains the Method of Agreement.
But we are already aware of how little value this method is, in cases
admitting Plurality of Causes: and social phenomena are those in which
the plurality prevails in the utmost possible extent.

Suppose that the observer makes the luckiest hit which could be given by
any conceivable combination of chances: that he finds two nations which
agree in no circumstance whatever, except in having a restrictive
system, and in being prosperous; or a number of nations, all prosperous,
which have no antecedent circumstances common to them all but that of
having a restrictive policy. It is unnecessary to go into the
consideration of the impossibility of ascertaining from history, or even
from cotemporary observation, that such is really the fact: that the
nations agree in no other circumstance capable of influencing the case.
Let us suppose this impossibility vanquished, and the fact ascertained
that they agree only in a restrictive system as an antecedent, and
industrial prosperity as a consequent. What degree of presumption does
this raise, that the restrictive system caused the prosperity? One so
trifling as to be equivalent to none at all. That some one antecedent is
the cause of a given effect, because all other antecedents have been
found capable of being eliminated, is a just inference, only if the
effect can have but one cause. If it admits of several, nothing is more
natural than that each of these should separately admit of being
eliminated. Now, in the case of political phenomena, the supposition of
unity of cause is not only wide of the truth, but at an immeasurable
distance from it. The causes of every social phenomenon which we are
particularly interested about, security, wealth, freedom, good
government, public virtue, general intelligence, or their opposites, are
infinitely numerous: especially the external or remote causes, which
alone are, for the most part, accessible to direct observation. No one
cause suffices of itself to produce any of these phenomena; while there
are countless causes which have some influence over them, and may
co-operate either in their production or in their prevention. From the
mere fact, therefore, of our having been able to eliminate some
circumstance, we can by no means infer that this circumstance was not
instrumental to the effect in some of the very instances from which we
have eliminated it. We can conclude that the effect is sometimes
produced without it; but not that, when present, it does not contribute
its share.

Similar objections will be found to apply to the Method of Concomitant
Variations. If the causes which act upon the state of any society
produced effects differing from one another in kind; if wealth depended
on one cause, peace on another, a third made people virtuous, a fourth
intelligent; we might, though unable to sever the causes from one
another, refer to each of them that property of the effect which waxed
as it waxed, and which waned as it waned. But every attribute of the
social body is influenced by innumerable causes; and such is the mutual
action of the coexisting elements of society, that whatever affects any
one of the more important of them, will by that alone, if it does not
affect the others directly, affect them indirectly. The effects,
therefore, of different agents not being different in quality, while the
quantity of each is the mixed result of all the agents, the variations
of the aggregate cannot bear an uniform proportion to those of any one
of its component parts.

§ 5. There remains the Method of Residues; which appears, on the first
view, less foreign to this kind of inquiry than the three other
methods, because it only requires that we should accurately note the
circumstances of some one country, or state of society. Making
allowance, thereupon, for the effect of all causes whose tendencies are
known, the residue which those causes are inadequate to explain may
plausibly be imputed to the remainder of the circumstances which are
known to have existed in the case. Something similar to this is the
method which Coleridge[8] describes himself as having followed in his
political essays in the _Morning Post_. "On every great occurrence I
endeavoured to discover in past history the event that most nearly
resembled it. I procured, whenever it was possible, the contemporary
historians, memorialists, and pamphleteers. Then fairly subtracting the
points of difference from those of likeness, as the balance favoured the
former or the latter, I conjectured that the result would be the same or
different. As, for instance, in the series of essays entitled 'A
comparison of France under Napoleon with Rome under the first Cæsars,'
and in those which followed, 'on the probable final restoration of the
Bourbons.' The same plan I pursued at the commencement of the Spanish
Revolution, and with the same success, taking the war of the United
Provinces with Philip II. as the groundwork of the comparison." In this
inquiry he no doubt employed the Method of Residues; for, in
"subtracting the points of difference from those of likeness," he
doubtless weighed, and did not content himself with numbering, them: he
doubtless took those points of agreement only, which he presumed from
their own nature to be capable of influencing the effect, and, allowing
for that influence, concluded that the remainder of the result would be
referable to the points of difference.

