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Title: Analysis of Mr. Mill's System of Logic
Author: Stebbing, W. (William), 1832-1926
Language: English
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Copyright Status: Not copyrighted in the United States. If you live elsewhere check the laws of your country before downloading this ebook. See comments about copyright issues at end of book.

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The author's aim has been to produce such a condensation of the original
work as may recall its contents to those who have read it, and may serve
those who are now reading it in the place of a full body of marginal
notes. Mr. Mill's conclusions on the true province and method of Logic
have a high substantive value, independent even of the arguments and
illustrations by which they are supported; and these conclusions may be
adequately, and, it is believed, with much practical utility, embodied
in an epitome. The processes of reasoning on which they depend, can, on
the other hand, be represented in outline only. But it is hoped that the
substance of every paragraph, necessary for the due comprehension of the
several steps by which the results have been reached, will be here
found at all events suggested.

The author may be allowed to add, that Mr. Mill, before publication,
expressed a favourable opinion of the manner in which the work had been
executed. Without such commendation the volume would hardly have been
offered to the public.

LONDON: _Dec. 21, 1865_.


INTRODUCTION                                                        1




      I. On the Necessity of commencing with an Analysis of
          Language in Logic                                         3

     II. Names                                                      3

    III. The Things denoted by Names                                7

     IV. Propositions                                              17

      V. The Import of Propositions                                19

     VI. Propositions merely Verbal                                24

    VII. The Nature of Classification, and the Five Predicables    26

   VIII. Definition                                                30



      I. Inference, or Reasoning in General                        35

     II. Ratiocination, or Syllogism                               36

    III. The Functions and Logical Value of the Syllogism          39

     IV. Trains of Reasoning, and Deductive Sciences               43

V. & VI. Demonstration and Necessary Truths                        46



      I. Preliminary Observations on Induction in general          53

     II. Inductions improperly so called                           54

    III. The ground of Induction                                   57

     IV. Laws of Nature                                            58

      V. The Law of Universal Causation                            60

     VI. The Composition of Causes                                 66

    VII. Observation and Experiment                                67

   VIII. & Note to IX. The Four Methods of Experimental
          Enquiry                                                  69

      X. Plurality of Causes, and intermixture of Effects          73

     XI. The Deductive Method                                      76

    XII. & XIII. The Explanation and Examples of the Explanation
          of Laws of Nature                                        77

    XIV. The Limits to the Explanation of Laws of Nature;
          and Hypotheses                                           79

     XV. Progressive Effects, and continued Action of
          Causes                                                   81

    XVI. Empirical Laws                                            83

   XVII. Chance, and its Elimination                               85

  XVIII. The Calculation of Chances                                87

    XIX. The Extension of Derivative Laws to Adjacent Cases        89

     XX. Analogy                                                   91

     XXI. The Evidence of the Law of Universal Causation           92

    XXII. Uniformities of Coexistence not dependent on Causation   94

   XXIII. Approximate Generalisations, and Probable Evidence       96

    XXIV. The remaining Laws of Nature                             99

     XXV. The grounds of Disbelief                                103



      I. Observation and Description                              107

     II. Abstraction, or the Formation of Conceptions             108

    III. Naming as Subsidiary to Induction                        111

     IV. The Requisites of a Philosophical Language, and the
          Principles of Definition                                112

      V. The Natural History of the Variation in the Meaning
          of Terms                                                115

     VI. Terminology and Nomenclature                             117

    VII. Classification, as Subsidiary to Induction               121

   VIII. Classification by Series                                 124



      I. Fallacies in general                                     127

     II. Classification of Fallacies                              128

    III. Fallacies of Simple Inspection; or, à priori Fallacies   130

     IV. Fallacies of Observation                                 134

      V. Fallacies of Generalisation                              137

     VI. Fallacies of Ratiocination                               141

    VII. Fallacies of Confusion                                   143



      I. Introductory Remarks                                     148

     II. Liberty and Necessity                                    148

    III. There is, or may be, a Science of Human Nature           150

     IV. The Laws of Mind                                         151

      V. Ethology, or the Science of the Formation of Character   153

     VI. General Considerations on the Social Science             155

    VII. The Chemical, or Experimental, Method in the Social
          Science                                                 156

   VIII. The Geometrical, or Abstract Method                      157

     IX. The Physical, or Concrete Deductive Method               158

      X. The Inverse Deductive, or Historical Method              161

     XI. The Logic of Practice, or Art; including Morality
          and Policy                                              165



No adequate definition is possible till the properties of the thing to
be defined are known. Previously we can define only the scope of the
inquiry. Now, Logic has been considered as both the science of
reasoning, i.e. the analysis of the mental process when we reason, and
the art of reasoning, i.e. the rules for the process. The term
_reasoning_, however, is not wide enough. _Reasoning_ means either
syllogising, or (and this is its truer sense) the drawing inferences
from assertions already admitted. But the Aristotelian or Scholastic
logicians included in Logic terms and propositions, and the Port Royal
logicians spoke of it as equivalent to the art of thinking. Even
popularly, accuracy of classification, and the extent of command over
premisses, are thought clearer signs of logical powers than accuracy of
deduction. On the other hand, the definition of logic as a 'science
treating of the operations of the understanding in the search of truth,'
though wide enough, would err through including truths known from
intuition; for, though doubtless many seeming intuitions are processes
of inference, questions as to what facts are _real intuitions_ belong
to Metaphysics, not to Logic.

Logic is the science, not of Belief, but of Proof, or Evidence. Almost
all knowledge being matter of inference, the fields of Logic and of
Knowledge coincide; but the two differ in so far that Logic does not
find evidence, but only judges of it. All science is composed of data,
and conclusions thence: Logic shows what relations must subsist between
them. All inferential knowledge is true or not, according as the laws of
Logic have been obeyed or not. Logic is Bacon's _Ars Artium_, the
science of sciences. Genius sometimes employs laws unconsciously; but
only genius: as a rule, the advances of a science have been ever found
to be preceded by a fuller knowledge of the laws of Logic applicable to
it. Logic, then, may be described as the science of the operations of
the understanding which aid in the estimation of evidence. It includes
not only the process of proceeding from the known to the unknown, but,
as auxiliary thereto, Naming, Definition, and Classification.
Conception, Memory, and other like faculties, are not treated by it; but
it presupposes them. Our object, therefore, must be to analyse the
process of inference and the subsidiary operations, besides framing
canons to test any given evidence. We need not, however, carry the
analysis beyond what is necessary for the practical uses of Logic; for
one step in analysis is good without a second, and our purpose is simply
to see the difference between good and ill processes of inference.
Minuter analysis befits Metaphysics; though even that science, when
stepping beyond the interrogation of our consciousness, or rather of our
memory, is, as all other sciences, amenable to Logic.





The fact of Logic being a portion of the art of thinking, and of
thought's chief instrument being words, is one reason why we must first
inquire into the right use of words. But further, the import of
propositions cannot really be examined apart from that of words; and
(since whatever can be an object of belief assumes the form of a
proposition, and in propositions all truth and error lie) this is a
paramount reason why we must, as a preliminary, consider the import of
names, the neglecting which, and confining ourselves to things, would
indeed be to discard all past experience. The right method is, to take
men's classifications of things as shown by names, correcting them as we



Hobbes's assertion that a name is a sign, not of a thing, but of our
conception of it, is untrue (unless he merely mean that the conception,
and not the thing itself, is imparted to the hearer); for we intend by
a name, not only to make men conceive what we conceive, but to inform
them what we believe as to the things themselves.

Names may be divided according to five principles of classification. The
_first_ way of dividing them is into General (not as equivalent to
Collective) and Individual names; the _second_, into Concrete, i.e. the
names of objects, and Abstract, i.e. the names of attributes (though
Locke improperly extends the term to all names gained by abstraction,
that is, to all general names). An abstract name is sometimes general,
e.g. colour, and sometimes singular, e.g. milk-whiteness. It may be
objected to calling attributes abstract, that also concrete adjectives,
e.g. white, are attributes. But a word is the name of the things of
which it can be predicated. Hence, white is the name of all things so
coloured, given indeed because of the quality, but really the name of
the thing, and no more the name of the quality than are names generally,
since every one of them, if it signifies anything at all, must imply an

The _third_ division is into Connotative and Non-connotative (the latter
being wrongly called Absolute). By _connotative_ are meant, not (as Mr.
James Mill explains it) words which, pointing directly to one thing,
tacitly refer to another, but words which denote a subject and imply an
attribute; while _non-connotatives_ signify a subject only, or attribute
only. All concrete general names are connotative. They are also called
_denominative_, because the subject denoted receives a common name (e.g.
snow is named white) from the attribute connoted. Even some abstracts
are connotative, for attributes may have attributes ascribed to them,
and a word which denotes attributes may connote an attribute of them;
e.g. fault connotes hurtfulness. Proper names, on the other hand, though
concrete, are not connotative. They are merely distinguishing marks,
given perhaps originally for a reason, but, when once given, independent
of it, since the reason is proved to be no part of the sense of the word
by the fact that the name is still used when the reason is forgotten.
But other individual names are connotative. Some of these, viz. those
connoting some attribute or some set of attributes possessed by one
object only, e.g. Sun, God, are really general names, though happening
to be predicable only of a single object. But there are also real
connotative individual names, part of whose meaning is, that there
exists only one individual with the connoted attribute, e.g. The first
Emperor, The father of Socrates; and it is so with many-worded names,
made up of a general name limited by other words, e.g. The present Prime
Minister of England. In short, the meaning of all names, which have any
meaning, resides, not in what they denote, but in what they connote.
There perpetually, however, arises a difficulty of deciding how much
they do connote, that is, what difference in the object would make a
difference in the name. This vagueness comes from our learning the
connotation, through a rude generalisation and analysis, from the
objects denoted. Thus, men use a name without any precise reference to a
definite set of attributes, applying it to new objects on account of
superficial resemblance, so that at length all common meaning
disappears. Even scientific writers, from ignorance, or from the
aversion which men at large feel to the use of new names, often force
old terms to express an ever-growing number of distinctions. But every
concrete general name should be given a definite connotation with the
least possible change in the denotation; and this is what is aimed at in
every definition of a general name already in use. But we must not
confound the use of names of indeterminate connotation, which is so
great an evil, with the employment, necessitated by the paucity of names
as compared with the demand, of the same words with different
connotations in different relations.

A _fourth_ division of names is into Positive and Negative. When the
positive is connotative, so is the corresponding negative, for the
non-possession of an attribute is itself an attribute. Names negative in
form, e.g. unpleasant, are often really positive; and others, e.g. idle,
sober, though seemingly positive, are really negative. Privatives are
names which are equivalent each to a positive and a negative name taken
together. They connote both the absence of certain attributes, and the
presence of others, whence the presence of the defaulting ones might
have been expected. Thus, blind would be applied only to a non-seeing
member of a seeing class.

The _fifth_ division is into Relative and (that we may economise the
term Absolute for an occasion when none other is available) Non-relative
names. Correlatives, when concrete, are of course connotative. A
relation arises from two individuals being concerned in the same series
of facts, so that the signification of neither name can be explained
except by mentioning another: and any two correlatives connote, not the
same attribute indeed, but just this series of facts, which is exactly
the same in both cases.

Some make a _sixth_ division, viz. Univocals, i.e. names predicated of
different individuals in the same sense, and Æquivocals, i.e. names
predicated of different individuals in different senses. But these are
not two kinds of names, but only two modes of using them; for an
æquivocal name is two names accidentally coinciding in sound. An
intermediate case is that of a name used analogically or metaphorically,
that is, in two senses, one its primary, the other its secondary sense.
The not perceiving that such a word is really two has produced many



Logic is the theory of Proof, and everything provable can be exhibited
as a proposition, propositions alone being objects of belief. Therefore,
the import of propositions, that is, the import of predication, must be
ascertained. But, as to make a proposition, i.e. to predicate, is to
assert one _thing_ of another _thing_, the way to learn the import of
predication is, by discovering what are the _things_ signified by names
which are capable of being subject or predicate. It was with this object
that Aristotle formed his Categories, i.e. an attempted enumeration of
all nameable things by the _summa genera_ or highest predicates, one or
other of which must, he asserted, be predicable of everything. His,
however, is a rude catalogue, without philosophical analysis of the
rationale even of familiar distinctions. For instance, his Relation
properly includes Action, Passivity, and Local Situation, and also the
two categories of Position [Greek: pote] and [Greek: pou], while the
difference between [Greek: pou] and [Greek: keisthai] is only verbal,
and [Greek: echein] is not a _summum genus_ at all. Besides--only
substantives and attributes being there considered--there is no category
for sensation and other mental states, since, though these may rightly
be placed, so far as they express their relation, if active, to their
objects, if passive to their causes, in the Categories of Actio and
Passio, the things, viz., the mental states, do not belong there.

The absence of a well-defined concrete name answering to the abstract
_existence_, is one great obstacle to renewing Aristotle's attempt. The
words used for the purpose commonly denote substances only, though
attributes and feelings are equally existences. Even _being_ is
inadequate, since it denotes only _some_ existences, being used by
custom as synonymous with _substance_, both material and spiritual. That
is, it is applied to what excites feelings and has attributes, but not
to feelings and attributes themselves; and if we called extension,
virtue, &c., _beings_, we should be accused of believing in the Platonic
self-existing ideas, or Epicurus's sensible forms--in short, of deeming
attributes substances. To fill this gap, the abstract, _entity_, was
made into a concrete, equivalent to _being_. Yet even _entity_ implies,
though not so much as _being_, the notion of substance. In fact, every
word originally connoting simply existence, gradually enlarges its
connotation to mean _separate_ existence, i.e. existence freed from the
condition of belonging to a substance, so as to exclude attributes and
feelings. Since, then, all the terms are ambiguous, that among them (and
the same principle applies to terms generally) will be employed here
which seems on each occasion to be _least_ ambiguous: and terms will be
used even in improper senses, when these by familiar association convey
the proper meaning.

_Nameable things_ are--I. Feelings or States of Consciousness.--A
feeling, being anything of which the mind is conscious, is synonymous
with _state of consciousness_. It is commonly confined to the sensations
and emotions, or to the emotions alone; but it is properly a genus,
having for species, Sensation, Emotion, Thought, and Volition. By
thought is meant all that we are internally conscious of when we think;
e.g. the idea of the sun, and not the sun itself, is a thought; and so,
not even an imaginary thing like a ghost, but only the idea of it, is a
thought. In like manner, a sensation differs both from the object
causing it, and the attribute ascribed to the object. Yet language
(except in the case of the sensations of hearing) has seldom provided
the sensations with separate names; so that we have to name the
sensation from the object or the attribute exciting it, though we might
_conceive_ the sensation to exist, though it never actually does,
without an exciting cause. Again, another distinction has to be attended
to, viz. the difference between the sensation and the state of the
bodily organs, which is the physical agency producing it. This
distinction escapes notice partly by reason of the division of the
feelings into bodily and mental. But really there is no such division,
even sensations being states of the sentient mind, and not of the body.
The difference, in fact, between sensations, thoughts, and emotions, is
only in the different agency producing the feeling; it being, in the
case of the sensations, a bodily, and, for the other two, a mental
state. Some suppose, after the sensation, in which, they say, the mind
is passive, a distinct active process called perception, which is the
direct recognition of an external object, as the cause of the sensation.
Probably, perceptions are simply cases of belief claiming to be
intuitive, i.e. free of external evidence. But, at any rate, any
question as to their nature is irrelevant to an inquiry like the
present, viz. how we get the non-original part of our knowledge. And so
also is the distinction in German metaphysics, between the mind's _acts_
and its passive _states_. Enough for us now that they are all states of
the mind.

II. Substances.--Logicians think they have defined substance and
attribute, when they have shown merely what difference the use of them
respectively makes in the grammar of a sentence. They say an attribute
must be an attribute _of_ something, but that a substance is
self-existent (being followed, if a relative, by _of_, not _quâ_
substance, but _quâ_ the relation). But this _of_, as distinguishing
attributes, itself needs explanation: besides, we can no more conceive a
substance independent of attributes, than an attribute independent of a
substance. Metaphysicians go deeper into the distinction than logicians.
Substances, most of them say, are either bodies or minds; and, of these,
a body is the external cause to which we ascribe sensations. Berkeley
and the Idealists, however, deny that there exists any cause of
sensations (except, indeed, a First Cause). They argue that the _whole_
of our notion of a body consists of a number of our own or others'
sensations occurring together habitually (so that, the thought of one
being associated with the thought of the others, we get what Hartley and
Locke call a complex idea). They deny that a residuum would remain if
all the attributes were pared off; for that, though the sensations are
bound together by a law, the existence of a _substratum_ is but one of
many forms of mentally realising the connection. And they ask how it
is,--since so long as the sensations occurred in the old order, we
should not miss such a _substratum_, supposing it to have once existed
_and to have perished_--that we can know it exists even now? Their
opponents used formerly to reply, that the uniform order of sensations
implies an external cause determining the law of the order; and that the
attributes _inhere_ in this external cause or substratum, viz. matter.
But at last it was seen that the existence of matter could not be proved
by extrinsic evidence; consequently, now the answer to the idealist
argument simply is, that the belief in an external cause of sensations
is universal, and as intuitive as our knowledge of sensations
themselves. Even Kant allows this (notwithstanding his belief in the
existence of a universe of _things in themselves_, i.e. Noümena, as
contrasted with the mental representation of them, where the sensations,
he thinks, furnish the matter, and the laws of the mind, the form).
Brown even traced up to the sensations of touch, combined with the
sensations seated in the muscular frame, those very properties, viz.,
extension and figure, which Reid referred to as proving that some
qualities must exist, not in the sensations, but in the things
themselves, _since_ they cannot possibly be copies of any impression on
the senses. We have, in truth, no right to consider a thing's sensible
qualities akin to its nature, unless we suppose an absurdity, viz. that
a cause must, as such, resemble its effects. In any case, the question
whether Ontology be a possible science, concerns, not Logic, but the
nature and laws of intuitive knowledge. And the question as to the
nature of Mind is as out of place here as that about Body. As body is
the unknown exciting cause of sensations, so mind, the other kind of
substance, is the unknown recipient both of the sensations and of all
the other feelings. Though I call a something _myself_, as distinct from
the series of feelings, the 'thread of consciousness,' yet this self
shows itself only through its capacity of feeling or being conscious;
and I can, with my present faculties, conceive the gaining no new
information but about as yet unknown faculties of feeling. In short, as
body is the unsentient cause of all feelings, so mind is the sentient
_subject_ (in the German sense) of them, viz. that which feels them.
About this inner nature we know nothing, and Logic cares nothing.

III. Attributes.--Qualities are the first class of attributes. Now, if
we know nothing about bodies but the sensations they excite, we can mean
nothing by the attributes of bodies but sensations. Against this it has
been urged that, though we know nothing of sensible objects except the
sensations, the quality which we ascribe on the _ground_ of the
sensation may yet be a real hidden power or quality in the object, of
which the sensation is only the evidence. Seemingly, this doctrine
arises only from the tendency to suppose that there must be two
different things to answer to two names when not quite synonymous.
Quality and sensation are probably names for the same thing viewed in
different lights. The doctrine of an entity _per se_, called quality, is
a relic of the scholastic _occult causes_; the only intelligible cause
of sensation being the presence of the assemblage of phenomena, called
the _object_. Why the presence of the object causes the sensation, we
know not; and, granting an _occult cause_, we are still in the dark as
to how _that_ produces the effect. However, the question belongs to
metaphysics; and it suits this doctrine, as well as the opposed one, to
say that a quality has for its _foundation_ a sensation.

Relations form the second class of attributes. In all cases of relation
there exists some fact into which the relatives enter as parties
concerned; and this is the _fundamentum relationis_. Whenever two things
are involved in some one fact, we may ascribe to them a relation
grounded on it, however general the fact may be. As, then, a quality is
an attribute based on the fact of a sensation, so a relation is an
attribute based on a fact into which two objects enter jointly. This
fact in both is always composed entirely of states of consciousness; and
this, whether it be complicated, as in many legal relations, or simple,
as in the relations expressed by _antecedent_ and _consequent_ and by
_simultaneous_, where the fact consists merely of the two things so
related, since the consciousness either of the succession or of the
simultaneousness of the two sensations which represent the things, is a
feeling not added to, but involved in _them_, being a condition under
which we must suppose things. And so, likewise, with the relations of
likeness and unlikeness. The feeling of these sometimes cannot be
analysed, when the _fundamentum relationis_ is, as in the case of two
simple sensations, e.g. two sensations of white, only the two sensations
themselves, the consequent feeling of their resemblance being, like that
of their succession or simultaneousness, apparently involved in the
sensations themselves. Sometimes, again, the likeness or unlikeness is
complex, and therefore can be analysed into simpler cases. In any case,
likeness or unlikeness must resolve itself into likeness or unlikeness
between states of our own or some other mind; and this, whether the
feeling of the resemblance or dissimilarity relate to bodies or to
attributes, since the former we know only through the sensations they
are supposed to excite, and the latter through the sensations on which
they are grounded. And so, again, when we say that two relations are
alike (one of the many senses of analogy), we simply assert resemblance
between the facts constituting the two _fundamenta relationis_. Several
relations, called by different names, are really cases of resemblance.
Thus, equality, i.e. the exact resemblance existing between things in
respect of their quantity, is often called identity.

The _third_ species of attributes is Quantity. The assertion of likeness
or unlikeness in quantity, as in quality, is always founded on a
likeness or unlikeness in the sensations excited. What the difference is
all who have had the sensations know, but it cannot be explained to
those who never had them.

In fine, all the attributes classed under Quality and Quantity are the
powers bodies have of exciting certain sensations. So, Relation
generally is but the power which an object has of joining its
correlative in producing the series of sensations, which is the only
sign of the existence of the fact on which they both are grounded. The
relations of succession and simultaneousness, indeed, are not based on
any fact (i.e. any feeling) distinct from the related objects. But these
relations are themselves states of consciousness; resemblance, for
example, being nothing but our feeling of resemblance: at least, we
ascribe these relations to objects or attributes simply because they
hold between the feelings which the objects excite and on which the
attributes are grounded. And as with the attributes of bodies, so also
those of minds are grounded on states of consciousness. Considered in
itself, we can predicate of a mind only the series of its own feelings:
e.g. by _devout_ we mean that the feelings implied in that word form an
oft-recurring part of the series of feelings filling up the sentient
existence of that mind. Again, attributes may be ascribed to a mind as
to a body, as grounded on the thoughts or emotions (not the sensations,
for only bodies excite them) which it excites in others: e.g. when we
call a character admirable, we mean that it causes feelings in us of
admiration. Sometimes, under one word really two attributes are
predicated, one a state of the mind, the other of other minds affected
by thinking of it: e.g. He is generous. Sometimes, even bodies have the
attribute of producing an emotion: e.g. That statue is beautiful.

The general result is, that there are three chief kinds of nameable
things:--1. Feelings distinct from the objects exciting and the organs
supposed to convey them, and divisible into four classes, perceptions
being only a particular case of belief, which is itself a sort of
thought, while actions are only volitions followed by an effect. 2.
Substances, i.e. the unknown cause and the unknown recipient of our
sensations. 3. Attributes, subdivisible into Quality, Relation,
Quantity. Of these ([Greek: a]) qualities, like substances, are known
only by the states of consciousness which they excite, and on which they
are based, and by which alone, though they are treated as a distinct
class, they can be described. ([Greek: b]) Relations also, with four
exceptions, are based on some fact, i.e. a series of states of
consciousness. ([Greek: g]) Quantity is, in the same way, based on our
sensations. In short, all attributes are only our sensations and other
feelings, or something involved in them. We may, then, classify nameable
things thus:--1, Feelings; 2, Minds; 3, Bodies, together with the
properties whereby they are _popularly_ (though the evidence is very
deficient) supposed to excite sensations; 4, the relations of Succession
and Coexistence, Likeness and Unlikeness, which subsist really only
between states of consciousness.

These four classes are a substitute for Aristotle's abortive Categories.
As they comprise all nameable things, every fact is made up of them or
some of them; those that are called _subjective_ facts being composed
wholly of feelings as such, and the _objective_ facts, though composed
wholly or partly of substances and attributes, being grounded on
corresponding subjective facts.



The copula is a mere sign of predication, though it is often confounded
with _to be_, the verb of existence (and that not merely by Greeks, but
even by moderns, whose larger experience how one word in one language
often answers to several in another, should have saved them from
thinking that things with a common name must have a common nature). The
_first_ division of propositions is into Affirmative and Negative, the
copula in the latter being _is not_. Hobbes and others, by joining the
_not_ to the predicate, made the latter what they call a _negative
name_. But as a negative name is one expressing the _absence_ of an
attribute, we thus in fact merely deny its presence, and therefore the
affirmative guise these thinkers give to negative propositions is only a
fiction. Again, _modal_ propositions cannot be reduced to the common
form by joining the modality to the predicate, and turning, e.g. The sun
_did_ rise, into, The sun is a thing having risen; for the past time is
not a particular kind of rising, and it affects not the predicate, but
the predication, i.e. the applicability of the predicate to the subject.
There are, however, certain cases in which the qualification may be
detached from the copula; e.g. in such expressions as, _may be_, _is
perhaps_; for, then we really do not mean to assert anything about the
fact, but only about the state of our mind about it, so that it is not
the predication which is affected: e.g. Cæsar _may be_ dead, may
properly be rendered, I am not sure that he is alive.

The _second_ division is into Simple and Complex. Several propositions
joined by a conjunction do not make a complex proposition. The
conjunction, so far from making the two one, adds another, as being an
abbreviation generally of an additional proposition: e.g. _and_ is an
abbreviation of one additional proposition, viz. We must think of the
two together; while _but_ is an abbreviation of two additional
propositions, viz. We must think of them together, and we must recollect
there is a contrast between them. But hypothetical propositions, i.e.
both disjunctives and conditionals, are true complex propositions, since
with several terms they contain but a single assertion. Thus, in, If the
Koran comes from God, Mahomet is God's prophet, we do not assert the
truth of either of the simple propositions therein contained (viz. the
Koran comes from God, and Mahomet is God's prophet), but only the
inferribility of one from the other. The only difference, then, between
a hypothetical and a categorical proposition, is that the former is
always an assertion about an assertion (though some categoricals are so
likewise; e.g. That the whole is greater than its parts, is an axiom).
Their conspicuous place in treatises on Logic arises from this attribute
which they predicate of a proposition (for a proposition, like other
things, has attributes), viz. its being an inference from something
else, being, with reference to Logic, its chief attribute.

The _third_ common division is into Universal, Particular, Indefinite,
and Singular. A proposition whose subject is an individual name, even if
not a proper name, is singular, e.g. The founder of Rome was killed. In
particular propositions, if the part of the class meant by the _some_
were specified, the proposition would become either singular, or
universal with a different subject including all the part. Indefinite in
Logic is a solecism like _doubtful gender_ in grammar, for the speaker
must mean to make either a particular or a universal assertion.



The object of an inquiry into the nature of propositions must be to
analyse, either, 1, the state of mind called belief, or 2, what is
believed. Philosophers have usually, but wrongly, thought the former,
i.e. an analysis of the act of judgment, the chief duty of Logic,
considering a proposition to consist in the denying or affirming one
_idea_ of another. True, we must have the two ideas in the mind
together, in order to believe the assertion about the two _things_; but
so we must also in order to disbelieve it. True also, that besides the
putting the ideas together, there may be a mental process; but this has
nothing to do with the import of propositions, since they are assertions
about things, i.e. facts of external nature, not about the ideas of
them, i.e. facts in our mental history. Logic has suffered from stress
being laid on the relation between the ideas rather than the phenomena,
nature thus coming to be studied by logicians second-hand, that is to
say, as represented in our minds. Our present object, therefore, must
be to investigate judgments, not judgment, and to inquire what it is
which we assert when we make a proposition.

Hobbes (though he certainly often shows his belief that all propositions
are not merely about the meaning of words, and that general names are
given to things on account of their attributes) declares that what we
assert, is our belief that the subject and predicate are names of the
same thing. This is, indeed, a property of all true propositions, and
the only one true of all. But it is not the scientific definition of
propositions; for though the mere collocation which makes a proposition
a proposition, signifies only this, yet that _form_, combined with other
_matter_, conveys much more meaning. Hobbes's principle accounts _fully_
only for propositions where both terms are proper names. He applied it
to others, through attending, like all nominalists, to the denotation,
and not the connotation of words, holding them to be, like proper names,
mere marks put upon individuals. But when saying that, e.g. Socrates is
wise, is a true proposition, because of the conformity of import between
the terms, he should have asked himself why _Socrates_ and _wise_ are
names of the same person. He ought to have seen that they are given to
the same person, not because of the intention of the maker of each word,
but from the resemblance of their connotation, since a word means
properly certain attributes, and, only secondarily, objects denoted by
it. What we really assert, therefore, in a proposition, is, that where
we find certain attributes, we shall find a certain other one, which is
a question not of the meaning of names, but of the laws of nature.

Another theory virtually identical with Hobbes's, is that commonly
received, which makes predication consist in referring things to a
_class_; that is (since a class is only an indefinite number of
individuals denoted by a general name), in viewing them as some of those
to be called by that general name. This view is the basis of the _dictum
de omni et nullo_, on which is supposed to rest the validity of all
reasoning. Such a theory is an example of [Greek: hysteron proteron]: it
explains the cause by the effect, since the predicate cannot be known
for a class name which includes the subject, till several propositions
having it for predicate have been first assented to. This doctrine seems
to suppose all individuals to have been made into parcels, with the
common name outside; so that, to know if a general name can be
predicated correctly of the subject, we need only search the roll so
entitled. But the truth is, that general names are marks put, not upon
definite objects, but upon collections of objects ever fluctuating. We
may frame a class without knowing a single individual belonging to it:
the individual is placed in the class because the proposition is true;
the proposition is not made true by the individual being placed there.

Analysis of different propositions shows what is the real import of
propositions not simply verbal. Thus, we find that even a proposition
with a proper name for subject, means to assert that an individual thing
has the attributes connoted by the predicate, the name being thought of
only as means for giving information of a physical fact. This is still
more the case in propositions with connotative subjects. In these the
denoted objects are indicated by some of their attributes, and the
assertion really is, that the predicate's set of attributes constantly
accompanies the subject's set. But as every attribute is grounded on
some fact or phenomenon, a proposition, when asserting the attendance of
one or some attributes on others, really asserts simply the attendance
of one phenomenon on another; e.g. When we say Man is mortal, we mean
that where certain physical and moral facts called humanity are found,
there also will be found the physical and moral facts called death. But
analysis shows that propositions assert other things besides (although
this is indeed their ordinary import) this coexistence or sequence of
two phenomena, viz. two states of consciousness. Assertions in
propositions about those unknowable entities (_noümena_) which are the
hidden causes of phenomena, are made, indeed, only in virtue of the
knowable _phenomena_. Still, such propositions do, besides asserting the
sequence or coexistence of the phenomena, assert further the _existence_
of the noümena; and, moreover, in affirming the existence of a noümenon,
which is an unknowable _cause_, they assert _causation_ also. Lastly,
propositions sometimes assert _resemblance_ between two phenomena. It is
not true that, as some contend, every proposition whose predicate is a
general name affirms resemblance to the other members of the class; for
such propositions generally assert only the possession by the subject of
certain common peculiarities; and the assertion would be true though
there were no members of the class besides those denoted by the
subject. Nevertheless, _resemblance alone_ is _sometimes_ predicated.
Thus, when individuals are put into a class as belonging to it, not
absolutely, but rather than to any other, the assertion is, not that
they have the attributes connoted, but that they resemble those having
them more than they do other objects. So, again, _only resemblance_ is
predicated, when, though the predicate is a class name, the class is
based on general unanalysable resemblance. The classes in question are
those of the simple feelings; the names of feelings being, like all
concrete general names, connotative, but only of a mere resemblance.

In short, one of _five_ things, viz. Existence, Coexistence (or, to be
more particular, Order in Place), Sequence (or, more particularly, Order
in Time, which comprises also the _mere fact of Coexistence_),
Causation, and Resemblance, is asserted or denied in every proposition.
This division is an exhaustive classification with respect to all things
that can be believed. Although only propositions with concrete terms
have been spoken of, it is equally the fact that, in propositions with
an abstract term or terms, we predicate one of these same _five_ things.
There cannot be any difference in the import of these two classes of
propositions, since there is none in the import of their terms, for the
real signification of a concrete term resides in its connotation (so
that in a concrete proposition we really predicate an attribute), and
what the concrete term connotes forms the whole sense of the abstract.
Thus, all propositions with abstract terms can be turned into equivalent
ones with concrete, the new terms being either the names which connote
the attributes, or names of the facts which are the _fundamenta_ of the
attributes: e.g. Thoughtlessness is danger, is equivalent to,
Thoughtless actions (the _fundamentum_) are dangerous.

Finally, as these _five_ are the only things affirmable, so are they the
only things deniable.



The object of Logic is to find how propositions are to be proved. As
preliminary to this, it has been already shown that the Conceptualist
view of propositions, viz. that they assert a relation between two
ideas, and the Nominalist, that they assert agreement or disagreement
between the meanings of two names, are both wrong as general theories:
for that _generally_ the import of propositions is, to affirm or deny
respecting a phenomenon, or its hidden source, one of five kinds of
facts. There is, however, a class of propositions which relate not to
matter of fact, but to the meaning of names, and which, therefore, as
names and their meanings are arbitrary, admit not of truth or falsity,
but only of agreement or disagreement with usage. These _verbal_
propositions are not only those in which both terms are proper names,
but also some, viz. _essential_ propositions, thought to be more closely
related to things than any others. The Aristotelians' belief that
objects are made what they are called by the inherence of a certain
_general substance_ in the individuals which get from it all their
essential properties, prevented even Porphyry (though more reasonable
than the mediæval Realists) from seeing that the only difference between
altering a non-essential (or _accidental_) property, which, he says,
makes the thing [Greek: alloion], and altering an essential one, which
makes it [Greek: allo] (i.e. a different thing), is, that the latter
change makes the object change its name. But even when it was no longer
believed that there are real entities answering to general terms, the
doctrine based upon it, viz. that a thing's essence is that without
which the thing could neither be, nor be conceived to be, was still
generally held, till Locke convinced most thinkers that the supposed
essences of classes are simply the significations of their _names_. Yet
even Locke supposed that, though the essences of classes are _nominal_,
_individuals_ have _real_ essences, which, though unknown, are the
causes of their sensible properties.

An accidental proposition (i.e. in which a property not connoted by the
subject is predicated of it) tacitly asserts the existence of a thing
corresponding to the subject; otherwise, such a proposition, as it does
not explain the name, would assert nothing at all. But an essential
proposition (i.e. in which a property connoted by the subject is
predicated of it) is identical. The only use of such propositions is to
_define_ words by unfolding the meaning involved in a name. When, as in
mathematics, important consequences seem to follow from them, such
really follow from the tacit assumption, through the ambiguity of the
copula, of the real existence of the _object_ named.

Accidental propositions include, 1, those with a proper name for
subject, since an individual has no essence (although the schoolmen,
and rightly, according to their view of genera and species as entities
inhering in the individuals, attributed to the individual the essence of
his class); and, 2, all general or particular propositions in which the
predicate connotes any attribute not connoted by the subject. Accidental
propositions may be called _real_; they add to our knowledge. Their
import may be expressed (according as the attention is directed mainly,
either to what the proposition means, or to the way in which it is to be
used), either, by the formula: The attributes of the subject are always
(or never) accompanied by those signified by the predicate; or, by the
formula: The attributes of the subject are evidence, or a mark, of the
presence of those of the predicate. For the purposes of reasoning, since
propositions enter into _that_, not as ultimate results, but as means
for establishing other propositions, the latter formula is preferable.



It is merely an accident when general names are names of classes of real
objects: e.g. The unity of God, in the Christian sense, and the
non-existence of the things called dragons, do not prevent those names
being general names. The using a name to connote attributes, turns the
things, whether real or imaginary, into a class. But, in predicating the
name, we predicate only the attributes; and even when a name (as, e.g.
those in Cuvier's system) is introduced as a means of grouping certain
objects together, and not, as usually, as a means of predication, it
still signifies nothing but the possession of certain attributes.

Classification (as resulting from the use of general language) is the
subject of the Aristotelians' Five Predicables, viz. _Genus_, _Species_,
_Differentia_, _Proprium_, _Accidens_. These are a division of general
names, not based on a distinction in their meaning, i.e. in the
attributes connoted, but on a distinction in the class denoted. They
express, not the meaning of the predicate itself, but its relation (a
varying one) to the subject. Commonly, the names of any two classes (or,
popularly, the classes themselves), one of which includes all the other
and more, are called respectively _genus_ and _species_. But the
Aristotelians, i.e. the schoolmen, meant by _differences in kind_
(_genere_ or _specie_) something which was in its nature (and not merely
with reference to the connotation of the name) distinct from
_differences_ in the _accidents_. Now, it is the fact that, though a
fresh class may be founded on the smallest distinction in attributes,
yet that some classes have, to separate them from other classes, no
common attributes except those connoted by the name, while others have
innumerable common qualities (from which we have to select a few samples
for connotation) not referrible to a common source. The ends of language
and of classification would be subverted if the latter (not if the
former) sorts of _difference_ were disregarded. Now, it was these only
that the Aristotelians called _kinds_ (_genera_ or _species_), holding
_differences_ made up of _certain_ and _definite_ properties to be
_differences_ in the _accidents_ of things. In conformity with this
distinction--and it is a true one--any class, e.g. negro as opposed to
white man, may, according as physiology shall show the _differences_ to
be infinite or finite, be discovered to be a distinct _kind_ or
_species_ (though not according to the naturalist's construction of
_species_, as including all descended from the same stock), or merely a
subdivision of the _kind_ or _species_, Man. Among _kinds_, a _genus_ is
a class divisible into other _kinds_, though it may be itself a species
in reference to higher _genera_; that which is not so divisible, is an
individual's _proximate kind_ or _infima species_ (_species
prædicabilis_ and also _subjicibilis_), whose common properties must
include all the common properties of every other real _kind_ to which
the individual can be referred.

The Aristotelians said that the _differentia_ must be of the _essence_
of the subject. They vaguely understood, indeed, by the _essence_ of a
thing, that which makes it the _kind_ of thing that it is. But, as a
_kind_ is such from innumerable qualities not flowing from a common
source, logicians selected the qualities which make the thing be what it
is called, and termed these the essence, not merely of the _species_,
but, in the case of the _infima species_, of the individual also. Hence,
the distinction between the predicables, Differentia, Proprium, and
Accidens, is founded, not on the nature of things, but on the
connotation of names. The _specific difference_ is that which must be
added to the connotation of the _genus_ to complete the connotation of
the _species_. A _species_ may have various _differences_, according to
the principle of the particular classification. A _kind_, and not
merely a class, may be founded on any one of these, if there be a host
of properties behind, of which this one is the index, and not the
source. Sometimes a name has a technical as well as an ordinary
connotation (e.g. the name Man, in the Linnæan system, connotes a
certain number of incisor and canine teeth, instead of its usual
connotation of rationality and a certain general form); and then the
word is in fact ambiguous, i.e. two names. _Genus_ and _Differentia_ are
said to be of the essence; that is, the properties signified by them are
connoted by the name denoting the _species_. But both _proprium_ and
_accidens_ are said to be predicated of the species _accidentally_. A
proprium of the species, however, is predicated of the species
necessarily being an attribute, not indeed connoted by the name, but
following from an attribute connoted by it. It follows, either by way of
demonstration as a conclusion from premisses, or by way of causation as
effect from cause; but, in either case, _necessarily_. Inseparable
accidents, on the other hand, are attributes universal, so far as we
know, to the species (e.g. blackness to crows), but not _necessary_;
i.e. neither involved in the meaning of the name of the species, nor
following from attributes which are. Separable accidents do not belong
to all, or if to all, not at all times (e.g. the fact of being born, to
man), and sometimes are not constant even in the same individual (e.g.
to be hot or cold).



A definition is a proposition declaring either the special or the
ordinary meaning, i.e. in the case of connotative names, the
connotation, of a word. This may be effected by stating directly the
attributes connoted; but it is more usual to predicate of the subject of
definition one name of synonymous, or several which, when combined, are
of equivalent, connotation. So that, a definition of a name being thus
generally the sum total of the essential propositions which could be
framed with that name for subject, is really, as Condillac says, an
_analysis_. Even when a name connotes only a single attribute, it (and
also the corresponding abstract name itself) can yet be defined (in this
sense of being analysed or resolved into its elements) by declaring the
connotation of that attribute, whether, if it be a union of several
attributes (e.g. Humanity), by enumerating them, or, if only one (e.g.
Eloquence), by dissecting the fact which is its foundation. Even when
the fact which is the foundation of the attribute is a simple feeling,
and therefore incapable of analysis, still, if the simple feeling have a
name, the attribute and the object possessing it may be defined by
reference to the fact: e.g. a white object is definable as one exciting
the sensation of white; and whiteness, as the power of exciting that
sensation. The only names, abstract or concrete, incapable of analysis,
and therefore of definition, are proper names, as having no meaning, and
also the names of the simple feelings themselves, since these can be
explained only by the resemblance of the feelings to former feelings
called by the same or by an exactly synonymous name, which consequently
equally needs definition.

Though the only accurate definition is one declaring all the facts
involved in the name, i.e. its connotation, men are usually satisfied
with anything which will serve as an index to its denotation, so as to
guard them from applying it inconsistently. This was the object of
logicians when they laid down that a species must be defined _per genus
et differentiam_, meaning by the _differentia one_ attribute included in
the essence, i.e. in the connotation. And, in fact, one attribute, e.g.
in defining man, Rationality (Swift's Houyhnhms having not been as yet
discovered) often does sufficiently mark out the objects denoted. But,
besides that a definition of this kind ought, in order to be complete,
to be _per genus et differentias_, i.e. by _all_ the connoted attributes
not implied in the name of the _genus_, still, even if all were given, a
_summum genus_ could not be so defined, since it has no superior genus.
And for merely marking out the objects denoted, Description, in which
none of the connoted attributes are given, answers as well as logicians'
so-called _essential_ definition. In Description, any one or a
combination of attributes may be given, the object being to make it
exactly coextensive with the name, so as to be predicable of the same
things. Such a description may be turned into an essential definition by
a change of the connotation (not the denotation) of the name; and, in
fact, thus are manufactured almost all scientific definitions, which,
being landmarks of classification, and not meant to declare the meaning
of the name (though, in fact, they do declare it in its new use), are
ever being modified (as is the definition of a science itself) with the
advance of knowledge. Thus, a technical definition helps to expound the
artificial classification from which it grows; but ordinary definition
cannot expound, as the Aristotelians fancied it could, the natural
classification of things, i.e. explain their division into _kinds_, and
the relations among the _kinds_: for the properties of every _kind_ are
innumerable, and all that definition can do is to state the connotation
of the name.