Whatever may be the efficacy of this method, it is, as we long ago
remarked, not a method of pure observation and experiment; it concludes,
not from a comparison of instances, but from the comparison of an
instance with the result of a previous deduction. Applied to social
phenomena, it presupposes that the causes from which part of the effect
proceeded are already known; and as we have shown that these cannot have
been known by specific experience, they must have been learnt by
deduction from principles of human nature; experience being called in
only as a supplementary resource, to determine the causes which produced
an unexplained residue. But if the principles of human nature may be had
recourse to for the establishment of some political truths, they may for
all. If it be admissible to say, England must have prospered by reason
of the prohibitory system, because after allowing for all the other
tendencies which have been operating, there is a portion of prosperity
still to be accounted for; it must be admissible to go to the same
source for the effect of the prohibitory system, and examine what
account the laws of human motives and actions will enable us to give of
_its_ tendencies. Nor, in fact, will the experimental argument amount to
anything, except in verification of a conclusion drawn from those
general laws. For we may subtract the effect of one, two, three, or four
causes, but we shall never succeed in subtracting the effect of all
causes except one: while it would be a curious instance of the dangers
of too much caution, if, to avoid depending on _à priori_ reasoning
concerning the effect of a single cause, we should oblige ourselves to
depend on as many separate _à priori_ reasonings as there are causes
operating concurrently with that particular cause in some given

We have now sufficiently characterized the gross misconception of the
mode of investigation proper to political phenomena, which I have termed
the Chemical Method. So lengthened a discussion would not have been
necessary, if the claim to decide authoritatively on political doctrines
were confined to persons who had competently studied any one of the
higher departments of physical science. But since the generality of
those who reason on political subjects, satisfactorily to themselves and
to a more or less numerous body of admirers, know nothing whatever of
the methods of physical investigation beyond a few precepts which they
continue to parrot after Bacon, being entirely unaware that Bacon's
conception of scientific inquiry has done its work, and that science
has now advanced into a higher stage; there are probably many to whom
such remarks as the foregoing may still be useful. In an age in which
chemistry itself, when attempting to deal with the more complex chemical
sequences, those of the animal or even the vegetable organism, has found
it necessary to become, and has succeeded in becoming, a Deductive
Science--it is not to be apprehended that any person of scientific
habits, who has kept pace with the general progress of the knowledge of
nature, can be in danger of applying the methods of elementary chemistry
to explore the sequences of the most complex order of phenomena in



§ 1. The misconception discussed in the preceding chapter is, as we
said, chiefly committed by persons not much accustomed to scientific
investigation: practitioners in politics, who rather employ the
commonplaces of philosophy to justify their practice, than seek to guide
their practice by philosophic principles: or imperfectly educated
persons, who, in ignorance of the careful selection and elaborate
comparison of instances required for the formation of a sound theory,
attempt to found one upon a few coincidences which they have casually

The erroneous method of which we are now to treat, is, on the contrary,
peculiar to thinking and studious minds. It never could have suggested
itself but to persons of some familiarity with the nature of scientific
research; who,--being aware of the impossibility of establishing, by
casual observation or direct experimentation, a true theory of sequences
so complex as are those of the social phenomena,--have recourse to the
simpler laws which are immediately operative in those phenomena, and
which are no other than the laws of the nature of the human beings
therein concerned. These thinkers perceive (what the partisans of the
chemical or experimental theory do not) that the science of society must
necessarily be deductive. But, from an insufficient consideration of the
specific nature of the subject matter,--and often because (their own
scientific education having stopped short in too early a stage) geometry
stands in their minds as the type of all deductive science, it is to
geometry rather than to astronomy and natural philosophy, that they
unconsciously assimilate the deductive science of society.

Among the differences between geometry (a science of coexistent facts,
altogether independent of the laws of the succession of phenomena), and
those physical Sciences of Causation which have been rendered deductive,
the following is one of the most conspicuous: That geometry affords no
room for what so constantly occurs in mechanics and its applications,
the case of conflicting forces; of causes which counteract or modify one
another. In mechanics we continually find two or more moving forces
producing, not motion, but rest; or motion in a different direction from
that which would have been produced by either of the generating forces.
It is true that the effect of the joint forces is the same when they act
simultaneously, as if they had acted one after another, or by turns; and
it is in this that the difference between mechanical and chemical laws
consists. But still the effects, whether produced by successive or by
simultaneous action, do, wholly or in part, cancel one another: what the
one force does, the other, partly or altogether, undoes. There is no
similar state of things in geometry. The result which follows from one
geometrical principle has nothing that conflicts with the result which
follows from another. What is proved true from one geometrical theorem,
what would be true if no other geometrical principles existed, cannot be
altered and made no longer true by reason of some other geometrical
principle. What is once proved true is true in all cases, whatever
supposition may be made in regard to any other matter.