Both these two modes, viz. the essential but incomplete Definition, and
the accidental, or Description, are imperfect; but the Realists'
distinction between definition of names and of things is quite
erroneous. Their doctrine is now exploded; but many propositions
consistent with it alone (e.g. that the science of geometry is deduced
from definitions) have been retained by Nominalists, such as Hobbes.
Really a definition, as such, cannot explain a thing's nature, being
merely an identical proposition explaining the meaning of a word. But
definitions of names _known to be names of really existing objects_, as
in geometry, include two propositions, one a definition and another a
postulate. The latter affirms the existence of a thing answering to the
name. The science is based on the postulates (whether they rest on
intuition or proof), for the demonstration appeals to them alone, and
not on the definitions, which indeed might, though at some cost of
brevity, be dispensed with entirely. It has been argued that, at any
rate, definitions are premisses of science, _provided_ they give such
meanings to terms as suit existing things: but even so, the inference
would obviously be from the existence, not of the name which means, but
of the thing which has the properties.

One reason for the belief that demonstrative truths follow from the
definitions, not from the postulates, was because the postulates are
never quite true (though in reality so much of them is true as is true
of the conclusions). Philosophers, therefore, searching for something
more accurately true, surmised that definitions must be statements and
analyses, neither of words nor of things, as such, but of ideas; and
they supposed the subject-matter of all demonstrative sciences to be
abstractions of the mind. But even allowing this (though, in fact, the
mind cannot so abstract one property, e.g. length, from all others; it
only _attends_ to the one exclusively), yet the conclusions would still
follow, not from the mere definitions, but from the postulates of the
real existence of the ideas.

Definitions, in short, are of names, not things: yet they are not
therefore arbitrary; and to determine what _should be_ the meaning of a
term, it is often necessary to look at the objects. The obscurity as to
the connotation arises through the objects being named before the
attributes (though it is from the latter that the concrete general terms
get their meaning), and through the same name being popularly applied to
different objects on the ground of general resemblance, without any
distinct perception of their common qualities, especially when these are
complex. The philosopher, indeed, uses general names with a definite
connotation; but philosophers do not make language--it grows: so that,
by degrees, the same name often ceases to connote even general
resemblance. The object in remodelling language is to discover if the
things denoted have common qualities, i.e. if they form a class; and, if
they do not, to form one artificially for them. A language's rude
classifications often serve, when retouched, for philosophy. The
transitions in signification, which often go on till the different
members of the group seem to connote nought in common, indicate, at any
rate, a striking resemblance among the objects denoted, and are
frequently an index to a real connection; so that arguments turning
apparently on the double meaning of a term, may perhaps depend on the
connection of two ideas. To ascertain the link of connection, and to
procure for the name a distinct connotation, the resemblances of things
must be considered. Till the name has got a distinct connotation, it
cannot be defined. The philosopher chooses for his connotation of the
name the attributes most important, either directly, or as the
differentiæ leading to the most interesting propria. The enquiry into
the more hidden agreement on which these obvious agreements depend,
often itself arises under the guise of enquiries into the definition of
a name.





The preceding book treated, not of the proper subject of logic, viz. the
nature of proof, but of assertion. Assertions (as, e.g. definitions)
which relate to the meaning of words, are, since _that_ is arbitrary,
incapable of truth or falsehood, and therefore of proof or disproof. But
there are assertions which are subjects for proof or disproof, viz. the
propositions (the real, and not the verbal) whose subject is some fact
of consciousness, or its hidden cause, about which is predicated, in the
affirmative or negative, one of five things, viz. existence, order in
place, order in time, causation, resemblance: in which, in short, it is
asserted, that some given subject does or does not possess some
attribute, or that two attributes, or sets of attributes, do or do not
(constantly or occasionally) coexist.

A proposition not believed on its own evidence, but inferred from
another, is said to be _proved_; and this process of inferring, whether
syllogistically or not, is _reasoning_. But whenever, as in the
deduction of a particular from a universal, or, in Conversion, the
assertion in the new proposition is the same as the whole or part of
the assertion in the original proposition, the inference is only
apparent; and such processes, however useful for cultivating a habit of
detecting quickly the concealed identity of assertions, are not

Reasoning, or Inference, properly so called, is, 1, Induction, when a
proposition is inferred from another, which, whether particular or
general, is less general than itself; 2, Ratiocination, or Syllogism,
when a proposition is inferred from others equally or more general; 3, a
kind which falls under neither of these descriptions, yet is the basis
of both.



The syllogistic figures are determined by the position of the middle
term. There are four, or, if the fourth be classed under the first,
three. But syllogisms in the other figures can be reduced to the first
by conversion. Such reduction may not indeed be necessary, for different
arguments are suited to different figures; the first figure, says
Lambert, being best adapted to the discovery or proof of the properties
of things; the second, of the distinctions between things; the third, of
instances and exceptions; the fourth, to the discovery or exclusion of
the different species of a genus. Still, as the premisses of the first
figure, got by reduction, are really the same as the original ones, and
as the only arguments of great scientific importance, viz. those in
which the conclusion is a universal affirmative, can be proved in the
first figure alone, it is best to hold that the two elementary forms of
the first figure are the universal types, the one in affirmatives, the
other in negatives, of all correct ratiocination.

The _dictum de omni et nullo_, viz. that whatever can be affirmed or
denied of a class can be affirmed or denied of everything included in
the class, which is a true account generalised of the constituent parts
of the syllogism in the first figure, was thought the basis of the
syllogistic theory. The fact is, that when universals were supposed to
have an independent objective existence, this dictum stated a supposed
law, viz. that the _substantia secunda_ formed part of the properties of
each individual substance bearing the name. But, now that we know that a
class or universal is nothing but the individuals in the class, the
dictum is nothing but the identical proposition, that whatever is true
of certain objects is true of each of them, and, to mean anything, must
be considered, not as an axiom, but as a circuitous definition of the
word _class_.

It was the attempt to combine the nominalist view of the signification
of general terms with the retention of the dictum as the basis of all
reasoning, that led to the self-contradictory theories disguised under
the ultra-nominalism of Hobbes and Condillac, the ontology of the later
Kantians, and (in a less degree) the abstract ideas of Locke. It was
fancied that the process of inferring new truths was only the
substitution of one arbitrary sign for another; and Condillac even
described science as _une langue bien faite_. But language merely
enables us to remember and impart our thoughts; it strengthens, like an
artificial memory, our power of thought, and is thought's powerful
instrument, but not its exclusive subject. If, indeed, propositions in a
syllogism did nothing but refer something to or exclude it from a class,
then certainly syllogisms might have the dictum for their basis, and
import only that the classification is consistent with itself. But such
is not the primary object of propositions (and it is on this account, as
well as because men will never be persuaded in common discourse to
_quantify_ the predicate, that Mr. De Morgan's or Sir William Hamilton's
_quantification of the predicate_ is a device of little value). What is
asserted in every proposition which conveys real knowledge, is a fact
dependent, not on artificial classification, but on the laws of nature;
and as ratiocination is a mode of gaining real knowledge, the principle
or law of all syllogisms, with propositions not purely verbal, must be,
for affirmative syllogisms, that; Things coexisting with the same thing
coexist with one another; and for negative, that; A thing coexisting
with another, with which a third thing does not coexist, does not
coexist with that third thing. But if (see _suprà_, p. 26) propositions
(and, of course, all combinations of them) be regarded, not
speculatively, as portions of our knowledge of nature, but as memoranda
for practical guidance, to enable us, when we know that a thing has one
of two attributes, to infer it has the other, these two axioms may be
translated into one, viz. Whatever has any mark has that which it is a
mark of; or, if both premisses are universal, Whatever is a mark of any
mark, is a mark of that of which this last is a mark.



The question is, whether the syllogistic process is one of inference,
i.e. a process from the known to the unknown. Its assailants say, and
truly, that in every syllogism, considered as an argument to prove the
conclusion, there is a _petitio principii_; and Dr. Whately's defence of
it, that its object is to unfold assertions wrapped up and implied (i.e.
in fact, _asserted unconsciously_) in those with which we set out,
represents it as a sort of trap. Yet, though no reasoning from generals
to particulars can, as such, prove anything, the conclusion _is_ a _bonâ
fide_ inference, though not an inference from the general proposition.
The general proposition (i.e. in the first figure, the major premiss)
contains not only a record of many particular facts which we have
observed or inferred, but also instructions for making inferences in
unforeseen cases. Thus the inference is completed in the major premiss;
and the rest of the syllogism serves only to decipher, as it were, our
own notes.

Dr. Whately fails to make out that syllogising, i.e. reasoning from
generals to particulars, is the _only_ mode of reasoning. No additional
evidence is gained by interpolating a general proposition, and therefore
we may, if we please, reason directly from the individual cases, since
it is on these alone that the general proposition, if made, would rest.
Indeed, thus are in fact drawn, as well the inferences of children and
savages, and of animals (which latter having no signs, can frame no
general propositions), as even those drawn by grown men generally, from
personal experience, and particularly the inferences of men of high
practical genius, who, not having been trained to generalise, can apply,
but not state, their principles of action. Even when we have general
propositions we need not use them. Thus Dugald Stewart showed that the
axioms need not be expressly adverted to in order to make good the
demonstrations in Euclid; though he held, inconsistently, that the
definitions must be. All general propositions, whether called axioms, or
definitions, or laws of nature, are merely abridged statements of the
particular facts, which, as occasion arises, we either think we may
proceed on as proved, or intend to assume.

In short, all inference is from particulars to particulars; and general
propositions are both registers or memoranda of such former inferences,
and also short formulæ for making more. The major premiss is such a
formula; and the conclusion is an inference drawn, not from, but
according to that formula. The _actual_ premisses are the particular
facts whence the general proposition was collected inductively; and the
syllogistic rules are to guide us in reading the register, so as to
ascertain what it was that we formerly thought might be inferred from
those facts. Even where ratiocination is independent of induction, as,
when we accept from a man of science the doctrine that all A is B; or
from a legislator, the law that all men shall do this or that, the
operation of drawing thence any particular conclusion is a process, not
of inference, but of interpretation. In fact, whether the premisses are
given by authority, or derived from our own (or predecessors')
observation, the object is always simply to interpret, by reference to
certain marks, an intention, whether that of the propounder of the
principle or enactment, or that which we or our predecessors had when we
framed the general proposition, so that we may draw no inferences that
were not _intended_ to be drawn. We assent to the conclusion in a
syllogism on account of its consistency with what we interpret to have
been the intention of the framer of the major premiss, and not, as Dr.
Whately held, because the supposition of a false conclusion from the
premisses involves a contradiction, since, in fact, the denial, e.g.
that an individual now living will die, is not _in terms_ contradictory
to the assertion that his ancestors and their contemporaries (to which
the general proposition, as a record of facts, really amounts) have all

But the syllogistic form, though the process of inference, which there
always is when a syllogism is used, lies not in this form, but in the
act of generalisation, is yet a great collateral security for the
correctness of that generalisation. When all possible inferences from a
given set of particulars are thrown into one general expression (and, if
the particulars support one inference, they always will support an
indefinite number), we are more likely both to feel the need of weighing
carefully the sufficiency of the experience, and also, through seeing
that the general proposition would equally support some conclusion which
we _know_ to be false, to detect any defect in the evidence, which, from
bias or negligence, we might otherwise have overlooked. But the
syllogistic form, besides being useful (and, when the validity of the
reasoning is doubtful, even indispensable) for verifying arguments, has
the acknowledged merit of all general language, that it enables us to
make an induction once for all. We _can_, indeed, and in simple cases
habitually _do_, reason straight from particulars; but in cases at all
complicated, all but the most sagacious of men, and they also, unless
their experience readily supplied them with parallel instances, would be
as helpless as the brutes. The only counterbalancing danger is, that
general inferences from insufficient premisses may become hardened into
general maxims, and escape being confronted with the particulars.

The major premiss is not really part of the argument. Brown saw that
there would be a _petitio principii_ if it were. He, therefore,
contended that the conclusion in reasoning follows from the minor
premiss alone, thus suppressing the appeal to experience. He argued,
that to reason is merely to analyse our general notions or abstract
ideas, and that, _provided_ that the relation between the two ideas,
e.g. of _man_ and of _mortal_, has been first perceived, we can evolve
the one directly from the other. But (to waive the error that a
proposition relates to ideas instead of things), besides that this
_proviso_ is itself a surrender of the doctrine that an argument
consists simply of the minor and the conclusion, the perception of the
relation between two ideas, one of which is not implied in the name of
the other, must obviously be the result, not of analysis, but of
experience. In fact, both the minor premiss, and also the expression of
our former experience, must _both_ be present in our reasonings, or the
conclusion will not follow. Thus, it appears that the universal type of
the reasoning process is: Certain individuals possess (as I or others
have observed) a given attribute; An individual resembles the former in
certain other attributes: Therefore (the conclusion, however, not being
conclusive from its form, as is the conclusion in a syllogism, but
requiring to be sanctioned by the canons of induction) he resembles them
also in the given attribute. But, though this, and not the syllogistic,
is the universal type of reasoning, yet the syllogistic process is a
useful test of inferences. It is expedient, _first_, to ascertain
generally what attributes are marks of a certain other attribute, so as,
subsequently, to have to consider, _secondly_, only whether any given
individuals have those former marks. Every process, then, by which
anything is inferred respecting an unobserved case, we will consider to
consist of both these last-mentioned processes. Both are equally
induction; but the name may be conveniently confined to the process of
establishing the general formula, while the interpretation of this will
be called 'Deduction.'



The minor premiss always asserts a resemblance between a new case and
cases previously known. When this resemblance is not obvious to the
senses, or ascertainable at once by direct observation, but is itself
matter of inference, the conclusion is the result of a train of
reasoning. However, even then the conclusion is really the result of
induction, the only difference being that there are two or more
inductions instead of one. The inference is still from particulars to
particulars, though drawn in conformity, not to one, but to several
formulæ. This need of several formulæ arises merely from the fact that
the marks by which we perceive that an inference can be drawn (and of
which marks the formulæ are records) happen to be recognisable, not
directly, but only through the medium of other marks, which were, by a
previous induction, collected to be marks of them.

All reasoning, then, is induction: but the difficulties in sciences
often lie (as, e.g. in geometry, where the inductions are the simple
ones of which the axioms and a few definitions are the formulæ) not at
all in the inductions, but only in the formation of trains of reasoning
to prove the minors; that is, in so combining a few simple inductions as
to bring a new case, by means of one induction within which it evidently
falls, within others in which it cannot be directly seen to be included.
In proportion as this is more or less completely effected (that is, in
proportion as we are able to discover marks of marks), a science, though
always remaining inductive, tends to become also _deductive_, and, to
the same extent, to cease to be one of the _experimental_ sciences, in
which, as still in chemistry, though no longer in mechanics, optics,
hydrostatics, acoustics, thermology, and astronomy, each generalisation
rests on a special induction, and the reasonings consist but of one step

An experimental science may become deductive by the mere progress of
experiment. The mere connecting together of a few detached
generalisations, or even the discovery of a great generalisation working
only in a limited sphere, as, e.g. the doctrine of chemical equivalents,
does not make a science deductive as a whole; but a science is thus
transformed when some comprehensive induction is discovered connecting
hosts of formerly isolated inductions, as, e.g. when Newton showed that
the motions of all the bodies in the solar system (though each motion
had been separately inferred and from separate marks) are all marks of
one like movement. Sciences have become deductive usually through its
being shown, either by deduction or by direct experiment, that the
varieties of some phenomenon in them uniformly attend upon those of a
better known phenomenon, e.g. every variety of sound, on a distinct
variety of oscillatory motion. The science of number has been the grand
agent in thus making sciences deductive. The truths of numbers are,
indeed, affirmable of all things only in respect of their quantity; but
since the variations of _quality_ in various classes of phenomena have
(e.g. in mechanics and in astronomy) been found to correspond regularly
to variations of _quantity_ in the same or some other phenomena, every
mathematical formula applicable to quantities so varying becomes a mark
of a corresponding general truth respecting the accompanying variations
in quality; and as the science of quantity is, so far as a science can
be, quite deductive, the theory of that special kind of qualities
becomes so likewise. It was thus that Descartes and Clairaut made
geometry, which was already partially deductive, still more so, by
pointing out the correspondence between geometrical and algebraical



All sciences are based on induction; yet some, e.g. mathematics, and
commonly also those branches of natural philosophy which have been made
deductive through mathematics, are called Exact Sciences, and systems of
Necessary Truth. Now, their necessity, and even their alleged certainty,
are illusions. For the conclusions, e.g. of geometry, flow only
seemingly from the definitions (since from definitions, as such, only
propositions about the meaning of words can be deduced): really, they
flow from an implied assumption of the existence of real things
corresponding to the definitions. But, besides that the existence of
such things is not actual or possible consistently with the constitution
of the earth, neither can they even be _conceived_ as existing. In fact,
geometrical points, lines, circles, and squares, are simply copies of
those in nature, to a part alone of which we choose to _attend_; and the
definitions are merely some of our first generalisations about these
natural objects, which being, though equally true of all, not exactly
true of any one, must, actually, when extended to cases where the error
would be appreciable (e.g. to lines of perceptible breadth), be
corrected by the joining to them of new propositions about the
aberration. The exact correspondence, then, between the facts and those
first principles of geometry which are involved in the so-called
definitions, is a fiction, and is merely _supposed_. Geometry has,
indeed (what Dugald Stewart did not perceive), some first principles
which are true without any mixture of hypothesis, viz. the axioms, as
well those which are indemonstrable (e.g. Two straight lines cannot
enclose a space) as also the demonstrable ones; and so have all sciences
some exactly true general propositions: e.g. Mechanics has the first law
of motion. But, generally, the necessity of the conclusions in geometry
consists only in their following necessarily from certain _hypotheses_,
for which same reason the ancients styled the conclusions of all
deductive sciences _necessary_. That the hypotheses, which form part of
the premisses of geometry, must, as Dr. Whewell says, not be
arbitrary--that is, that in their positive part they are observed facts,
and only in their negative part hypothetical--happens simply because our
aim in geometry is to deduce conclusions which may be true of real
objects: for, when our object in reasoning is not to investigate, but to
illustrate truths, arbitrary hypotheses (e.g. the operation of British
political principles in Utopia) are quite legitimate.

The ground of our belief in axioms is a disputed point, and one which,
through the belief arising too early to be traced by the believer's own
recollection, or by other persons' observation, cannot be settled by
reference to actual dates. The axioms are really only generalisations
from experience. Dr. Whewell, however, and others think that, though
suggested, they are not proved by experience, and that their truth is
recognised _à priori_ by the constitution of the mind as soon as the
meaning of the proposition is understood. But this assumption of an _à
priori_ recognition is gratuitous. It has never been shown that there is
anything in the facts inconsistent with the view that the recognition of
the truth of the axioms, however exceptionally complete and instant,
originates simply in experience, equally with the recognition of
ordinary physical generalisations. Thus, that we see a property of
geometrical forms to be true, without inspection of the material forms,
is fully explained by the capacity of geometrical forms of being painted
in the imagination with a distinctness equal to reality, and by the fact
that experience has informed us of that capacity; so that a conclusion
on the faith of the imaginary forms is really an induction from
observation. Then, again, there is nothing inconsistent with the theory
that we learn by experience the truth of the axioms, in the fact that
they are conceived by the mind as universally and necessarily true, that
is, that we cannot figure them to ourselves as being false. Our capacity
or incapacity of conceiving depends on our associations. Educated minds
can break up their associations more easily than the uneducated; but
even the former not entirely at will, even when, as is proved later,
they are erroneous. The Greeks, from ignorance of foreign languages,
believed in an inherent connection between names and things. Even Newton
imagined the existence of a subtle ether between the sun and bodies on
which it acts, because, like his rivals the Cartesians, he could not
conceive a body acting where it is not. Indeed, inconceivableness
depends so completely on the accident of our mental habits, that it is
the essence of scientific triumphs to make the contraries of once
inconceivable views themselves appear inconceivable. For instance,
suppositions opposed even to laws so recently discovered as those of
chemical composition appear to Dr. Whewell himself to be inconceivable.
What wonder, then, that an acquired incapacity should be mistaken for a
natural one, when not merely (as in the attempt to conceive space or
time as finite) does experience afford no model on which to shape an
opposed conception, but when, as in geometry, we are unable even to call
up the geometrical ideas (which, being impressions of form, exactly
resemble, as has been already remarked, their prototypes), e.g. of two
straight lines, in order to try to conceive them inclosing a space,
without, by the very act, repeating the scientific experiment which
establishes the contrary.

Since, then, the axioms and the misnamed definitions are but inductions
from experience, and since the definitions are only hypothetically true,
the deductive or demonstrative sciences--of which these axioms and
definitions form together the first principles--must really be
themselves inductive and hypothetical. Indeed, it is to the fact that
the results are thus only conditionally true, that the necessity and
certainty ascribed to demonstration are due.

It is so even with the Science of Number, i.e. arithmetic and algebra.
But here the truth has been hidden through the errors of two opposite
schools; for while many held the truths in this science to be _à
priori_, others paradoxically considered them to be merely verbal, and
every process to be simply a succession of changes in terminology, by
which equivalent expressions are substituted one for another. The excuse
for such a theory as this latter was, that in arithmetic and algebra we
carry no ideas with us (not even, as in a geometrical demonstration, a
mental diagram) from the beginning, when the premisses are translated
into signs, till the end, when the conclusion is translated back into
things. But, though this is so, yet in every step of the calculation,
there is a real inference of facts from facts: but it is disguised by
the comprehensive nature of the induction, and the consequent generality
of the language. For numbers, though they must be numbers of something,
may be numbers of anything; and therefore, as we need not, when using an
algebraical symbol (which represents all numbers without distinction),
or an arithmetical number, picture to ourselves all that it stands for,
we may picture to ourselves (and this not as a sign of things, but as
being itself a thing) the number or symbol itself as conveniently as any
other single thing. That we are conscious of the numbers or symbols, in
their character of things, and not of mere signs, is shown by the fact
that our whole process of reasoning is carried on by predicating of them
the properties of things.

Another reason why the propositions in arithmetic and algebra have been
thought merely verbal, is that they seem to be _identical_ propositions.
But in 'Two pebbles and one pebble are equal to three pebbles,' equality
but not identity is affirmed; the subject and predicate, though names of
the same objects, being names of them in different states, that is, as
producing different impressions on the senses. It is on such inductive
truths, resting on the evidence of sense, that the Science of Number is
based; and it is, therefore, like the other deductive sciences, an
inductive science. It is also, like them, hypothetical. Its inductions
are the definitions (which, as in geometry, assert a fact as well as
explain a name) of the numbers, and two axioms, viz. The sums of equals
are equal; the differences of equals are equal. These axioms, and
so-called definitions are themselves exactly, and not merely
hypothetically, true. Yet the conclusions are true only on the
assumption that, 1 = 1, i.e. that all the numbers are numbers of the
same or equal units. Otherwise, the certainty in arithmetical processes,
as in those of geometry or mechanics, is not _mathematical_, i.e.
unconditional certainty, but only certainty of inference. It is the
enquiry (which can be gone through once for all) into the inferences
which can be drawn from assumptions, which properly constitutes all
demonstrative science.

New conclusions may be got as well from fictitious as from real
inductions; and this is even consciously done, viz. in the _reductio ad
absurdum_, in order to show the falsity of an assumption. It has even
been argued that all ratiocination rests, in the last resort, on this
process. But as this is itself syllogistic, it is useless, as a proof of
a syllogism, against a man who denies the validity of this kind of
reasoning process itself. Such a man cannot in fact be forced to a
contradiction in terms, but only to a contradiction, or rather an
infringement, of the fundamental maxim of ratiocination, viz. 'Whatever
has a mark, has what it is a mark of;' and, since it is only by
admitting premisses, and yet rejecting a conclusion from them, that this
axiom is infringed, consequently nothing is _necessary_ except the
connection between a conclusion and premisses.





As all knowledge not intuitive comes exclusively from inductions,
induction is the main topic of Logic; and yet neither have
metaphysicians analysed this operation with a view to practice, nor, on
the other hand, have discoverers in physics cared to generalise the
methods they employed.

Inferences are equally _inductive_, whether, as in science, which needs
its conclusions for record, not for instant use, they pass through the
intermediate stage of a general proposition (to which class Dr. Whewell,
without sanction from facts, or from the usage of Reid and Stewart, the
founders of modern English metaphysical terminology, limits the term
induction), or are drawn direct from particulars to a supposed parallel
case. Neither does it make any difference in the _character_ of the
induction, whether the process be experiment or ratiocination, and
whether the object be to infer a general proposition or an individual
fact. That, in the latter case, the difficulty of the practical
enquiries, e.g. of a judge or an advocate, lies chiefly in selecting
from among all approved general propositions those inductions which suit
his case (just as, even in deductive sciences, the ascertaining of the
inductions is easy, their combination to solve a problem hard) is not to
the point: the legitimacy of the inductions so selected must at all
events be tried by the same test as a new general truth in science.
Induction, then, may be treated here as though it were the operation of
discovering and proving general propositions; but this is so only
because the evidence which justifies an inference respecting one unknown
case, would justify a like inference about a whole class, and is really
only another form of the same process: because, in short, the logic of
science is the universal logic applicable to all human enquiries.



Induction is the process by which what is true at certain times, or of
certain individuals, is inferred to be true in like circumstances at all
times, or of a whole class. There must be an inference from the known to
the unknown, and not merely from a less to a more general expression.
Consequently, there is no valid induction, 1, in those cases laid down
in the common works on Logic as the only perfect instances of induction,
viz. where what we affirm of the class has already been ascertained to
be true of each individual in it, and in which the seemingly general
proposition in the conclusion is simply a number of singular
propositions written in an abridged form; or, 2, when, as often in
mathematics, the conclusion, though really general, is a mere summing up
of the different propositions from which it is drawn (whether actually
ascertained, or, as in the case of the uncalculated terms of an
arithmetical series, when once its law is known, readily to be
understood); or, 3, when the several parts of a complex phenomenon,
which are only capable of being observed separately, have been pieced
together by one conception, and made, as it were, one fact represented
in a single proposition.

Dr. Whewell sets out this last operation, which he terms the
_colligation of facts_, as induction, and even as the type of induction
generally. But, though induction is always colligation, or (as we may,
with equal accuracy, characterise such a general expression obtained by
abstraction simply connecting observed facts by means of common
characters) _description_, colligation, or description, as such, though
a necessary preparation for induction, is not induction. Induction
explains and predicts (and, as an incident of these powers, describes).
Different explanations collected by real induction from supposed
parallel cases (e.g. the Newtonian and the _Impact_ doctrines as to the
motions of the heavenly bodies), or different predictions, i.e.
different determinations of the conditions under which similar facts may
be expected again to occur (e.g. the stating that the position of one
planet or satellite so as to overshadow another, and, on the other hand,
that the impending over mankind of some great calamity, is the condition
of an eclipse), cannot be true together. But, for a colligation to be
correct, it is enough that it enables the mind to represent to itself as
a whole all the separate facts ascertained at a given time, so that
successive tentative descriptions of a phenomenon, got by guessing till
a guess is found which tallies with the facts, may, though conflicting
(e.g. the theories respecting the motions of the heavenly bodies), be
_all_ correct _so far as they go_. Induction is proof, the inferring
something unobserved from something observed; and to provide a proper
test of proof is the special purpose of inductive logic. But colligation
simply sums up the facts observed, as seen under a new point of view.
Dr. Whewell contends that, besides the sum of the facts, colligation
introduces, as a principle of connection, a conception of the mind not
existing in the facts. But, in fact, it is only because this conception
is a copy of something in the facts, although our senses are too weak to
recognise it directly, that the facts are rightly classed under the
conception. The conception is often even got by abstraction from the
facts which it colligates; but also when it is a hypothesis, borrowed
from strange phenomena, it still is accepted as true only because found
actually, and as a fact, whatever the origin of the knowledge of the
fact, to fit and to describe as a whole the separate observations. Thus,
though Kepler's consequent inference that, _because_ the orbit of a
planet is an ellipse, the planet would _continue_ to revolve in that
same ellipse, was an induction, his previous application of the
conception of an ellipse, abstracted from other phenomena, to sum up his
direct observations of the successive positions occupied by the
different planets, and thus to describe their orbits, was no induction.
It altered only the _predicate_, changing--The successive places of,
e.g. Mars, are A, B, C, and so forth, into--The successive places of,
e.g. Mars, are points in an ellipse: whereas induction always widens the



Induction is generalisation from experience. It assumes, that whatever
is true in any one case, is true in all cases of a certain description,
whether past, present, or future (and not merely in future cases, as is
wrongly implied in the statement by Reid's and Stewart's school, that
the principle of induction is 'our intuitive conviction that the future
will resemble the past'). It assumes, in short, that the course of
nature is uniform, that is, that all things take place according to
general laws. But this general axiom of induction, though by it were
discovered the obscure laws of nature, is no explanation of the
inductive process, but is itself an induction (not, as some think, an
intuitive principle which experience _verifies_ only), and is arrived at
after many separate phenomena have been first observed to take place
according to general laws. It does not, then, _prove_ all other
inductions. But it is a _condition_ of their proof. For any induction
can be turned into a syllogism by supplying a major premiss, viz. What
is true of this, that, &c. is true of the whole class; and the process
by which we arrive at this immediate major may be itself represented by
another syllogism or train of syllogisms, the major of the ultimate
syllogism, and which therefore is the warrant for the immediate major,
being this axiom, viz. that there is uniformity, at all events, in the
class of phenomena to which the induction relates, and a uniformity
which, if not foreknown, may now be known.

But though the course of nature is uniform, it is also infinitely
various. Hence there is no certainty in the induction in use with the
ancients, and all non-scientific men, and which Bacon attacked, viz.
'Inductio per enumerationem simplicem, ubi non reperitur instantia
contradictoria'--_unless_, as in a few cases, we must have known of the
contradictory instances if existing. The scientific theory of induction
alone can show why a general law of nature may sometimes, as when the
chemist first discovers the existence and properties of a before unknown
substance, be inferred from a single instance, and sometimes (e.g. the
blackness of all crows) not from a million.



The uniformity of the course of nature is a complex fact made up of all
the separate uniformities in respect to single phenomena. Each of these
separate uniformities, if it be not a mere case of and result from
others, is a law of nature; for, though _law_ is used for any general
proposition expressing a uniformity, _law of nature_ is restricted to
cases where it has been thought that a separate act of creative will is
necessary to account for the uniformity. Laws of nature, in the
aggregate, are the fewest general propositions from which all the
uniformities in the universe might be deducted. Science is ever tending
to resolve one law into a higher. Thus, Kepler's three propositions,
since having been resolved by Newton into, and shown to be cases of the
three laws of motion, may be indeed called laws, but not laws of nature.

Since every correct inductive generalisation is either a law of nature,
or a result from one, the problem of inductive logic is to unravel the
web of nature, tracing each thread separately, with the view, 1, of
ascertaining what are the _several_ laws of nature, and, 2, of following
them into their results. But it is impossible to frame a scientific
method of induction, or test of inductions, unless, unlike Descartes, we
start with the hypothesis that some trustworthy inductions have been
already ascertained by man's involuntary observation. These spontaneous
generalisations must be revised; and the same principle which common
sense has employed to revise them, correcting the narrower by the wider
(for, in the end, experience must be its own test), serves also, only
made more precise, as the real type of scientific induction. As
preliminary to the employment of this test, nature must be surveyed,
that we may discover which are respectively the invariable and the
variable inductions at which man has already arrived unscientifically.
Then, by connecting these different ascertained inductions with one
another through ratiocination, they become mutually confirmative, the
strongest being made still stronger when bound up with the weaker, and
the weakest at least as strong as the weakest of those from which they
are deduced (as in the case of the Torricellian experiment) while those
leading deductively to incompatible consequences become each other's
test, showing that one must be given up (e.g. the old farmers' bad
induction that seed never throve if not sown during the increase of the
moon). It is because a survey of the uniformities ascertained to exist
in nature makes it clear that there are certain and universal
uniformities serving as premisses whence crowds of lower inductions may
be deduced, and so be raised to the same degree of certainty, that a
logic of induction is possible.



Phenomena in nature stand to each other in two relations, that of
simultaneity, and that of succession. On a knowledge of the truths
respecting the succession of facts depends our power of predicting and
influencing the future. The object, therefore, must be to find some law
of succession not liable to be defeated or suspended by any change of
circumstances, by being tested by, and deduced from which law, all other
uniformities of succession may be raised to equal certainty. Such a law
is not to be found in the class of laws of number or of space; for
though these are certain and universal, no laws except those of space
and number can be deduced from them by themselves (however important
_elements_ they may be in the ascertainment of uniformities of
succession). But causation is such a law; and of this, moreover, all
cases of succession whatever are examples.

This _Law of Causation_ implies no particular theory as to the ultimate
production of effects by _efficient_ causes, but simply implies the
existence of an invariable order of succession (on our assurance of
which the validity of the canons of inductive logic depends) found by
observation, or, when not yet observed, believed, to obtain between an
invariable antecedent, i.e. the _physical_ cause, and an invariable
consequent, the effect. This sequence is generally between a consequent
and the _sum_ of several antecedents. The cause is really the sum total
of the conditions, positive and negative; the negative being stated as
one condition, the same always, viz. the absence of counteracting causes
(since one cause generally counteracts another by the same law whereby
it produces its own effects, and, therefore, the particular mode in
which it counteracts another may be classed under the positive causes).
But it is usual, even with men of science, to reserve the name _cause_
for an antecedent _event_ which completes the assemblage of conditions,
and begins to exist immediately before the effect (e.g. in the case of
death from a fall, the slipping of the foot, and not the weight of the
body), and to style the permanent facts or _states_, which, though
existing immediately before, have also existed long previously, the
_conditions_. But indeed, popularly, any condition which the hearer is
least likely to be aware of, or which needs to be dwelt upon with
reference to the particular occasion, will be selected as the cause,
even a negative condition (e.g. the sentinel's absence from his post, as
the cause of a surprise), though from a mere negation no consequence can
really proceed. On the other hand, the object which is popularly
regarded as standing in the relation of _patient_, and as being the mere
theatre of the effect, is never styled _cause_, being included in the
phrase describing the effect, viz. as the object, of which the effect is
_a state_. But really these so-called _patients_ are themselves agents,
and their properties are positive conditions of the effect. Thus, the
death of a man who has taken prussic acid is as directly the effect of
the organic properties of the man, i.e. the _patient_, as of the poison,
i.e. the _agent_.

To be a cause, it is not enough that the sequence _has been_ invariable.
Otherwise, night might be called the cause of day; whereas it is not
even a condition of it. Such relations of succession or coexistence, as
the succession of day and night (which Dr. Whewell contrasts as _laws of
phenomena_ with _causes_, though, indeed, the latter also are laws of
phenomena, only more universal ones), result from the coexistence of
real causes. The causes themselves are followed by their effects, not
only invariably, but also _necessarily_, i.e. _unconditionally_, or
subject to none but negative conditions. _This_ is material to the
notion of a cause. But another question is not material, viz. whether
causes _must_ precede, or may, at times, be simultaneous with (they
certainly are never preceded by) their effects. In some, though not in
all cases, the causes do invariably continue _together with_ their
effects, in accordance with the schools' dogma, _Cessante causâ, cessat
et effectus_; and the hypothesis that, in such cases, the effects are
produced _afresh_ at each instant by their cause, is only a verbal
explanation. But the question does not affect the theory of causation,
which remains intact, even if (in order to take in cases of simultaneity
of cause and effect) we have to define a cause, as the assemblage of
phenomena, which occurring, some other phenomenon invariably and
unconditionally commences, or has its origin.

There exist certain original natural agents, called permanent causes
(some being objects, e.g. the earth, air, and sun; others, cycles of
events, e.g. the rotation of the earth), which together make up nature.
All other phenomena are immediate or remote effects of these causes.
Consequently, as the state of the universe at one instant is the
consequence of its state at the previous instant, a person (but only if
of more than human powers of calculation, and subject also to the
possibility of the order being changed by a new volition of a supreme
power) might predict the whole future order of the universe, if he knew
the original distribution of all the permanent causes, with the laws of
the succession between each of them and its different mutually
independent effects. But, in fact, the distribution of these permanent
causes, with the reason for the proportions in which they coexist, has
not been reduced to a law; and this is why the sequences or coexistences
among the effects of several of them together cannot rank as laws of
nature, though they are invariable while the causes coexist. For this
same reason (since the proximate causes are traceable ultimately to
permanent causes) there are no original and independent uniformities of
coexistence between effects of different (proximate) causes, though
there may be such between different effects of the same cause.

Some, and particularly Reid, have regarded man's voluntary agency as
the true type of causation and the exclusive source of the idea. The
facts of inanimate nature, they argue, exhibit only antecedence and
sequence, while in volition (and this would distinguish it from physical
causes) we are conscious, prior to experience, of power to produce
effects: volition, therefore, whether of men or of God, must be, they
contend, an efficient cause, and the only one, of all phenomena. But, in
fact, they bring no positive evidence to show that we could have known,
apart from experience, that the effect, e.g. the motion of the limbs,
would follow from the volition, or that a volition is more than a
physical cause. In lieu of positive evidence, they appeal to the
supposed conceivableness of the direct action of will on matter, and
inconceivableness of the direct action of matter on matter. But there is
no inherent law, to this effect, of the conceptive faculty: it is only
because our voluntary acts are, from the first, the most direct and
familiar to us of all cases of causation, that men, as is seen from the
structure of languages (e.g. their active and passive voices, and
impersonations of inanimate objects), get the _habit_ of borrowing them
to explain other phenomena by a sort of original Fetichism. Even Reid
allows that there is a tendency to assume volition where it does not
exist, and that the belief in it has its sphere gradually limited, in
proportion as fixed laws of succession among external objects are

This proneness to require the appearance of some necessary and natural
connection between the cause and its effect, i.e. some reason _per se_
why the one should produce the other, has infected most theories of
causation. But the selection of the particular agency which is to make
the connection between the physical antecedent and its consequent seem
_conceivable_, has perpetually varied, since it depends on a person's
special habits of thought. Thus, the Greeks, Thales, Anaximenes, and
Pythagoras, thought respectively that water, air, or number is such an
agency explaining the production of physical effects. Many moderns,
again, have been unable to _conceive_ the production of effects by
volition itself, without some intervening agency to connect it with
them. This medium, Leibnitz thought, was some _per se_ efficient
physical antecedent; while the Cartesians imagined for the purpose the
theory of Occasional Causes, that is, supposed that God, not _quâ_ mind,
or _quâ_ volition, but _quâ_ omnipotent, intervenes to connect the
volition and the motion: so far is the mind from being forced to think
the action of mind on matter more _natural_ than that of matter on
matter. Those who believe volition to be an efficient cause are guilty
of exactly the same error as the Greeks, or Leibnitz or Descartes; that
is, of requiring an _explanation_ of physical sequences by something
[Greek: aneu hou to aition ouk an pot' eiê aition]. But they are guilty
of another error also, in inferring that volition, even if it is an
_efficient_ cause of so peculiar a phenomenon as nervous action, must
therefore be the efficient cause of all other phenomena, though having
scarcely a single circumstance in common with them.



An effect is almost always the result of the concurrence of several
causes. When all have their full effect, precisely as if they had
operated _successively_, the joint effect (and it is not inconsistent to
give the name of _joint effect_ even to the mutual obliteration of the
separate ones) may be _deduced_ from the laws which govern the causes
when acting separately. Sciences in which, as in mechanics, this
principle, viz. the _composition of causes_, prevails, are deductive and
demonstrative. Phenomena, in effect, do generally follow this principle.
But in some classes, e.g. chemical, vital, and mental phenomena, the
laws of the elements when called on to work together, cease and give
place to others, so that the joint effect is not the sum of the separate
effects. Yet even here the more general principle is exemplified. For
the new _heteropathic_ laws, besides that they never supersede _all_ the
old laws (thus, The weight of a chemical compound is equal to the sum of
the weight of the elements), have been often found, especially in the
case of vital and mental phenomena, to enter _unaltered_ into
composition with one another, so that complex facts may thus be
_deducible_ from comparatively simple laws. It is even possible that, as
has been already partly effected by Dalton's law of definite
proportions, and the law of isomorphism, chemistry itself, which is now
the least deductive of sciences, may be made deductive, through the laws
of the combinations being ascertained to be, though not compounded of
the laws of the separate agencies, yet derived from them according to a
fixed principle.

The proposition, that effects are proportional to their causes, is
sometimes laid down as an independent axiom of causation: it is really
only a particular case of the composition of causes; and it fails at the
same point as the latter principle, viz. when an addition does not
become compounded with the original cause, but the two together generate
a new phenomenon.



Since the whole of the present facts are the infallible result of the
whole of the past, so that if the prior state of the entire universe
could recur it would be followed by the present, the process of
ascertaining the relations of cause and effect is an analysis or
resolution of this complex uniformity into the simpler uniformities
which make it up. We must first mentally analyse the facts, not making
this analysis minuter than is needed for our object at the time, but at
the same time not regarding (as did the Greeks their verbal
classifications) a mental decomposition of facts as ultimate. When we
have thus succeeded in looking at any two successive chaotic masses (for
such nature keeps at each instant presenting to us) as so many distinct
antecedents and consequents, we must analyse the facts themselves, and
try, by varying the circumstances, to discover which of the antecedents
and consequents (for many are always present together) are related to
each other.

Experiment and observation are the two instruments for thus varying the
circumstances. When the enquiry is, What are the effects of a given
cause? experiment is far the superior, since it enables us not merely to
produce many more and more opportune variations than nature, which is
not arranged on the plan of facilitating our studies, offers
spontaneously, but, what is a greater advantage, though one less
attended to, also to insulate the phenomenon by placing it among known
circumstances, which can be then infinitely varied by introducing a
succession of well-defined new ones.

Observation cannot ascertain the effects of a given cause, because it
cannot, except in the simplest cases, discover what are the concomitant
circumstances; and therefore sciences in which experiment cannot be
used, either at all, as in astronomy, or commonly, as in mental and
social science, must be mainly deductive, not inductive. When, however,
the object is to discover causes by means of their effects, observation
alone is primarily available, since new effects could be artificially
produced only through their causes, and these are, in the supposed case,
unknown. But even then observation by itself cannot directly discover
causes, as appears from the case of zoology, which yet contains many
recognised uniformities. We have, indeed, ascertained a real uniformity
when we observe some one antecedent to be invariably found along with
the effects presented by nature. But it is only by reversing the
process, and experimentally producing the effects by means of that
antecedent, that we can prove it to be unconditional, i.e. the cause.