Now a conception, similar to this last, would appear to have been formed
of the social science, in the minds of the earlier of those who have
attempted to cultivate it by a deductive method. Mechanics would be a
science very similar to geometry, if every motion resulted from one
force alone, and not from a conflict of forces. In the geometrical
theory of society, it seems to be supposed that this is really the case
with the social phenomena; that each of them results always from only
one force, one single property of human nature.

At the point which we have now reached, it cannot be necessary to say
anything either in proof or in illustration of the assertion that such
is not the true character of the social phenomena. There is not, among
these most complex and (for that reason) most modifiable of all
phenomena, any one over which innumerable forces do not exercise
influence; which does not depend on a conjunction of very many causes.
We have not, therefore, to prove the notion in question to be an error,
but to prove that the error has been committed; that so mistaken a
conception of the mode in which the phenomena of society are produced,
has actually been ascertained.

§ 2. One numerous division of the reasoners who have treated social
facts according to geometrical methods, not admitting any modification
of one law by another, must for the present be left out of
consideration; because in them this error is complicated with, and is
the effect of, another fundamental misconception, of which we have
already taken some notice, and which will be further treated of before
we conclude. I speak of those who deduce political conclusions not from
laws of nature, not from sequences of phenomena, real or imaginary, but
from unbending practical maxims. Such, for example, are all who found
their theory of politics on what is called abstract right, that is to
say, on universal precepts; a pretension of which we have already
noticed the chimerical nature. Such, in like manner, are those who make
the assumption of a social contract, or any other kind of original
obligation, and apply it to particular cases by mere interpretation. But
in this the fundamental error is the attempt to treat an art like a
science, and to have a deductive art; the irrationality of which will be
shown in a future chapter. It will be proper to take our exemplification
of the geometrical theory from those thinkers who have avoided this
additional error, and who entertain, so far, a juster idea of the nature
of political inquiry.

We may cite, in the first instance, those who assume as the principle of
their political philosophy that government is founded on fear; that the
dread of each other is the one motive by which human beings were
originally brought into a state of society, and are still held in it.
Some of the earlier scientific inquirers into politics, in particular
Hobbes, assumed this proposition, not by implication, but avowedly, as
the foundation of their doctrine, and attempted to build a complete
philosophy of politics thereupon. It is true that Hobbes did not find
this one maxim sufficient to carry him through the whole of his subject,
but was obliged to eke it out by the double sophism of an original
contract. I call this a double sophism; first, as passing off a fiction
for a fact, and, secondly, assuming a practical principle, or precept,
as the basis of a theory; which is a _petitio principii_, since (as we
noticed in treating of that Fallacy) every rule of conduct, even though
it be so binding a one as the observance of a promise, must rest its own
foundations on the theory of the subject, and the theory, therefore,
cannot rest upon it.

§ 3. Passing over less important instances, I shall come at once to the
most remarkable example afforded by our own times of the geometrical
method in politics; emanating from persons who were well aware of the
distinction between science and art; who knew that rules of conduct must
follow, not precede, the ascertainment of laws of nature, and that the
latter, not the former, is the legitimate field for the application of
the deductive method. I allude to the interest-philosophy of the Bentham

The profound and original thinkers who are commonly known under this
description, founded their general theory of government on one
comprehensive premise, namely, that men's actions are always determined
by their interests. There is an ambiguity in this last expression; for,
as the same philosophers, especially Bentham, gave the name of an
interest to anything which a person likes, the proposition may be
understood to mean only this, that men's actions are always determined
by their wishes. In this sense, however, it would not bear out any of
the consequences which these writers drew from it; and the word,
therefore, in their political reasonings, must be understood to mean
(which is also the explanation they themselves, on such occasions, gave
of it) what is commonly termed private, or worldly, interest.

Taking the doctrine, then, in this sense, an objection presents itself
_in limine_ which might be deemed a fatal one, namely, that so sweeping
a proposition is far from being universally true. Human beings are not
governed in all their actions by their worldly interests. This, however,
is by no means so conclusive an objection as it at first appears;
because in politics we are for the most part concerned with the conduct
not of individual persons, but either of a series of persons (as a
succession of kings) or a body or mass of persons, as a nation, an
aristocracy, or a representative assembly. And whatever is true of a
large majority of mankind, may without much error be taken for true of
any succession of persons, considered as a whole, or of any collection
of persons in which the act of the majority becomes the act of the whole
body. Although, therefore, the maxim is sometimes expressed in a manner
unnecessarily paradoxical, the consequences drawn from it will hold
equally good if the assertion be limited as follows--Any succession of
persons, or the majority of any body of persons, will be governed in the
bulk of their conduct by their personal interests. We are bound to allow
to this school of thinkers the benefit of this more rational statement
of their fundamental maxim, which is also in strict conformity to the
explanations which, when considered to be called for, have been given by