Five canons may be laid down as the principles of experimental enquiry.
The first is that of the Method of Agreement, viz.: _If two or more
instances of the phenomenon under investigation have only one
circumstance in common, the circumstance in which alone all the
circumstances agree is the cause or the effect of the given phenomenon._
The second canon is that of the Method of Difference, viz.: _If an
instance in which the phenomenon occurs and an instance in which it does
not occur have every circumstance in common, save one, and that one
occurs only in the former, that one circumstance is the effect, or the
cause, or a necessary part of the cause, of the phenomenon._

These two are the simplest modes of singling out from the facts which
precede or follow a phenomenon, those with which it is connected by an
invariable law. Both are methods of elimination, their basis being, for
the method of agreement, that whatever can be eliminated _is not_, and
for that of difference, that whatever cannot be eliminated _is_
connected with the given phenomenon by a law. It is only, however, by
the method of difference, which is a method of artificial experiment
(and by experiment we can introduce into the pre-existing facts a change
perfectly definite), that we can, at least by direct experience, arrive
with certainty at causes. The method of agreement is chiefly useful as
preliminary to and suggestive of applications of the method of
difference, or as an inferior resource in its stead, when, as in the
case of many spontaneous operations of nature, we have no power of
producing the phenomenon.

When we have power to produce the phenomenon, but only by the agency,
not of a single antecedent, but of a combination, the method of
agreement can be improved (though it is even then inferior to the direct
method of difference) by a double process being used, each proof being
independent and corroborative of the other. This may be called the
Indirect Method of Difference, or the Joint Method of Agreement and
Difference, and its canon will be: _If two or more instances in which
the phenomenon occurs have only one circumstance in common, while two or
more instances in which it does not occur have nothing in common save
the absence of that circumstance, the circumstance in which alone the
two sets of instances differ, is the effect, or the cause, or a
necessary part of the cause, of the phenomenon._

The fourth canon is that of the Method of Residues, viz.: _Subduct from
any phenomenon such part as is known by previous inductions to be the
effect of certain antecedents, and the residue of the phenomenon is the
effect of the remaining antecedents._ This method is a modification of
the method of difference, from which it differs in obtaining, of the
two required instances, only the positive instance, by observation or
experiment, but the negative, by deduction. Its certainty, therefore, in
any given case, is conditional on the previous inductions having been
obtained by the method of difference, and on there being in reality no
remaining antecedents _besides_ those given as such.

The fifth canon is that of the Method of Concomitant Variations, viz.:
_Whatever phenomenon varies in any manner whenever another phenomenon
varies in some particular manner, is either a cause or an effect of that
phenomenon, or_ (since they may be effects of a common cause) _is
connected with it through some fact of causation._ Through this method
alone can we find the laws of the permanent causes. For, though those of
the permanent causes whose influence is local may be escaped from by
changing the scene of the observation or experiment, many can neither be
excluded nor even kept isolated from each other; and, therefore, in such
cases, the method of difference, which requires a negative instance, and
that of agreement, which requires the different instances to agree only
in one circumstance, in order to prove causation, are (together with the
methods which are merely forms of these) equally inapplicable. But,
though many permanent antecedents insist on being always present, and
never present alone, yet we have the resource of making or finding
instances in which (the accompanying antecedents remaining unchanged)
their influence is _varied_ and _modified_. This method can be used most
effectually when the variations of the cause are variations of
quantity; and then, if we know the absolute quantities of the cause and
the effect, we may affirm generally that, at least within our limits of
observation, the variations of the cause will be attended by similar
variations of the effect; it being a corollary from the principle of the
composition of causes, that more of the cause is followed by more of the
effect. This method is employed usually when the method of difference is
impossible; but it is also of use to determine according to what law the
quantity or different relations of an effect ascertained by the method
of difference follow those of the cause.

These four methods are the only possible modes of experimental enquiry.
Dr. Whewell attacks them, first, on the ground (and the canon of
ratiocination was attacked on the same) that they assume the reduction
of an argument to formulæ, which (with the procuring the evidence) is
itself the chief difficulty. And this is in truth the case: but, to
reduce an argument to a particular form, we must first know what the
form is; and in showing us this, Inductive Logic does a service the
value of which is tested by the number of faulty inductions in vogue.
Dr. Whewell next implies a complaint that no discoveries have ever been
made by these four methods. But, as the analogous argument against the
syllogism was invalidated by applying equally as against all reasoning,
which must be reducible to syllogism, so this also falls by its own
generality, since, if true against these methods, it must be true
against all observation and experiment, since these must ever proceed by
one of the four. And, moreover, even if the four methods were not
methods of discovery, as they are, they would yet be subjects for logic,
as being, at all events, the sole methods of Proof, which (unless Dr.
Whewell be correct in his view that inductions are simply conceptions
consistent with the facts they colligate) is the principal topic of


[1] Chap. IX. consists of 'Miscellaneous Examples of the Four Methods,'
which cannot be well represented in an abridged form.



The difficulty in tracing the laws of nature arises chiefly from the
Intermixture of Effects, and from the Plurality of Causes. The
possibility of the latter in any given case--that is, the possibility
that the same effect may have been produced by different causes--makes
the Method of Agreement (when applied to positive instances)
inconclusive, if the instances are few; for that Method involves a tacit
supposition, that the same effect in different instances, which have
_one_ common antecedent, must follow in all from the same cause, viz.
from their common antecedent. When the instances are varied and very
many (how many, it is for the Theory of Probability to consider), the
supposition, that the presence in all of the common antecedent may be
simply a coincidence, is rebutted; and this is the sole reason why mere
_number_ of instances, differing only in immaterial points, is of any
value. As applied, indeed, to negative instances, i.e. to those
resembling each other in the absence of a certain circumstance, the
Method of Agreement is not vitiated by Plurality of Causes. But the
negative premiss cannot generally be worked unless an affirmative be
joined with it: and then the Method is the Joint Method of Agreement and
Difference. Thus, to find the cause of Transparency, we do not enquire
in what circumstance the numberless _non_-transparent objects agree; but
we enquire, first, in what the few transparent ones agree; and then,
whether all the opaque do not agree in the _absence_ of this

Not only may there be Plurality of Causes, the whole of the effect being
produced now by one, now by another antecedent; but there may also be
Intermixture of Effects, through the interference of different causes
with each other, so that part of the total effect is due to one, and
part to another cause. This latter contingency, which, more than all
else, complicates, the study of nature, does not affect the enquiry into
those (the exceptional) cases, where, as in chemistry, the total effect
is something quite different to the separate effects, and governed by
different laws. There the great problem is to discover, not the
properties, but the cause of the new phenomenon, i.e. the particular
conjunction of agents whence it results; which could indeed never be
ascertained by specific enquiry, were it not for the peculiarity, not of
all these cases (e.g. not of mental phenomena), but of many, viz. that
the heterogeneous effects of combined causes often reproduce, i.e. are
_transformed into_ their causes (as, e.g. water into its components,
hydrogen and oxygen). The great difficulty is _not_ there to discover
the properties of the new phenomenon itself, for these can be found by
experiment like the _simple_ effects of any other cause; since, in this
class of cases the effects of the separate causes give place to a new
effect, and thereby cease to need consideration as separate effects. But
in the far larger class of cases, viz. when the total effect is the
exact sum of the separate effects of all the causes (the case of the
Composition of Causes), at no point may it be overlooked that the effect
is not simple but complex, the result of various separate causes, all of
which are always tending to produce the whole of their several natural
effects; having, it may be, their _effects_ modified, disturbed, or even
prevented by each other, but always preserving their _action_, since
laws of causation cannot have exceptions.

These complex effects must be investigated by _deducing_ the law of the
effect from the laws of the separate causes on the combination of which
it depends. No inductive method is conclusive in such cases (e.g. in
physiology, or _à fortiori_, in politics and history), whether it be the
method of simple observation, which compares instances, whether positive
or negative, to see if they agree in the presence or the absence of one
common antecedent, or the empirical method, which proceeds by directly
trying different combinations (either made or found) of causes, and
watching what is the effect. Both are inconclusive; the former, because
an effect may be due to the concurrence of many causes, and the latter,
because we can rarely know what all the coexisting causes are; and still
more rarely whether a certain portion (if not all) of the total effect
is not due to these other causes, and not to the combination of causes
which we are observing.



The deductive method is the main source of our knowledge of complex
phenomena, and the sole source of all the theories through which vast
and complicated facts have been embraced under a few simple laws. It
consists of processes of Induction, Ratiocination, and Verification.
First, by one of the four inductive methods, the simple laws (whence may
be _deduced_ the complex) of each separate cause which shares in
producing the effect, must be first ascertained. This is difficult, when
the causes or rather tendencies cannot be observed singly. Such is the
case in physiology, since the different agencies which make up an
organized body cannot be separated without destroying the phenomenon;
consequently there our sole resource is to produce experimentally, or
find (as in the case of diseases), pathological instances in which only
one organ at a time is affected. Secondly, when the laws of the causes
have been found, we calculate the effect of any given combination of
them by ratiocination, which may have (though not necessarily) among its
premisses the theorems of the sciences of number and geometry. Lastly,
as it might happen that some of the many concurring agencies have been
unknown or overlooked, the conclusions of ratiocination must be
_verified_; that is, it must be explained why they do not, or shown that
they do, accord with _observed_ cases of at least equal complexity, and
(which is the most effectual test) that the empirical laws and
uniformities, if any, arrived at by direct observation, can be deduced
from and so accounted for by them, as, e.g. Kepler's laws of the
celestial motions by Newton's theory.



The aim, in the deductive method, is either to discover the law of the
effect, or to account for it by _explaining_ it, that is, by pointing
out some more general phenomenon (though often less familiar to us) of
which this is a case and a partial exemplification, or some laws of
causation which produce it by their joint or successive action. This
explanation may be made, either--1. By resolving the laws of the complex
effect into its elements, which consist as well of the separate laws of
the causes which share in producing it, as also of their collocation,
i.e. the fact that these separate laws have been so combined; or--2. By
resolving the law which connects two links, not proximate, in a chain of
causation, into the laws which connect each link with the intermediate
links; or--3. By the _subsumption_ or gathering up of several laws under
one which amounts to the sum of them all, and which is the recognition
of the same sequence in different sets of instances. In the first two of
the processes, laws are resolved into others, which both extend to more
cases, i.e. are more _general_, and also, as being laws of nature, of
which the complex laws are but results, are more _certain_, i.e. more
_unconditional_ and more _universally true_. In the third process, laws
are resolved into others which are indeed more _general_, but not more
_certain_, since they are in fact the same laws, and therefore, subject
to the same exceptions.

Liebig's researches, e.g. into the Contagious Influence of Chemical
Action, and his Theory of Respiration, are among the finest examples,
since Newton's exposition of the law of gravitation, of the use of the
deductive method for _explanation_.[2] But the method is as available
for explaining mental as physical facts. It is destined to predominate
in philosophy. Before Bacon's time deductions were accepted as
sufficient, when neither had the premisses been established by proper
canons of experimental enquiry, nor the results tested by verification
by specific experience. He therefore changed the method of the sciences
from deductive to experimental. But, now that the principles of
deduction are better understood, it is rapidly reverting from
experimental to deductive. Only it must not be supposed that the
inductive part of the process is yet complete. Probably, few of the
great generalisations fitted to be the premisses for future deductions
will be found among truths now known. Some, doubtless, are yet unthought
of; others known only as laws of some limited class of facts, as
electricity once was. They will probably appear first in the shape of
hypotheses, needing to be tested by canons of legitimate induction.


[2] These, and other illustrations in chap. xiii., cannot be usefully
represented in an abridged form.



The constant tendency of science, operating by the Deductive Method, is
to resolve all laws, even those which once seemed ultimate and not
derivative, into others still more general. But no process of
_resolving_ will ever reduce the number of ultimate laws below the
number of those varieties of our feelings which are distinguishable in
quality, and not merely in quantity or degree. The _ideal_ limit of the
explanation of natural phenomena is to show that each of these ultimate
facts has (since the differences in the different cases of it affect our
sensations as differences in degree only, and not in quality) only one
sort of cause or mode of production; and that all the seemingly
different modes of production or causes of it are resolvable into one.
But _practically_ this limit is never attained. Thus, though various
laws of Causes of Motion have been resolved into others (e.g. the fall
of bodies to the earth, and the motions of the planets, into the one law
of mutual attraction), many causes of it remain still unresolved and

Hypotheses are made for the sake of this resolving and explaining of
laws. When we do not _know_ of any more general laws into which to
resolve an uniformity, we then (either on no or on insufficient
evidence) _suppose_ some, imagining either causes (as, e.g. Descartes
did the Vortices), or the laws of their operation (as did Newton
respecting the planetary central force); but we never feign both cause
and law. The use of a hypothesis is to enable us to apply the Deductive
Method before the laws of the causes have been ascertained by Induction.
In those cases where a false law could not have led to a true result (as
was the case with Newton's hypothesis as to the law of the Attractive
force) the third part of the process in the Deductive Method, viz.
Verification, which shows that the results deduced are true, amounts to
a complete induction, and one conforming to the canon of the Method of
Difference. But this is the case only when either the cause is known to
be one given agent (and only its law is unknown), or to be one of
several given agents.

An assumed cause, on the other hand, cannot be accepted as true simply
_because_ it explains the phenomena (since two conflicting hypotheses
often do this even originally, or, as Dr. Whewell himself allows, may at
any rate by modifications be made to do it); nor _because_ it moreover
leads to the prediction of other results which turn out true (since this
shows only what was indeed apparent already from its agreement with the
old facts, viz. that the phenomena are governed by laws partially
identical with the laws of other causes); nor _because_ we cannot
imagine any other hypothesis which will account for the facts (since
there may be causes unknown to our present experience which will equally
account for them). The utility of such assumptions _of causes_ depends
on their being, in their own nature, _capable_ (as Descartes' Vortices
were not, though possibly the Luminiferous Ether may be) of being, at
some time or other, proved directly by independent evidence to be the
causes. And this was, perhaps, all that Newton meant by his _veræ
causæ_, which alone, he said, may be assigned as causes of phenomena.
Assumptions of causes, which fulfil this condition, are, in science,
even indispensable, with a view both to experimental inquiry, and still
more to the application of the Deductive Method. They may be accepted,
not indeed, as Dr. Whewell thinks they may be, as proof, but as
suggesting a line of experiment and observation which may result in
proof. And this is actually the method used by practical men for
eliciting the truth from involved statements. They first extemporise,
from a few of the particulars, a rude theory of the mode in which the
event happened; and then keep altering it to square with the rest of the
facts, which they review one by one.

The attempting, as in Geology, to conjecture, in conformity with known
laws, in what former collocations of known agents (though _not_ known to
have been formerly present) individual existing facts may have
originated, is not Hypothesis but Induction; for then we do not
_suppose_ causes, but legitimately infer from known effects to unknown
causes. Of this nature was Laplace's theory, whether weak or not, as to
the origin of the earth and planets.



Sometimes a complex effect results, not (as has been supposed in the
last four chapters) from several, but from _one_ law. The following is
the way.

Some effects are instantaneous (e.g. some sensations), and are
prolonged only by the prolongation of the causes; others are in their
own nature permanent. In some cases of the latter class, the original is
also the proximate cause (e.g. Exposure to moist air is both the
original and the proximate cause of iron rust). But in others of the
same class, the permanency of the effect is only the permanency of a
series of changes. Thus, e.g. in cases of Motion, the original force is
only the _remote_ cause of any link (after the very first) in the
series; and the motion immediately preceding it, being itself a compound
of the original force and any retarding agent, is its _proximate_ cause.
When the original cause is permanent as well as the effect (e.g. Suppose
a continuance of the iron's exposure to moist air), we get a progressive
series of effects arising from the cause's accumulating influence; and
the sum of these effects amounts exactly to what a number of
successively introduced similar causes would have produced. Such cases
fall under the head of Composition of Causes, with this peculiarity,
that, as the causes (to regard them as plural) do not come into play all
at once, the effect at each instant is the sum of the effects only of
the then acting causes, and the result will appear as an ascending
series. Each addition in such case takes place according to a fixed law
(equal quantities in equal times); and therefore it can be computed
deductively. Even when, as is sometimes the case, a cause is at once
permanent and progressive (as, e.g. the sun, by its position becoming
more vertical, increases the heat in summer) so that the quantities
added are unequal, the effect is still progressive, resulting from its
cause's continuance and progressiveness combined.

In _all_ cases whatever of progressive effects, the succession not
merely between the cause and the effect, but also between the first and
latter stages of the effect, is uniform. Hence, from the invariable
sequence of two terms (e.g. Spring and Summer) in a series going through
any continued and uniform process of variation, we do not presume that
one is the cause and the others the effect, but rather that the whole
series is an effect.



Empirical laws are derivative laws, of which the derivation is not
known. They are observed uniformities, which we compare with the result
of any deduction to verify it; but of which the _why_, and also the
limits, are unrevealed, through their being, though resolvable, not yet
resolved into the simpler laws. They depend usually, not solely on the
ultimate laws into which they are resolvable; but on those, together
with an ultimate fact, viz. the mode of coexistence of some of the
component elements of the universe. Hence their untrustworthiness for
scientific purposes; for, till they have been resolved (and then a
derivative law ceases to be empirical), we cannot know whether they
result from the different effects of one cause, or from effects of
different causes; that is, whether they depend on laws, or on laws and a
collocation. And if they thus depend on a collocation, they can be
received as true only within the limits of time and space, and also
circumstance, in which they have been observed, since the mode of the
collocation of the permanent causes is not reducible to a law, there
being no principle known to us as governing the distribution and
relative proportions of the primæval natural agents.

Uniformities cannot be proved by the Method of Agreement alone to be
laws of causation; they must be tested by the Method of Difference, or
explained deductively. But laws of causation themselves are either
ultimate or derivative. Signs, previous to actual proof by _resolution_
of them, of their being derivative, are, either that we can _surmise_
the existence of a link between the known antecedent and the consequent,
as e.g. in the laws of chemical action; or, that the antecedent is some
very complex fact, the effects of which are probably (since most complex
cases fall under the Composition of Causes) compounded of the effects of
its different elements. But the laws which, though laws of causation,
are thus presumably derivative laws only, need, equally with the
uniformities which are not known to be laws of causation at all, to be
explained by deduction (which they then in turn verify), and are less
_certain_ than when they have been resolved into the ultimate laws.
Consequently they come under the definition of Empirical Laws, equally
with uniformities not known to be laws of causation. However, the latter
are far more _uncertain_; for as, till they are resolved, we cannot tell
on how many collocations, as well as laws, they may not depend, we must
not rely on them beyond the exact limits in which the observations were
made. Therefore, the name _Empirical Laws_ will generally be confined
here to these.



Empirical laws are certain only in those limits within which they have
been _observed_ to be true. But, even within those limits, the
connection of two phenomena may, as the same effect may be produced by
several different causes, be due to Chance; that is, it may, though
being, as all facts must be, the result of some law, be a coincidence
whence, simply because we do not know all the circumstances, _we_ have
no ground to infer an uniformity. When neither Deduction, nor the Method
of Difference, can be applied, the only way of inferring that
coincidences are not casual, is by observing the frequency of their
occurrence, not their absolute frequency, but whether they occur _more_
often than chance would (that is, more often than the positive frequency
of the phenomena would) account for. If, in such cases, we could ascend
to the causes of the two phenomena, we should find at some stage some
cause or causes common to both. Till we can do this, the fact of the
connection between them is only an empirical law; but still it is a law.

Sometimes an effect is the result partly of chance, and partly of law:
viz. when the total effect is the result partly of the effects of casual
conjunctions of causes, and partly of the effects of some constant cause
which they blend with and modify. This is a case of Composition of
Causes. The object being to find _how much_ of the result is
attributable to a given constant cause, the only resource, when the
variable causes cannot be wholly excluded from the experiment, is to
ascertain what is the effect of all of _them_ taken together, and then
to eliminate this, which is the casual part of the effect, in reckoning
up the results. If the results of frequent experiments, in which the
constant cause is kept invariable, oscillate round one point, that
average or middle point is due to the constant cause, and the variable
remainder to chance; that is, to causes the coexistence of which with
the constant cause was merely casual. The test of the sufficiency of
such an induction is, whether or not an increase in the number of
experiments materially alters the average.

We can thus discover not merely _how much_ of the effect, but even
whether _any_ part of it whatever is due to a constant cause, when this
latter is so uninfluential as otherwise to escape notice (e.g. the
loading of dice). This case of the Elimination of Chance is called _The
discovery of a residual phenomenon by eliminating the effects of

The mathematical doctrine of chances, or Theory of Probabilities,
considers what deviation from the average chance by itself can possibly
occasion in some number of instances smaller than is required for a fair



In order to calculate chances, we must know that of several events one,
and no more, must happen, and also not know, or have any reason to
suspect, which of them that one will be. Thus, with the simple knowledge
that the issue must be one of a certain number of possibilities, we
_may_ conclude that one supposition is most probable _to us_. For this
purpose it is not _necessary_ that specific experience or reason should
have also proved the occurrence of each of the several events to be, as
a fact, equally frequent. For, the probability of an event is not a
quality of the event (since every event is in itself certain), but is
merely a name for the degree of ground _we_ have, with our present
evidence, for expecting it. Thus, if we know that a box contains red,
white, and black balls, though we do not know in what proportions they
are mingled, we have numerically appreciable grounds for considering the
probability to be two to one against any one colour. Our judgment may
indeed be said in this case to rest on the experience we have of the
laws governing the frequency of occurrence of the different cases; but
such experience is universal and axiomatic, and not specific experience
about a particular event. Except, however, in games of chance, the
purpose of which requires ignorance, such specific experience can
generally be, and should be gained. And a slight improvement in the data
profits more than the most elaborate application of the calculus of
probabilities to the bare original data, e.g. to such data, when we are
calculating the credibility of a witness, as the proportion, even if it
could be verified, between the number of true and of erroneous
statements a man, _quâ_ man, may be supposed to make during his life.
Before applying the Doctrine of Chance, therefore, we should lay a
foundation for an evaluation of the chances by gaining positive
knowledge of the facts. Hence, though not a _necessary_, yet a most
usual condition for calculating the probability of a fact is, that we
should possess a _specific_ knowledge of the proportion which the cases
in which facts of the particular sort occur bear to the cases in which
they do not occur.

Inferences drawn correctly according to the Doctrine of Chances depend
ultimately on causation. This is clearest, when, as sometimes, the
probability of an event is deduced from the frequency of the occurrence
of the causes. When its probability is calculated by merely counting and
comparing the number of cases in which it has occurred with those in
which it has not, the law, being arrived at by the Method of Agreement,
is only empirical. But even when, as indeed generally, the numerical
data are obtained in the latter way (since usually we can judge of the
frequency of the causes only through the medium of the empirical law,
which is based on the frequency of the effects), still then, too, the
inference really depends on causation alone. Thus, an actuary infers
from his tables that, of any hundred living persons under like
conditions, five will reach a given age, not simply because that
proportion have reached it in times past, but because that fact shows
the existence there of a particular proportion between the _causes_
which shorten and the causes which prolong life to the given extent.



Derivative laws are inferior to ultimate laws, both in the extent of the
propositions, and in their degree of certainty within that extent. In
particular, the uniformities of coexistence and sequence which obtain
between effects depending on different primæval causes, vary along with
any variation in the collocation of these causes. Even when the
derivative uniformity is between different effects of the same cause, it
cannot be trusted to, since one or more of the effects may be producible
by another cause also. The effects, even, of derivative laws of
_causation_ (resulting, i.e. the laws, from the combination of several
causes) are not independent of collocations; for, though laws of
causation, whether ultimate or derivative, are themselves universal,
being fulfilled even when counteracted, the peculiar probability of the
latter kind of laws of causation being counteracted (as compared with
ultimate laws, which are liable to frustration only from one set of
counteracting causes) is fatal to the universality of the derivative
uniformities made up of the sequences or coexistences of their effects;
and, therefore, such derivative uniformities as the latter are to be
relied on only when the collocations are known not to have changed.

Derivative laws, not causative, may certainly be extended beyond the
limits of observation, but only to cases _adjacent_ in time. Thus, we
may not predict that the sun will rise this day 20,000 years, but we can
predict that it will rise to-morrow, on the ground that it has risen
every day for the last 5,000 years. The latter prediction is lawful,
_because_, while we know the causes on which its rising depends, we
know, also, that there has existed hitherto no perceptible cause to
counteract them; and that it is opposed to experience that a cause
imperceptible for so long should start into immensity in a day. If the
uniformity is empirical only, that is, if we do not know the causes, and
if we infer that they remain uncounteracted from their effects alone, we
still can extend the law to adjacent cases, but only to cases still more
closely adjacent in time; since we can know neither whether changes in
these unknown causes may not have occurred, nor whether there may not
exist now an adverse cause capable after a time of counteracting them.

An empirical law cannot generally be extended, in reference to _Place_,
even to adjacent cases (since there is no uniformity in the collocations
of primæval causes). Such an extension is lawful only if the new cases
are _presumably_ within the influence of the same individual causes,
even though unknown. When, however, the causes are known, and the
conjunction of the effects is deducible from laws of the causes, the
derivative uniformity may be extended over a wider space, and with less
abatement for the chance of counteracting causes.



One of the many meanings of _Analogy_ is, Resemblance of Relations. The
value of an analogical argument in this sense depends on the showing
that, on the common circumstance which is the _fundamentum relationis_,
the rest of the circumstances of the case depend. But, generally, _to
argue from analogy_ signifies to infer from resemblance in some points
(not necessarily in _relations_) resemblance in others. Induction does
the same: but analogy differs from induction in not requiring the
previous proof, by comparison of instances, of the invariable
conjunction between the known and the unknown properties; though it
requires that the latter should not have been ascertained to be
_unconnected_ with the common properties.

If a fair proportion of the properties of the two cases are known, every
resemblance affords ground for expecting an indefinite number of other
resemblances, among which the property in question may perhaps be found.
On the other hand, every dissimilarity will lead us to expect that the
two cases differ in an indefinite number of properties, including,
perhaps, the one in question. These dissimilarities may even be such as
would, in regard to one of the two cases, imply the absence of that
property; and then every resemblance, as showing that the two cases have
a similar nature, is even a reason for presuming against the presence of
that property. Hence, the value of an analogical argument depends on
the extent of ascertained resemblance as compared, first, with the
amount of ascertained difference, and next, with the extent of the
unexplored region of unascertained properties.

The conclusions of analogy are not of direct use, unless when the case
to which we reason is a case _adjacent_, not, as before, in time or
place, but in _circumstances_. Even then a complete induction should be
sought after. But the great value of analogy, even when faint, in
science, is that it may suggest observations and experiments, with a
view to establishing positive scientific truths, for which, however, the
hypotheses based on analogies must never be mistaken.



The validity of all the four inductive methods depends on our assuming
that there is a cause for every event. The belief in this, i.e. in the
law of universal causation, some affirm, is an instinct which needs no
warrant other than all men's disposition to believe it; and they argue
that to demand evidence of it is to appeal to the intellect from the
intellect. But, though there is no appeal from the faculties all
together, there may be from one to another: and, as belief is not proof
(for it may be generated by association of ideas as well as by
evidence), a case of belief does require to be proved by an appeal to
something else, viz. to the faculties of sense and consciousness.

The law of universal causation is, in fact, a generalisation from many
partial uniformities of sequence. Consequently, like these, which cannot
have been arrived at by any strict inductive method (for all such
methods presuppose the law of causation itself), it must itself be based
on inductions _per simplicem enumerationem_, that is, generalisations of
observed facts, from the mere absence of any known instances to the
contrary. This unscientific process is, it is true, usually delusive;
but only because, and in proportion as, the subject-matter of the
observation is limited in extent. Its results, whenever the number of
coincidences is too large for chance to explain, are empirical laws.
These are ordinarily true only within certain limits of time, place, and
circumstance, since, beyond these, there may be different collocations
or counteracting agencies. But the subject-matter of the law of
universal causation is so diffused that there is no time, place, or set
of circumstances, at least within the portion of the universe within our
observation, and adjacent cases, but must prove the law to be either
true or false. It has, in fact, never been found to be false, but in
ever increasing multitudes of cases to be true; and phenomena, even
when, from their rarity or inaccessibility, or the number of modifying
causes, they are not reducible _universally_ to any law, yet _in some
instances_ do conform to this. Thus, it may be regarded as coextensive
with all human experience, at which point the distinction between
empirical laws and laws of nature vanishes. Formerly, indeed, it was
only a very high probability; but, with our modern experience, it is,
practically, absolutely certain, and it confirms the particular laws of
causation, whence itself was drawn, when there seem to be exceptions to
them. All narrower inductions got by simple enumeration are unsafe,
till, by the application to them of the four methods, the supposition of
their falsity is shown to contradict _this_ law, though it was itself
arrived at by simple enumeration.



Besides uniformities of succession, which always depend on causation,
there are uniformities of coexistence. These also, whenever the
coexisting phenomena are effects of causes, whether of one common cause
or of several different causes, depend on the laws of their cause or
causes; and, till resolved into these laws, are mere empirical laws. But
there are some uniformities of coexistence, viz. those between the
ultimate properties of _kinds_, which do not depend on causation, and
therefore seem entitled to be classed as a peculiar sort of laws of
nature. As, however, the presumption always is (except in the case of
those _kinds_ which are called _simple substances_ or elementary natural
agents), that a thing's properties really depend on causes though not
traced, and we _never_ can be certain that they do not; we cannot safely
claim (though it _may_ be an ultimate truth) higher certainty than that
of an empirical law for any generalisation about coexistence, that is to
say (since _kinds_ are known to us only by their properties, and,
consequently, all assertions about them are assertions about the
coexistence of something with those properties), about the properties of

Besides, no rigorous inductive system can be applied to the uniformities
of coexistence, since there is no general axiom related to them, as is
the law of causation to those of succession, to serve as a basis for
such a system. Thus, Bacon's practical applications of his method
failed, from his supposing that we can have previous certainty that a
property must have an invariable coexistent (as it must have an
invariable antecedent), which he called its form. He ought to have seen
that his great logical instrument, elimination, is inapplicable to
coexistences, since things, which agree in having certain apparently
ultimate properties, often agree in nothing else; even the properties
which (e.g. Hotness) are effects of causes, generally being not
connected with the ultimate resemblances or diversities in the objects,
but depending on some outward circumstance.

Our only substitute for an universal law of coexistence is the ancients'
induction _per enumerationem simplicem ubi non reperitur instantia
contradictoria_, that is, the improbability that an exception, if any
existed, could have hitherto remained unobserved. But the certainty thus
arrived at can be only that of an empirical law, true within the limits
of the observations. For the coexistent property must be either a
property of the _kind_, or an accident, that is, something due to an
extrinsic cause, and not to the _kind_ (whose own indigenous properties
are always the same). And the ancients' class of induction can only
prove that _within given limits_, either (in the latter case) one
common, though unknown, cause has always been operating, or (in the
former case) that no new _kind_ of the object has _as yet_ or _by us_
been discovered.

The evidence is, of course (with respect both to the derivative and the
ultimate uniformities of coexistence), stronger in proportion as the law
is more general; for the greater the amount of experience from which it
is derived, the more probable is it that counteracting causes, or that
exceptions, if any, would have presented themselves. Consequently, it
needs more evidence to establish an exception to a very general, than to
a special, empirical law. And common usage agrees with this principle.
Still, even the greater generalisations, when not based on connection by
causation, are delusive, unless grounded on a separate examination of
_each_ of the included _infimæ species_, though certainly there is a
probability (no more) that a sort of parallelism will be found in the
properties of different kinds; and that their degree of unlikeness in
one respect bears some proportion to their unlikeness in others.



The inferences called _probable_ rest on approximate generalisations.
Such generalisations, besides the inferior assurance with which they
can be applied to individual cases, are _generally_ almost useless as
premisses in a deduction; and therefore in _Science_ they are valuable
chiefly as steps towards universal truths, the discovery of which is its
proper end. But in _practice_ we are forced to use them--1, when we have
no others, in consequence of not knowing what general property
distinguishes the portion of the class which have the attribute
predicated, from the portion which have it not (though it is true that
we can, in such a case, usually obtain a collection of exactly true
propositions by subdividing the class into smaller classes); and, 2,
when we _do_ know this, but cannot examine whether that general property
is present or not in the individual case; that is, when (as usually in
_moral_ inquiries) we could get universal majors, but not minors to
correspond to them. In any case an approximate generalisation can never
be more than an empirical law. Its authority, however, is less when it
composes the whole of our knowledge of the subject, than when it is
merely the most available form of our knowledge for practical guidance,
and the causes, or some certain mark of the attribute predicated, being
known to us as well as the effects, the proposition can be tested by our
trying to deduce it from the causes or mark. Thus, our belief that most
Scotchmen can read, rests on our knowledge, not merely that most
Scotchmen that we have known about could read, but also that most have
been at efficient schools.

Either a single approximate generalisation may be applied to an
individual instance, or several to the same instance. In the former
case, the proposition, as stating a general average, must be applied
only to average cases; it is, therefore, generally useless for guidance
in affairs which do not concern large numbers, and simply supplies, as
it were, the first term in a series of approximations. In the latter
case, when two or more approximations (not connected with each other)
are _separately_ applicable to the instance, it is said that two (or
more) _probabilities are joined by addition_, or, that there is a
_self-corroborative chain_ of evidence. Its type is: Most A are B; most
C are B; this is both an A and a C; therefore it is probably a B. On the
other hand, when the subsequent approximation or approximations is or
are applicable only by virtue of the application of the first, this is
joining two (or more) probabilities, _by way of Deduction_, which
produces a _self-infirmative chain_; and the type 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. As, in the former case, the probability increases at each
step, so, in the latter, it progressively dwindles. It is measured by
the probability arising from the first of the propositions, abated in
the ratio of that arising from the subsequent; and the error of the
conclusion amounts to the aggregate of the errors of all the premisses.

In two classes of cases (exceptions which prove the rule) approximate
can be employed in deduction as usefully as complete generalisations.
Thus, first, we stop at them sometimes, from the inconvenience, not the
impossibility, of going further; and, by adding provisos, we might
change the approximate into an universal proposition; the sum of the
provisos being then the sum of the errors liable to affect the
conclusion. Secondly, they are used in Social Science with reference to
masses with _absolute_ certainty, even without the addition of such
provisos. Although the premisses in the Moral and Social Sciences are
only probable, these sciences differ from the exact only in that we
cannot decipher so many of the laws, and not in the conclusions that we
do arrive at being less scientific or trustworthy.



There are, we have seen, five facts, one of which every proposition must
assert, viz. Existence, Order in Place, Order in Time, Causation, and
Resemblance. Causation is not fundamentally different from Coexistence
and Sequence, which are the two modes of Order in Time. They have been
already discussed. Of the rest, Existence, if of things in themselves,
is a topic for Metaphysics, Logic regarding the existence of _phenomena_
only; and as this, when it is not perceived directly, is proved by
proving that the unknown phenomenon is connected by _succession or
coexistence_ with some known phenomenon, the fact of Existence is not
amenable to any _peculiar_ inductive principles. There remain
Resemblance and Order in Place.

As for Resemblance, Locke indeed, and, in a more unqualified way, his
school, asserted that all reasoning is simply a comparison of two ideas
by means of a third, and that knowledge is only the perception of the
agreement or disagreement, that is, the resemblance or dissimilarity, of
two ideas: they did not perceive, besides erring in supposing ideas, and
not the phenomena themselves, to be the subjects of reasoning, that it
is only sometimes (as, particularly, in the sciences of Quantity and
Extension) that the agreement or disagreement of two things is the one
thing to be established. Reasonings, however, about _Resemblances_,
whenever the two things cannot be directly compared by the virtually
simultaneous application of our faculties to each, do agree with Locke's
account of reasoning; being, in fact, simply such a comparison of two
things through the medium of a third. There are laws or formulæ for
guiding the comparison; but the only ones which do not come under the
principles of Induction already discussed, are the mathematical axioms
of Equality, Inequality, and Proportionality, and the theorems based on
them. For these, which are true of all phenomena, or, at least, without
distinction of origin, have no connection with laws of Causation,
whereas all other theorems asserting resemblance have, being true only
of special phenomena originating in a certain way, and the resemblances
between which phenomena must be derived from, or be identical with, the
laws of their causes.

In respect to Order in Place, as well as in respect to Resemblance, some
mathematical truths are the only general propositions which, as being
independent of Causation, require separate consideration. Such are
certain geometrical laws, through which, from the position of certain
points, lines, or spaces, we infer the position of others, without any
reference to their physical causes, or to their special nature, except
as regards position or magnitude. There is no other peculiarity as
respects Order in Place. For, the Order in Place of effects is of course
a mere consequence of the laws of their causes; and, as for primæval
causes, in _their_ Order in Place, called their _collocation_, no
uniformities are traceable.

Hence, only the methods of Mathematics remain to be investigated; and
they are partly discussed in the Second Book. The directly inductive
truths of Mathematics are few: being, first, certain propositions about
existence, tacitly involved in the so-called definitions; and secondly,
the axioms, to which latter, though resting only on induction, _per
simplicem enumerationem_, there could never have been even any apparent
exceptions. Thus, every arithmetical calculation rests (and this is what
makes Arithmetic the type of a deductive science) on the evidence of the
axiom: The sums of equals are equals (which is coextensive with nature
itself)--combined with the definitions of the numbers, which are
severally made up of the explanation of the name, which connotes the way
in which the particular agglomeration is composed, and of the assertion
of a fact, viz. the physical property so connoted.

The propositions of Arithmetic affirm the modes of formation of given
numbers, and are true of all things under the condition of being divided
in a particular way. Algebraical propositions, on the other hand, affirm
the equivalence of different modes of formation of numbers generally,
and are true of all things under condition of being divided in _any_

Though the laws of Extension are not, like those of Number, remote from
visual and tactual imagination, Geometry has not commonly been
recognised as a strictly physical science. The reason is, first, the
possibility of collecting its facts as effectually from the ideas as
from the objects; and secondly, the illusion that its ideal data are not
mere hypotheses, like those in now deductive physical sciences, but a
peculiar class of realities, and that therefore its conclusions are
_exceptionally_ demonstrative. Really, all geometrical theorems are laws
of external nature. They might have been got by generalising from actual
comparison and measurement; only, that it was found practicable to
deduce them from a few obviously true general laws, viz. The sums of
equals are equals; things equal to the same thing are equal to one
another (which two belong to the Science of Number also); and, thirdly
(what is no merely verbal definition, though it has been so called):
Lines, surfaces, solid spaces, which can be so applied to one another as
to coincide, are equal. The rest of the premisses of Geometry consist of
the so-called definitions, which assert, together with one or more
properties, the real existence of objects corresponding to the names to
be defined. The reason why the premisses are so few, and why Geometry is
thus almost entirely deductive, is, that all questions of position and
figure, that is, of quality, may be resolved into questions of quantity
or magnitude, and so Geometry may be reduced to the one problem of the
measurement of magnitudes; that is, to the finding the equalities
between them.

Mathematical principles can be applied to other sciences. All causes
operate according to mathematical laws; an effect being ever dependent
on the quantity or a function of the agent, and generally on its
position too. Mathematical principles cannot, indeed, as M. Comte has
well explained, be usefully applied to physical questions, whenever the
causes are either too inaccessible for their numerical laws to be
ascertained, or are too complex for _us_ to compute the effect, or are
ever fluctuating. And, in proportion as physical questions cease to be
abstract and hypothetical, mathematical solutions of them become
imperfect. But the great value of mathematical training is, that we
learn to use its _method_ (which is the most perfect type of the
Deductive Method), that is, we learn to employ the laws of simpler
phenomena to explain and predict those of the more complex.



The result of examining evidence is not always belief, or even
suspension of judgment, but is sometimes positive disbelief. This can
ensue only when the affirmative evidence does not amount to full proof,
but is based on some approximate generalisation. In such cases, if the
negative evidence consist of a stronger, though still only an
approximate, generalisation, we think the fact improbable, and
disbelieve it provisionally; but if of a complete generalisation based
on a rigorous induction, it is disbelieved by us totally, and thought
impossible. Hence, Hume declared miracles incredible, as being, he
considered, contrary to a complete induction. Now, it is true that _in
the absence of any adequate counteracting cause_, a fact contrary to a
complete induction is incredible, whatever evidence it may be grounded
on; unless, indeed, the evidence go to prove the supposed law
inconsistent with some better established one. But when a miracle is
asserted, the presence of an adequate counteracting cause _is_ asserted,
viz. a direct interposition of an act of the will of a Being having
power over nature. Therefore, all that Hume proved is, that we cannot
believe in a miracle unless we believe in the power, and _the will_, of
the Deity to interfere with existing causes by introducing new ones; and
that, in default of such belief, not the most satisfactory evidence of
our senses or of testimony can hinder us from holding a seeming miracle
to be merely the result of some unknown natural cause. The argument of
Dr. Campbell and others against Hume, however, is untenable, viz. that,
as we do not disbelieve an alleged fact (which may be something
conforming to the uniform course of experience) merely because the
chances are against it, therefore we need never disbelieve any fact
supported by credible testimony (even if contrary to the uniform course
of experience). But this is to confound _improbability before the fact_,
which is _not_ always a ground for disbelief, with _improbability after
the fact_, which always is.

Facts which conflict with special laws of causation are only improbable
before the fact; that is, our disbelief depends on the improbability
that there could have been present, without our knowledge, at the time
and place of the event, an adequate counteracting cause. So, too, with
facts which conflict with the properties of _kinds_ (which are
uniformities of mere coexistence not proved to be dependent on
causation), that is, facts which assert the existence of a new _kind_;
such facts we disbelieve only if, the generalisation being sufficiently
comprehensive, some properties are said to have been found in the
supposed new _kind_ disjoined from others which always have been known
to accompany them. When the assertion would amount, if admitted, only to
the existence of an unknown cause or an anomalous _kind_,
_unconformable_, but, as Hume puts it, _not contrary_ to experience, in
circumstances so little explored, that it is credible hitherto unknown
things may there be found, and when prejudice cannot have tempted to the
assertion, one ought neither to admit nor to reject the testimony, but
to suspend judgment till it be confirmed or disproved from other
sources. Only facts, then, which are contradictory to the laws of
Number, Extension, and Universal Causation (since these know no
counteraction or anomaly), or to laws nearly as general, are improbable
after, as well as before the fact, and only these we should term
_absolutely impossible_, calling other facts _improbable_ only, or, at
most, _impossible in the circumstances of the case_.

Between these two species of improbabilities lie _coincidences_; that
is, combinations of chances presenting some unexpected regularity
assimilating them in so far to the results of law. It was thought by
d'Alembert that, though regular combinations are as probable as others
according to the mathematical theory, some physical law prevents them
from occurring so often. Now, stronger testimony may indeed be needed
to support the assertion of such a combination as, e.g. ten successive
throws of sixes at dice, because such a regular series is more likely
than an irregular series to be the result of design; and because even
the desire to excite wonder is likely to tempt men to assert the
occurrence falsely, though this probability must be estimated afresh in
every instance. But though such a series _seems_ peculiarly improbable,
it is only because the comparison is tacitly made, not between it and
any one particular previously fixed series of throws, but between all
regular and all irregular successions taken together. The fact is not in
itself more improbable; and no stronger evidence is needed to give it
credibility, apart from the reasons above mentioned, than in the case of
ordinary events.