The theory goes on to infer, quite correctly, that if the actions of
mankind are determined in the main by their selfish interests, the only
rulers who will govern according to the interest of the governed, are
those whose selfish interests are in accordance with it. And to this is
added a third proposition, namely, that no rulers have their selfish
interest identical with that of the governed, unless it be rendered so
by accountability, that is, by dependence on the will of the governed.
In other words (and as the result of the whole), that the desire of
retaining or the fear of losing their power, and whatever is thereon
consequent, is the sole motive which can be relied on for producing on
the part of rulers a course of conduct in accordance with the general

We have thus a fundamental theorem of political science, consisting of
three syllogisms, and depending chiefly on two general premises, in each
of which a certain effect is considered as determined only by one cause,
not by a concurrence of causes. In the one, it is assumed that the
actions of average rulers are determined solely by self-interest; in the
other, that the sense of identity of interest with the governed, is
produced and producible by no other cause than responsibility.

Neither of these propositions is by any means true; the last is
extremely wide of the truth.

It is not true that the actions even of average rulers are wholly, or
anything approaching to wholly, determined by their personal interest,
or even by their own opinion of their personal interest. I do not speak
of the influence of a sense of duty, or feelings of philanthropy,
motives never to be mainly relied on, though (except in countries or
during periods of great moral debasement) they influence almost all
rulers in some degree, and some rulers in a very great degree. But I
insist only on what is true of all rulers, viz. that the character and
course of their actions is largely influenced (independently of personal
calculation) by the habitual sentiments and feelings, the general modes
of thinking and acting, which prevail throughout the community of which
they are members; as well as by the feelings, habits, and modes of
thought which characterize the particular class in that community to
which they themselves belong. And no one will understand or be able to
decypher their system of conduct, who does not take all these things
into account. They are also much influenced by the maxims and traditions
which have descended to them from other rulers, their predecessors;
which maxims and traditions have been known to retain an ascendancy
during long periods, even in opposition to the private interests of the
rulers for the time being. I put aside the influence of other less
general causes. Although, therefore, the private interest of the rulers
or of the ruling class is a very powerful force, constantly in action,
and exercising the most important influence upon their conduct; there is
also, in what they do, a large portion which that private interest by no
means affords a sufficient explanation of: and even the particulars
which constitute the goodness or badness of their government, are in
some, and no small degree, influenced by those among the circumstances
acting upon them, which cannot, with any propriety, be included in the
term self-interest.

Turning now to the other proposition, that responsibility to the
governed is the only cause capable of producing in the rulers a sense of
identity of interest with the community; this is still less admissible
as an universal truth, than even the former. I am not speaking of
perfect identity of interest, which is an impracticable chimera; which,
most assuredly, responsibility to the people does not give. I speak of
identity in essentials; and the essentials are different at different
places and times. There are a large number of cases in which those
things which it is most for the general interest that the rulers should
do, are also those which they are prompted to do by their strongest
personal interest, the consolidation of their power. The suppression,
for instance, of anarchy and resistance to law,--the complete
establishment of the authority of the central government, in a state of
society like that of Europe in the middle ages,--is one of the strongest
interests of the people, and also of the rulers simply because they are
the rulers: and responsibility on their part could not strengthen,
though in many conceivable ways it might weaken, the motives prompting
them to pursue this object. During the greater part of the reign of
Queen Elizabeth, and of many other monarchs who might be named, the
sense of identity of interest between the sovereign and the majority of
the people was probably stronger than it usually is in responsible
governments: everything that the people had most at heart, the monarch
had at heart too. Had Peter the Great, or the rugged savages whom he
began to civilize, the truest inclination towards the things which were
for the real interest of those savages?

I am not here attempting to establish a theory of government, and am not
called upon to determine the proportional weight which ought to be given
to the circumstances which this school of geometrical politicians left
out of their system, and those which they took into it. I am only
concerned to show that their method was unscientific; not to measure the
amount of error which may have affected their practical conclusions.