The mental process which Logic deals with, viz. the investigation of
truth by means of evidence, is always a process of Induction. Since
Induction is simply the extension to a class of something observed to be
true of certain members of it, Observation is the first preliminary to
it. It is, therefore, right to consider, not indeed how or what to
observe (for this belongs to the art of Education), but under what
conditions observation is to be relied on. The sole condition is, that
the supposed observation should really be an observation, and not an
inference, whereas it is usually a compound of both, there being, in our
propositions, besides observation which relates only to the sensations,
an inference from the sensations to the objects themselves. Thus
so-called errors of sense are only erroneous inferences from sense. The
sensations themselves must be genuine; but, as they generally arise on a
certain arrangement of outward objects being present to the organs, we,
as though by instinct, infer this arrangement even when not existing.
The sole object, then, of the logic of observation, is to separate the
inferences from observation from the observations themselves, the only
thing really observed by the mind (to waive the metaphysical problem as
to the _perception_ of objects) being its own feelings or states of
consciousness, outward, viz. Sensations, and inward, viz. Thoughts,
Emotions, and Volitions.

As in the simplest observation much is inference, so, in describing an
observed fact, we not merely describe the fact, but are always forced to
class it, affirming the resemblance, in regard of whatever is the ground
of the name being given, between it and all other things denoted by the
name. The resemblance is sometimes perceived by direct comparison of the
objects together; sometimes (as, e.g. in the description of the earth's
figure as globular and so forth) it is inferred through intermediate
marks, i.e. deductively. When a hypothesis is made (e.g. by Kepler, as
to the figure of the earth's orbit), and then verified by comparison
with actual observations, Dr. Whewell calls the process Colligation of
Facts by appropriate Conceptions, and affirms it to be the whole of
Induction. But this also is only description, being really the ordinary
process of ascertaining resemblance by a comparison of phenomena; and,
though subsidiary to Induction, it is not itself Induction at all.



_This Chapter is a digression._

Abstract Ideas, that is, General Conceptions, certainly do exist,
however Metaphysics may decide as to their composition. They
_represent_ in our minds the whole classes of things called by the
general names; and, being implied in the mental operation whereby
classes are formed, viz. in the comparison of phenomena, to ascertain in
what they agree, cannot be dispensed with in induction, since such a
comparison is a necessary preliminary to an induction, and more than two
objects cannot well be compared without a type, in which capacity
conceptions serve.

But, though implied in the comparison, it does not follow that, as Dr.
Whewell supposes, they must have existed in the mind prior to
comparison. Sometimes, but only sometimes, they are pre-existent to the
comparison of the particular facts in question, being, as was Kepler's
hypothesis of an ellipse, familiar conceptions borrowed from different
facts, and _superinduced_, to use Dr. Whewell's expression, on the facts
in question. But even such conceptions are the results of former
comparisons of individual facts. And much more commonly (and these are
the more difficult cases in science) conceptions are not pre-existent
even in this sense; but they have to be got (e.g. the Idea of Polarity)
by abstraction, that is, by comparison, from among the very phenomena
which they afterwards serve to arrange, or, as Dr. Whewell says, to
_connect_. They seem to be pre-existent; but this is only because the
mind keeps ever forming conceptions from the facts, which at the time
are before it, and then tentatively applies these conceptions (which it
is always remodelling, dropping some which are found not to suit
after-found facts, and generalising others by a further effort of
abstraction) as types of comparison for phenomena subsequently
presented to it; so that, being found in these later stages of the
comparison already in the mind, they appear in the character simply of
types, and not as being also themselves results of comparison. Really
they are always both; and the term _comparison_ expresses as well their
origin as (and this far more exactly than to _connect_ or to
_superinduce_) their function.

Dr. Whewell says that conceptions must be _appropriate_ and _clear_.
They must, indeed, be appropriate relatively to the purpose in view (for
appropriateness is only relative); but they cannot avoid being
appropriate (though one may be more so than another) if our comparison
of the objects has led to a conception corresponding to any real
agreement in the facts: the ancients' and schoolmen's conceptions were
often absolutely inappropriate, because grounded on only apparent
agreement. So, again, they must be _clear_ in the following sense; that
is to say, a _sufficient number_ of facts must have been _carefully
observed_, and accurately _remembered_. It is also a condition (and one
implied in the latter qualities) of clearness, that the conception
should be _determinate_, that is, that we should know precisely what
agreements we include in it, and never vary the connotation except

Activity, carefulness, and accuracy in the observing and comparing
faculties are therefore needed; the first quality to produce
appropriateness, and the latter two, clearness. Moreover, _scientific
imagination_, i.e. the faculty of mentally arranging known elements into
new combinations, is necessary for forming true conceptions; and the
mind should be stored with previously acquired conceptions, kindred to
the subject of inquiry, since a comparison of the facts themselves often
fails to suggest the principle of their agreement; just as, in seeking
for anything lost, we often have to ask ourselves in what places it may
be hid, that we may search for it there.



As reasoning is from particulars to particulars, and consists simply in
recognising one fact as a mark of another, or a mark of a mark of
another, the only necessary conditions of the exertion of the reasoning
power are senses, to perceive that two facts are conjoined; and
association, as the law by which one of the two facts raises up the idea
of the other. The existence of artificial signs is not a third
_necessary_ condition. It is only, however, the rudest inductions (and
of such even brutes are capable) that can be made without language or
other artificial signs. Without such we could avail ourselves but little
of the experience of others; and (except in cases involving our intenser
sensations or emotions) of none of our own long past experience. It is
only through the medium of such permanent signs that we can register
uniformities; and the existence of uniformities is necessary to justify
an inference, even in a single case, and they can be ascertained once
for all.

General names are not, as some have argued, a mere contrivance to
economise words. For, if there were a name for every individual object,
but no general names, we could not record one uniformity, or the result
of a single comparison. To effect this, all indeed, that are
_indispensable_, are the abstract names of attributes; but, in fact, men
have always given general names to objects also.



Concrete general names (and the meaning of abstract names depends on the
concrete) should have a fixed and knowable connotation. This is easy
enough when, as in the case of new technical names, we choose the
connotation for ourselves; but it is hard when, as generally happens
with names in common use, the same name has been applied to different
objects, from only a vague feeling of resemblance. For, then, after a
time, general propositions are made, in which predicates are applied to
those names; and these propositions make up a loose connotation for the
class name, which, and the abstract at about this same period formed
from it, are consequently never understood by two people, or by the same
person at different times, in the same way. The logician has to fix this
fluctuating connotation, but so that the name may, if possible, still
_denote_ the things of which it is currently affirmed. To effect this
double object (which is called, though improperly, defining _not the
name but the thing_), he must select from the attributes in which the
denoted objects agree, choosing, as the common properties are always
many, and, in a _kind_, innumerable, those which are familiarly
predicated of the class, and out of them, if possible, or otherwise,
even in preference to them, the ones on which depend, or which are the
best marks of, those thus familiarly predicated. To do this
successfully, presumes a knowledge of all the common properties of the
class, and the relations between them of causation and dependence. Hence
the discussion of non-verbal definitions (which Dr. Whewell calls the
Explication of Conceptions) is part of the business of discovery. Hence,
too, disputes in science have often assumed the form of a battle of
definitions; such definitions being not arbitrary, but made with a view
to some tacitly assumed principle needing expression.

We ought, if possible, to define in consonance with the denotation. But
sometimes this is impossible, through the name having accumulated
_transitive_ applications, in its gradual extension from one object, in
relation to which it connotes one property, to another which resembles
the former, but in quite a different attribute. These _transitive_
applications, even when found to correspond in different languages, may
have arisen, not from any common quality in the objects, but from some
association of ideas founded on the common nature and condition of
mankind. When the association is so natural and habitual as to become
virtually indissoluble, the _transitive_ meanings are apt to coalesce in
one complex conception; and every new transition becomes a more
comprehensive generalisation of the term in question. In such cases the
ancients and schoolmen did not suspect, what otherwise they carefully
watched for, viz. ambiguities: not Plato, though his Comparisons and
Abstractions preparatory to Induction are perfect; not even Bacon, in
his speculations on Heat. Hence have sprung the various vain attempts to
trace a common idea in all the uses of a word, such as _Cause_
(Efficient, Material, Formal, and Final _Cause_), _the Good_, _the Fit_.

When a term is applied to many different objects agreeing _all_ only in
_one_ quality (e.g. things _beautiful_, in _agreeableness_), though
_most_ agree in something besides, it is better to exclude part of the
denotation than of the connotation, however indistinct: else language
ceases to keep alive old experience, alien perhaps to present
tendencies. In any case, words are always in danger of losing part of
their connotation. For, just one or two out of a complex cluster of
ideas, and sometimes merely the look or sound of the word itself, is
often all that is absolutely necessary for the suggesting another set of
ideas to continue the process of thought; and consequently, some
metaphysicians have even fancied that all reasoning is but the
mechanical use of terms according to a certain form. If persons be not
of active imaginations, the only antidote against the propensity to let
slip the connotation of names, is the habit of predicating of them the
properties connoted; though even the propositions themselves, as may be
seen from the way in which maxims of Religion, Ethics, and Politics are
used, are often repeated merely mechanically, not being questioned, but
also not being felt. Much of our knowledge recorded in words is ever
oscillating between its tendency, in consequence of different
generations attending exclusively to different properties in names, to
become partially dormant, and the counter-efforts of individuals, at
times, to revive it by tracing the forgotten properties historically in
the almost mechanically repeated formulas of propositions; and, when
they have been there rediscovered, promulgating them, not as
discoveries, but with authority as what men still profess to believe.
The danger is, lest the formula itself be dismissed by clear-headed
narrow-minded logicians, and the connotation fixed by them (in order
that the denotation may be extended) in accordance with the present use
of the term. Then, if the truths be at any time rediscovered, the
prejudice is against them as novelties. The _selfish_ theory of morals
partly fell because the inconsistency of received formulas with it
prompted a reconsideration of its basis. What would have been the result
if the formulas attaching odium to selfishness, praise to
self-sacrifice, had been dismissed, if this indeed had been possible!
Language, in short, is the depositary of all experience, which, being
the inheritance of posterity, we have a right to vary, but none to
curtail. We may improve the conclusions of our ancestors; we should not
let drop any of their premisses; we may alter a word's connotation; but
we must not destroy part of it.



The connotation of names shifts not only by reason of gradual
inattention to some of the common properties, which, if language were
ruled by convention alone, would be in their entirety both the perpetual
and the sole constituents of the connotation; but also from the
incorporation in the connotation, in addition to these, and often,
finally, to the _exclusion_ of them altogether, of other circumstances
at first only casually associated with it. These collateral associations
are the cause why there are so few exact synonymes; and why the
dictionary meaning, or Definition, is so bad a guide to its uses, as
compared with its history, since the latter explains the law of the
succession by showing the causes which determined the successive uses.

Two counter-movements are always going on in language. One is
generalisation, by which words are ever losing part of their
connotation, and becoming more general. This arises, partly from men,
such as historians and travellers, using words, especially those
expressing complicated mental and social facts strange to them, in a
loose sense, in ignorance of the true connotation; partly, from known
things multiplying faster than names for them; partly, also, from the
wish to give people some notion of a new object by reference to a known
thing resembling it however slightly. The other movement is
specialisation; and by it words (even the same words which, as, e.g.
_pagan_ and _villain_, later get generalised in a new direction) are
ever taking a fresh connotation, through their denotation being
diminished. Specialisations often occur even in scientific nomenclature,
a word which expressed general characters becoming confined to a
specific substance in which these characters are predominant. So it is
when any set of persons has to think of one species oftener than of any
other contained in the genus: e.g. some sportsmen mean partridges by the
term _birds_. But, as ideas of our pleasures and pains and their
supposed causes, cling, most of all, by association to what they have
been once connected with, the great source of specialisation is the
addition of the ideas of agreeableness or painfulness, and approbation
or censure, to the connotation. And hence arises the fallacy of
_question-begging_ names referred to later on.

It is the business of logicians not to ignore, for they cannot prevent,
transformations of terms in common use, but to trace and embody them,
and men's half unconscious reasons for them, in distinct definitions.



Not only must words have a fixed and knowable meaning; but also, no
important meaning should be without its word: that is, there should be a
name for everything which we have often to make assertions about. There
should be, therefore, first, names suited to describe all the individual
facts; secondly, a name for every important common property detected by
comparing those facts; and, thirdly, a name for every _kind_.

First, it conduces to brevity and clearness to have separate names for
the oft-recurring combinations of feelings; but, as these can be defined
without reference back to the feelings themselves, it is _enough_ for a
_descriptive_ terminology, if there be a name for every variety of
elementary feeling, since none of these can be defined, or indicated to
a person, except either by his having the sensation itself, or being
referred through a known mark to his remembrance of it. The meaning of
the name when given to a feeling is fixed, in the first instance, by
convention, and must be associated _immediately_, not through the usage
of ordinary language, with the feeling, so that it may at once recall
the latter. But even among the elementary feelings, those purely mental,
and also sensations, such as those from disease, the identity of which
in different persons cannot be determined, cannot be exactly
_described_. It is only the impressions on the outward senses, or those
inward feelings connected uniformly with outward objects (and,
consequently, sciences, such as botany, conversant with outward
objects), which are susceptible of an exact descriptive language.

Secondly, there must also be a separate name for every important common
property recognised through that comparison of observed instances which
is preparatory to induction (including names for the classes which we
artificially construct in virtue of those properties). For, although a
definition would often convey the meaning, both time and space are
saved, perspicuity promoted, and the attention excited and concentrated,
by giving a brief and compact name to each of the new _general
conceptions_, as Dr. Whewell calls them, that is, the new results of
abstraction. Thenceforward the name nails down and clenches the
unfamiliar combination of ideas, and suggests its own definition.

Thirdly, as, besides the artificial classes which are marked out from
neighbouring classes by definite properties to be arrived at by
abstraction, there are classes, viz. _kinds_, distinguished severally by
an unknown multitude of independent properties (and about which classes
therefore many assertions will be made), there must be a name for every
_kind_. That is, besides a terminology, there must be a nomenclature,
i.e. a collection of the names of all the lowest _kinds_, or _infimæ
species_. The Linnæan arrangements of plants and animals, and the French
of chemistry, are nomenclatures. The peculiarity of a name which belongs
to a nomenclature is, not that its meaning resides in its denotation
instead of its connotation (for it resides in its connotation, like that
of other concrete general names); but that, besides connoting certain
attributes which its definition explains, it also connotes that these
attributes are distinctive of a _kind_; and this fact its definition
cannot explain.

A philosophical language, then, must possess, first, precision, and next
(the subject of the present chapter), completeness. Some have argued
that, in addition, names are fitted for the purposes of thought in
proportion as they approximate to mere symbols in compactness, through
meaninglessness, and capability of use as counters without reference to
the various objects which, though utterly different, they may thus at
different times equally well represent. Such are, indeed, the qualities
enabling us to employ the figures of arithmetic and the symbols of
algebra perfectly mechanically according to general technical rules.
But, in the first place, in our direct inductions, at all events,
depending as they do on our perception of the particulars of the
agreement and difference of the phenomena, we could never dispense with
a distinct mental image of the latter. Further, even in deduction,
though a syllogism is conclusive from its mere form, if the terms are
unambiguous, yet the _practical_ validity of the reasoning depends on
the hypothesis that no counteracting cause has interfered with the truth
of the premisses. We can assure ourselves of this only by studying the
phenomena at every step. For it is only in geometry and algebra that
there is no danger from the Composition of Causes, or the superseding of
one set of laws by another; and that, therefore, the propositions are
categorically true. In sciences in general, then, the object should be,
so far from keeping individualising peculiarities out of sight, to
contrive the greatest possible obstacles to a merely mechanical use of
language: we should carefully keep alive a consciousness of its meaning,
by referring, by aid of derivation and the analogies between the ideas
of the roots and the derivatives, to the origin of words; and as words,
however philosophically constructed, are always tending, like coins, to
have their inscription worn off, we should be ever stamping them afresh.
This we shall effect, if we contemplate habitually, not the _formulas_
which record the laws of the phenomena (for, if so, the formulas will
themselves progressively lose their meaning), but the phenomena whence
the laws were collected; and we must conceive these phenomena in the
concrete, and clothe them in circumstances.



Every name which connotes an attribute thereby divides, but only
incidentally, all things, known and unknown, real and imagined, into two
classes, viz. those which have, and those which have not the attribute.
But sometimes the naming itself is but the secondary and subsidiary, and
the classification, the primary object. The general problem of such
classification is, to provide that things shall be thought of in such
groups, and the groups in such an order, as will best promote the
remembrance and ascertainment of their laws. Its subjects are _real
things_ exclusively, but _all_ real things, since, to place one object
in a group, we ought to know the divisions of nature at large.

Any property may be the basis for a classification; but those best
suited are properties which are causes, or, next, as the cause of a
class's chief peculiarities seldom serves as its diagnostic, any effect
which is a sure mark both of the cause and of the other effects. Only a
classification so grounded is scientific; the same also is not technical
or artificial, but natural, and emphatically _natural_ (as compared with
classifications in an inferior degree also _natural_, which are based on
properties important with reference to the reasoner's special practical
objects), when the classification is based on those properties which
would most impress one who knew all the properties, but was not
interested particularly in any one. Further, it is a great
recommendation of a classification, that it groups together things of
like general aspect; but this is not a _sine quâ non_: a group may be
_natural_ even if based on very _unobvious_ properties, provided these
are marks of many other properties, though certainly then there should
be also some more obvious property to act as a mark of the unobvious
ones which form the real basis.

As the first principle of _natural_ classification is that the classes
must be so formed that the objects composing each may have as many
properties in common as possible to serve as predicates, all _kinds_
should have places among the _natural_ groups, since the common
properties of _kinds_, and, therefore, the general assertions that can
be made about them, are innumerable. But _kinds_ are too few to make up
the whole of a classification: other classes also may be eminently
_natural_, though marked out from each other only by a definite number
of properties. Of neither sort of _natural_ groups is Dr. Whewell's
theory _strictly_ true, viz. that every _natural_ group is not
determined by definition, that is, by definite characters which can be
expressed in words, but is fixed by Type. He explains that a type is an
example of any class, for instance, a species of a genus, which
possesses all the characters and properties of the genus in a marked
way; that round this type-species are grouped all the other species,
which, though deviating from it in various directions and degrees, yet
are of closer affinity to it than to the centre of any other group; and
that this is the reason why propositions about _natural_ groups so often
state matters as being true not in all cases, but only in most. Now,
there is a truth, but only a partial truth, in this doctrine. It is
this: in forming _natural_ groups, species which want certain of the
class-characters, some one, and others another, are classed with those
(the majority) that have them all, because they are more like (that is,
in fact, have more of the common characters of) that particular group
than of any other. On account of the feeling of vagueness hence
engendered, we certainly, in deciding if an object belong to the group,
do generally (and _must_, when the classification is made expressly with
a view to a special inductive enquiry) refer mentally, not as a
substitute for, but in illustration of the definition of the group, to
some standard specimen which has _all_ the characters well developed.
But not the less, therefore, are all _natural_, equally with all
artificial, groups framed with distinct reference to certain definite
characters. In the case of _kinds_, a few characters are chosen as marks
of the rest. In the case of other _natural_ groups, the formation of the
larger groups, into which we collect the _infimæ species_, is suggested
indeed by resemblance to types (since we form each such larger group
round a selected _kind_ which serves as its exemplar); but the group
itself, when formed, is determined by definite characters.

Class names should by the mode of their construction help those who have
learnt about the thing, to remember it, and those who have not learnt,
now to learn, by being merely told the name. This is best effected, in
the case of _kinds_, when the word indicates by its very formation the
properties it connotes. But this is seldom possible. For, though a
_kind_-name connotes not all the _kind_-properties, but some only which
serve as sure marks of the rest, even these have been found too many to
be included conveniently in a name (except in Elementary Chemistry,
where every compound substance has one distinctive index-property, viz.
the chemical composition). A subsidiary resource is to point out the
_kind's_ nearest natural affinities. For instance, in the binary
Nomenclature of Botany and of Zoology, the name of every species
consists of the name of the _natural_ group next above, with a word
added expressive of some quality in the nature or mode of discovery, or
what not, of the particular species itself. By this device (obtaining at
present only in Botany and Zoology), as well is the expression, in the
name, of many of the _kind's characters_ secured, as the use of names
economised, and the memory relieved. Except for some such plan, what
hope of naming the 60,000 known species of Plants?



The object of Classification generally is to bring our ideas of objects
into the order best fitted for prosecuting inductive enquiries into the
laws of the phenomena generally. But a Classification which aims at
facilitating an inductive enquiry into the laws of some special
phenomenon, must be based on that phenomenon itself. The requisites of
such a classification are, first, the bringing into one class all
_kinds_ of things which exhibit the phenomenon; next, the arranging
them in a _series_, according to the degrees in which they exhibit it.
Such a classification has been largely applied in Comparative Anatomy
and Physiology (and these alone), since there has been found a
recognisable difference in the degree in which animals possess one main
phenomenon, viz. Animal Life.

This arrangement of the instances, whence the law is to be collected, in
a series, is that which is always implied in and is a condition of _any_
application of the method, viz. that of Concomitant Variations, which
must be used when conjoined circumstances cannot easily be separated by
experiment. But sometimes (and it is so in Zoology) the law of the
subject of the special enquiry (e.g. Animal Life) has such influence
over the general character of the objects, that all other differences
among them seem mere modifications of it; and then the classification
required for the special purpose becomes the determining principle of
the classification of the same objects for general purposes.