It is but justice to them, however, to remark, that their mistake was
not so much one of substance as of form; and consisted in presenting in
a systematic shape, and as the scientific treatment of a great
philosophical question, what should have passed for that which it really
was, the mere polemics of the day. Although the actions of rulers are by
no means wholly determined by their selfish interests, it is chiefly as
a security against those selfish interests that constitutional checks
are required; and for that purpose such checks, in England, and the
other nations of modern Europe, can in no manner be dispensed with. It
is likewise true, that in these same nations, and in the present age,
responsibility to the governed is the only means practically available
to create a feeling of identity of interest, in the cases, and on the
points, where that feeling does not sufficiently exist. To all this, and
to the arguments which may be founded on it in favour of measures for
the correction of our representative system, I have nothing to object;
but I confess my regret, that the small though highly important portion
of the philosophy of government, which was wanted for the immediate
purpose of serving the cause of parliamentary reform, should have been
held forth by thinkers of such eminence as a complete theory.

It is not to be imagined possible, nor is it true in point of fact, that
these philosophers regarded the few premises of their theory as
including all that is required for explaining social phenomena, or for
determining the choice of forms of government and measures of
legislation and administration. They were too highly instructed, of too
comprehensive intellect, and some of them of too sober and practical a
character, for such an error. They would have applied and did apply
their principles with innumerable allowances. But it is not allowances
that are wanted. There is little chance of making due amends in the
superstructure of a theory for the want of sufficient breadth in its
foundations. It is unphilosophical to construct a science out of a few
of the agencies by which the phenomena are determined, and leave the
rest to the routine of practice or the sagacity of conjecture. We either
ought not to pretend to scientific forms, or we ought to study all the
determining agencies equally, and endeavour, so far as it can be done,
to include all of them within the pale of the science; else we shall
infallibly bestow a disproportionate attention upon those which our
theory takes into account, while we misestimate the rest, and probably
underrate their importance. That the deductions should be from the whole
and not from a part only of the laws of nature that are concerned, would
be desirable even if those omitted were so insignificant in comparison
with the others, that they might, for most purposes and on most
occasions, be left out of the account. But this is far indeed from being
true in the social science. The phenomena of society do not depend, in
essentials, on some one agency or law of human nature, with only
inconsiderable modifications from others. The whole of the qualities of
human nature influence those phenomena, and there is not one which
influences them in a small degree. There is not one, the removal or any
great alteration of which would not materially affect the whole aspect
of society, and change more or less the sequences of social phenomena

The theory which has been the subject of these remarks is in this
country at least, the principal cotemporary example of what I have
styled the geometrical method of philosophizing in the social science;
and our examination of it has, for this reason, been more detailed than
would otherwise have been suitable to a work like the present. Having
now sufficiently illustrated the two erroneous methods, we shall pass
without further preliminary to the true method; that which proceeds
(conformably to the practice of the more complex physical sciences)
deductively indeed, but by deduction from many, not from one or a very
few, original premises; considering each effect as (what it really is)
an aggregate result of many causes, operating sometimes through the
same, sometimes through different mental agencies, or laws of human



§ 1. After what has been said to illustrate the nature of the inquiry
into social phenomena, the general character of the method proper to
that inquiry is sufficiently evident, and needs only to be
recapitulated, not proved. However complex the phenomena, all their
sequences and coexistences result from the laws of the separate
elements. The effect produced, in social phenomena, by any complex set
of circumstances, amounts precisely to the sum of the effects of the
circumstances taken singly: and the complexity does not arise from the
number of the laws themselves, which is not remarkably great; but from
the extraordinary number and variety of the data or elements--of the
agents which, in obedience to that small number of laws, co-operate
towards the effect. The Social Science, therefore (which, by a
convenient barbarism, has been termed Sociology,) is a deductive
science; not, indeed, after the model of geometry, but after that of the
more complex physical sciences. It infers the law of each effect from
the laws of causation on which that effect depends; not, however, from
the law merely of one cause, as in the geometrical method; but by
considering all the causes which conjunctly influence the effect, and
compounding their laws with one another. Its method, in short, is the
Concrete Deductive Method; that of which astronomy furnishes the most
perfect, natural philosophy a somewhat less perfect example, and the
employment of which, with the adaptations and precautions required by
the subject, is beginning to regenerate physiology.

Nor does it admit of doubt, that similar adaptations and precautions are
indispensable in sociology. In applying, to that most complex of all
studies, what is demonstrably the sole method capable of throwing the
light of science even upon phenomena of a far inferior degree of
complication, we ought to be aware that the same superior complexity
which renders the instrument of Deduction more necessary, renders it
also more precarious; and we must be prepared to meet, by appropriate
contrivances, this increase of difficulty.

The actions and feelings of human beings in the social state, are, no
doubt, entirely governed by psychological and ethological laws: whatever
influence any cause exercises upon the social phenomena, it exercises
through those laws. Supposing therefore th