To recognise the identity of phenomena which thus differ only in degree,
we must assume a type-species. This will be that _kind_ which has the
class-properties in their greatest intensity (and, therefore, most
easily studied with all their effects); and we must conceive the other
varieties as instances of degeneracy from that type.

The divisions of the series must be determined by the principles of
_natural_ grouping in general (that is, in effect, by natural affinity);
in subordination, however, to the principle of a natural series; that
is, in the same group must not be placed things which ought to occupy
different points of the general scale.

Zoology affords the only _complete_ example of the true principles of
rational classification, whether as to the formation of groups or of
series. Yet the same principles are applicable to all cases (to art and
business as well as science) where the various parts of a wide subject
have to be brought into mental co-ordination.





The habit of reasoning well is the only complete safeguard against
reasoning ill, that is, against drawing conclusions with insufficient
evidence, a practice which the various contradictory opinions,
particularly about the phenomena relating to Man, show to be even now
common, and that too among the most enlightened. But, to be able to
explain an error is a necessary condition of seeing the truth; for,
'Contrariorum eadem est Scientia.' Consequently, a work on Logic must
classify Fallacies, that is, the varieties of Apparent Evidence; for
they _can_ be classified, though not in respect of their negative
quality of being either not evidence at all, or inconclusive, yet in
respect of the positive property they have of _appearing_ to be

As Logic has been here treated as embracing the whole reasoning process,
so it must notice the fallacies incident to any part of it (not to
Ratiocination merely), whether arising from faulty Induction, or from
faulty Ratiocination, or from dispensing wholly with either or both of
them. It does not treat of errors from negligence, or from inexpertness
in using right methods, nor does it treat of errors from moral causes,
viz. Indifference to truth, or Bias by our wishes or our fears; for the
moral causes are but the _remote_ and _predisposing_, not the _exciting_
causes of opinions; and therefore inferences from them, since they must
always involve the intellectual operation of admitting insufficient
evidence as sufficient, really come under a classification of the things
which wrongly _appear_ evidence to the _understanding_.

Fallacies may be arranged, with reference either to the cause which
makes them (erroneously) appear evidence, or to the particular kind of
evidence they simulate. The following classification is grounded on both
these considerations jointly.



The business of Logic is, not to enumerate false opinions, but to
enquire what property in the facts led to them, that is, what
peculiarity of relation between two facts made us suppose them
habitually conjoined or disjoined, and thus regard the presence or
absence of the one as evidence of that of the other. For every such
property in the facts, or our mode of considering them, there is a
corresponding class of Fallacies.

As the supposed habitual connexion or repugnance of two facts may be
admitted, either as a self-evident and axiomatic truth, or as itself an
inference, the first great division is into Fallacies of Simple
Inspection or _à priori_ Fallacies, and Fallacies, of Inference. But
there is also an intermediate class. For, sometimes an inference is
erroneous through our not conceiving what our premisses precisely are,
and from our therefore substituting new premisses for the old, or a new
conclusion for the one we undertook to prove; and this is called the
Fallacy of Confusion. Under this head, indeed, of Fallacies of
Confusion, might strictly be brought almost any fallacy, though falling
also under some other head: for, some of the links in an argument,
especially if sophistical, are sure to be suppressed; and, it being left
doubtful which is the proposition to be supplied, we can seldom tell
with certainty under _which_ class the fallacy absolutely comes. It is,
however, convenient to reserve the name _Fallacy of Confusion_ for cases
where Confusion is the _sole_ cause of the error.

Cases, then, where there is more or less ground for the error in _the
nature of the apparent evidence itself_, the evidence being assumed to
be of a certain sort, and a false conclusion being drawn from it, may be
classed as Fallacies of Inference. According as the apparent evidence
consists of particular facts, or of foregone generalisations, we call
the errors Fallacies of Induction or of Deduction. Each of these
classes, again, may be subdivided into two species, according as the
apparent evidence is either false, or, though true, inconclusive. Such
subdivisions of the Fallacy of Induction are respectively called, in the
former case, Fallacies of Observation (including cases where the facts
are not directly observed, but inferred), and, in the latter, Fallacies
of Generalisation. Among Fallacies of Deduction, those which proceed on
false premisses have no specific name, for they must fall under one of
the other heads of Fallacies; but those, the premisses of which, though
true, do not support the conclusion, compose a subdivision, which may be
specified as Fallacies of Ratiocination.



There must be some _à priori_ knowledge, some propositions to be
received without proof; for there cannot be a chain suspended from
nothing. What these are is disputed, one school recognising as ultimate
premisses only the facts of our subjective consciousness, e.g.
Sensations, while Ontologists hold that the mind intuitively, and not
through experience, recognises as realities other existences, e.g.
Substances, which are suggested by, though not inferrible from, those
facts of consciousness. But, as both schools, in fact, allow that the
mind infers the _reality_ from the _idea_ of a thing, and that it may do
this unduly, there results a class of Fallacies resting on the tacit
assumption that the objects in nature have the same order as our ideas
of them. Hence not only arose the vulgar belief that facts which make us
think of an event are omens foreboding (e.g. lucky or unlucky names), or
even causing its occurrence; but even men of science both did and do
fall into this Fallacy. The following dogmas express the different forms
of this error:--

1. [Greek: a]. _Things which we cannot help thinking of together must
coexist_; thus Descartes held that, because existence is involved
(though really only by the thinker himself) in the idea of a geometrical
figure, a thing like the idea must exist. [Greek: b]. _Whatever is
inconceivable is false._ The latter proposition has been defended by
drawing a distinction between the principle, and its possibly wrong
application to facts, e.g. to Antipodes; but how can we ever know that
it has been rightly applied? Coleridge, again, has distinguished between
the unimaginable, which he thinks may possibly be true, and the
inconceivable, which he thinks cannot be; but Antipodes were imaginable
at the same period when they were inconceivable. In fact, as even to
Newton it seemed inconceivable, that a thing should act where it is not
(e.g. that the sun should act upon the earth without the medium of an
ether), simply because his mind was not familiar with the idea, so it
_may_ be with _our_ incapability (if not, indeed, resulting merely from
our limited faculties) of _conceiving_, e.g. that matter cannot think;
that space is infinite; that _ex nihilo nihil fit_. Leibnitz's tenet
that all _natural_ phenomena must be explicable _à priori_, and the
further assumption by some that Nature always acts by the simplest, i.e.
by the most easily conceivable means (and that, therefore, e.g. the
heavenly bodies have a circular movement), exhibit vividly this Fallacy
of Simple Inspection.

2. _Whatever can be thought of apart, or has a separate name, exists
apart as a separate entity_, e.g. Nature, Time, qualities, as e.g.
Whiteness, and, worst of all, the Substantiæ Secundæ. Mysticism is this
habit of ascribing objective existence to the subjective creations of
the mind, and reasoning from them to the things themselves.

3. _A fact must follow a certain law, because we see no reason for its
deviating from it in one way rather than in another._ This, which is the
same as the Principle of the Sufficient Reason, has been used to prove
the Law of Inertia (the very point to be proved, viz. that only external
force can be a sufficient reason for motion _in a particular direction_,
being assumed), and also the First Law of Motion, the argument being, in
the latter case, that a moving body, if it do _not_ continue of itself
to move uniformly in a straight line, must deviate right or left, and
that there is _no reason_ for its going one way more than the other: to
which the answer is, that, apart from experience, we could not know
whether or not there were a reason. Geometers often fall into this

4. _The differences in nature must correspond to our received
distinctions_ (in names and classifications). Thus, the Greeks thought
that, by determining the meanings of words, they ascertained facts.
Aristotle usually starts with 'We say thus or thus.' So, with the
_Doctrine of Contrarieties_, in which the Pythagoreans and others
assumed that oppositions in language imply similar ones in nature.
Hence, too, the ancient belief in the essential difference between the
laws of things terrestrial and things celestial, and in man's
incapability of imitating nature's works. Bacon's error (which vitiates
his inductive system) was analogous, in looking (either through his
eagerness for practical results, or a lingering belief that causes were
the sole object of philosophy) for the cause of given effects rather
than the effects of a given cause. Hence sprang his tacit assumption
(and that in enquiries into the causes of a thing's sensible qualities,
where it was especially fatal), that in all cases, e.g. of heat or cold,
the _forma_, or set of conditions, is _one_ thing. A similar notion,
viz. that each property of gold, as of other things, has its one
_forma_, produced the belief in Alchemy.

5. The conditions of a phenomenon often do resemble the phenomenon
itself, e.g. in cases of Motion, Contagion, Feelings; but it is a
Fallacy to suppose that _they must or probably will_. By this fancied
law men guided their conjectures. Thus, the _Doctrine of Signatures_
was, that substances showed their uses as medicines by external
resemblance, either to their supposed effect, or to the disease. So, the
Cartesians, and even Leibnitz, argued, that nothing physical but
previous motion could account for motion, explaining the human body's
voluntary motions by Nervous Vibrations or by Animal Spirits. Hence,
too, the inference that there is a correspondence between the physical
qualities of the cause, and like or like-named ones, either of the
phenomenon (e.g. between sharp particles and a sharp taste), or of its
effects (e.g. between the redness of Mars, and fire and slaughter as
results of that planet's influence). In metaphysics, the Epicureans'
doctrine of _species sensibiles_, and the moderns' of _perception
through ideas_, arose from this fallacy (combined with another, viz.
that a thing cannot act where it is not). Again, the conditions of a
thing are sometimes spoken of even as though they were the thing itself.
Thus, in the Novum Organon, heat (i.e. really the conditions of the
feeling of it) is called a kind of motion; and Darwin, in his Zoonomia,
after describing _idea_ as a kind of _notion of external things_,
defines it as _a motion of the fibres_. Cousin says: 'Tout ce qui est
vrai de l'effet est vrai de la cause,' though, the reverse _might_ be
true; and Coleridge affirms, as _an evident truth_, that mind and
matter, as having no common property, cannot act on each other. The same
fallacy led Leibnitz to his _pre-established harmony_, and Malebranche
to his _occasional causes_. So, Cicero argues that mental pleasures, if
arising from the bodily, could not, as they do, exceed their cause; and
Descartes, that the Efficient Cause must have all the perfections of the
effect. Conversely Descartes, too, and persons who assail, e.g. the
Principle of Population by reference to Divine benevolence (thus
implying that, because God is perfect, therefore what _they_ think
perfection must obtain in nature), assume that effects must resemble
their causes.



A fallacy of Observation (the first of the three fallacies of Proof) may
be either negative or positive.

1. The former, which is called Non-observation, is a case, not of a
positive mis-estimate of evidence, or of the proper faculties (whether
the senses or reason) not having been employed, but simply of the
non-employment of any of the faculties. It arises ([Greek: a]) from
neglect of instances. Sometimes this is when there is a stronger motive
to remember the instances on the one side, and the observers have
neglected the principle of the Elimination of Chance. Hence (the mind,
as Bacon says, being more moved by affirmative than by negative
instances) the belief in predictions, e.g. about the weather, because
they occasionally turn out correct; and the credit of the proverb, that
'Fortune favours fools,' since the cases of a wise man's success through
luck are forgotten in his more numerous successes through genius. But a
preconceived opinion is the _chief_ cause why opposing instances are
overlooked. Hence originate the errors about physical facts (e.g. of
Copernicus's foes, and friends, too, about the falling stone), and _à
fortiori_, on moral, social, and religious subjects, where yet stronger
feelings are involved.

The fallacy of Non-observation may occur ([Greek: b]) from neglect, not
of the material instances wholly, but of some material facts in them,
e.g. in cases of cures by quack remedies (such as Kenelm Digby's
'sympathetic powder'), of some attendant fact (as exclusion of air from
a wound, rest, regimen, and the like) which really worked the cure.
Sometimes the neglected fact is one ascertainable, not by the senses,
but by reasoning, which has been overlooked. Thus, Cousin's argument
that, if the sole end of punishment were to prevent crime by
intimidating intending criminals, the punishment of the innocent,
indiscriminately with the guilty, would have the same effect, ignores
the fact that the innocent would then be equally intimidated, and so the
punishment would be of no use as an example to criminals. So, in
Political Economy, where the effects of a cause often consist of two
sets of phenomena, the one obvious, the other deeper under the surface,
and exactly contrary, the latter is often neglected. This was why the
rapidly spent capital of the prodigal was supposed formerly to employ
more labour than the invested savings of the parsimonious, and the
purchase of native goods to encourage native industry more than the
purchase of foreign.

2. The error in Mal-observation, which is the _positive_ kind of
Mis-observation, is not the overlooking facts, but the seeing them
wrong. It arises from mistaking what is in fact inference (as much
_must_ be, whenever we try to observe or to describe) for perception,
which is infallible evidence of what is really perceived. The
Anti-Copernicans, when they appealed to common sense, made this mistake.
So do untrained persons generally in describing facts, especially
natural phenomena (e.g. apothecaries and nurses in stating symptoms),
and that, too, in proportion to their ignorance. We might expect this,
since usually the actual perceptions of the senses (e.g. the colour and
extension) are not of interest, except as marks whence to draw
inferences about something else (e.g. about the body, to which these
qualities belong). Painters, therefore, to know what the sensation
actually was, have to go through a special training. But this confusion
of inference with perception is still more likely in highly abstract
subjects; and, consequently, in these, mere, and often false inferences,
have continually been regarded as intuitive judgments.



This class includes whatever errors of generalisation are not mere
blunders, but arise from some wrong general conception of the inductive
process. Only a few kinds can be noted. 1. Under this Fallacy come
generalisations which _cannot_ be established by experience, e.g.
inferences from the order in the Solar System to other and unknown parts
of the universe; and also, except when a particular effect would
contradict either the laws of number and extension, or the universal law
of causality, all inferences from the fact that _we_ have never known of
a particular effect to its impossibility. 2. Those generalisations also
are fallacious which resolve, either, as in early Greece, all things
into one element, or, as often in modern times, impressions on the
senses, differing in quality, and not merely in degree, into the same;
e.g. heat, light, and (through vibrations) sensation, into motion;
mental, into nervous states; and vital phenomena, into mechanical or
chemical processes. In these theories, one fact has its laws applied to
another. It may possibly be a condition of that other; but even then the
mode in which the new fact is actually produced would have to be
explained by its own law, and not by that of the condition. 3. Again,
generalisations got by Simple Enumeration, fall under this Fallacy. That
sort of Induction 'precariò concludit,' says Bacon, 'et periculo
exponitur ab instantiâ contradictoriâ, ... ex his tantummodò quæ præsto
sunt pronuncians.' The ancients used it; and in questions relating to
man and society, it is still employed by _practical_ men. By it men
arrived at the various examples of the formula, _Whatsoever has never
been_ (e.g. a State without artificial distinctions of rank; negroes as
civilised as the white race) _will never be_; which, being inductions
without elimination, could at most form the ground only of the lowest
empirical laws. Higher empirical laws can be got, when a phenomenon
presents (as no negation can) a series of regular gradations, since
something may then be inferred from the observed as to the unobservable
terms of the series. Such is the law of man's necessary progression, in
contradiction to the above formula. But even this better generalisation
is similarly, though not as grossly, fallacious as the preceding, when,
though not itself a cause, but only a summary expression for the general
result of all the causes, it is accepted as _the_ law of human changes,
past and even future. So, empirical generalisations, from present to
past time, and from the character of one nation to that of another, are
similarly fallacious when employed as causal laws. 4. This Fallacy
occurs, not only when an empirical is confounded with a causal law, but
when causation is inferred improperly. The mistake sometimes lies in
inferring _à posteriori_ that one fact must be the cause of another
(e.g. the National Debt, or some special institution, of England's
prosperity), because of their casual conjunction; at other times, in
assuming _à priori_ that one of several coexisting agents is the sole
cause, and then deducing the effects from it exclusively. The latter is
properly False Theory. It has been exemplified in medicine by the
tracing of all diseases by one school, to viscidity of the blood, by
another, to the presence of some acid or alkali, and, in politics, by
the assumption that some special form of government or society is
absolutely good. 5. In False Analogies (which fall under this Fallacy)
there is no pretence of a conclusive induction. The argument from
Analogy is the inferring, in the absence of evidence either way, that an
object resembles a second object in one point, because it is seen to
resemble it in another point, which either is not known to be connected
with the first by causation (as, that the planets must be inhabited
because they obey the same astronomical laws with the earth, which is),
or which is known to be, not, indeed, its cause or its effect, but
either one of a set of conditions, which together are its cause, or an
occasional effect of its cause. Now, persons (usually from poverty, not
from luxuriance, of imagination) often overrate the weight of true
analogies; but the fallacy specially consists in inferring resemblance
in one point from resemblance in another, when the evidence is not only
not in favour of, but even positively against the connection of the two
by way of causation. It is so in the argument in favour of absolutism,
on the ground of its resemblance to paternal government in the one point
of irresponsibility, as though the assumed benefits of paternal rule
flowed from this quality. Similarly fallacious are the inferences,
through analogies, from the liability to decay of bodies natural to that
of bodies politic; from the supposed need of a _primum mobile_ in nature
to that of an irresponsible power in a state; and from the effects of a
decrease of a country's corn to the effects of a decrease of its gold
(the utility of which, but not of corn, depends on its value, and its
value on its scarcity). Such, also, were the Pythagorean inferences that
there is a music of the spheres, because the intervals between the
planets have the same proportion as the divisions of the monochord; and,
again, that the movements of the stars as being _divine_ must be
regular, because so are those even of orderly _men_. So, Aristotle and
other ancients supposed perfection to obtain in all natural facts,
because it appeared to exist in some; and so, the Stoics tried to prove
the equality of all crimes by reference to various similes and metaphors
(as, that the man held half an inch below the surface will be drowned as
certainly as the man at the bottom of the sea; and that want of skill is
shown as much in steering a straw-laden boat as a treasure galleon on to
the rocks). But, in fact, the connection by causation between the known
and the inferred resemblance, which is _assumed_ by these metaphors, is
the very thing which they are brought to prove. The real use of such
cases of analogy as metaphors is that they serve, not as an argument,
but as an assertion that one exists. Though they cannot prove, they
sometimes suggest the proof, and point to a case in which the same
grounds for a conclusion have been found adequate. Such are d'Alembert's
classification of successful politicians as either eagles or serpents;
and the statement, as an argument for education, that, in waste land
weeds will spring up; and such is _not_ Bacon's inference from the
levity of floating straw to the worthlessness of the _extant_ scientific
works of the ancients.

The great source of fallacious generalisation is bad classification, by
which things with no, or no important, common properties, are grouped
together. Worst is it, when a word which commonly signifies some
definite fact is applied to other facts only slightly similar. Bacon
(who has himself thus erred in his enquiries into heat) specifies, as
examples of this, the various applications (got, by unscientific
abstraction, from the original sense) of the word 'wet,' to flame, air,
dust, and glass, as well as to water. The application by Plato,
Aristotle, and other ancients, of the terms Generation, Corruption, and
[Greek: kinêsis] to many heterogeneous phenomena, with a mixture of the
ideas belonging to them severally, caused many perplexities, which may
be noticed under Fallacies of Confusion.



These fallacies (to which the name _Fallacy_ is commonly applied
exclusively) would generally be detected if the arguments were set out
formally; and the value of the syllogistic rules is, that they force the
reasoner to be aware what it is that he is really asserting. The
frequent errors in processes such as Conversion and Opposition, which
are in appearance, though not in reality, inferences from premisses, may
for convenience be here referred to. Such are the simple conversion of
an universal affirmative; the corresponding error in a hypothetical
proposition of inferring the truth of the antecedent from that of the
consequent; and the confusing of a contrary with a contradictory, which
amounts, in practice, to mistaking the reverse of wrong for right. But
fallacies of Ratiocination properly lie in syllogisms. They commonly
resolve themselves, when in a single syllogism, into the having more
than three terms, whether covertly, as through an undistributed middle,
or an illicit process, or avowedly. But the most dangerous and the
commonest of these fallacies arise in a chain of argument from _changing
the premisses_. One of the obscurer forms of this is the fallacy _a
dicto secundum quid_ (i.e. with a qualification, or condition,
expressed, or, more usually, understood) _ad dictum simpliciter_. Thus,
the Mercantile Theory was in favour of prohibiting all trade which tends
to carry out more money than it brings in, on the ground that money is
riches, though it is so only if the money can be _freely_ spent. Such,
too, was the argument (used to support the doctrine that tithes fall on
the landlord) that, because now the rent of tithe-free land exceeds that
of tithed land, the rent from the latter would be increased by the
abolition of all tithes. There was a similar fallacy in the use of the
maxim, that individuals are the best judges of their pecuniary
interests, against Mr. Wakefield's scheme for concentrating settlers.
Cases in which the condition of _time_ is dropped, fall under this same
particular fallacy, as, when the maxim that prices always find their
level, is construed as meaning that they are always _at_ their level. It
is the same with the reasoning (especially in political and social
subjects), upon principles, which are true in the absence of all
modifying causes, as though no such causes _could_ exist. Other
analogous fallacies are those _a dicto simpliciter ad dictum secundum
quid_ (the converse of the preceding), and _a dicto secundum quid ad
dictum secundum alterum quid_.



Under this head come all fallacies which arise, not so much from a false
estimate of the probative force of known evidence, as from an indistinct
conception what the evidence is.

1. Thus, where there is an ambiguous middle, or a term used in different
senses in the premisses and in the conclusion, the argument proceeds as
though there were evidence to the point, when, in fact, there is none.
This error does not occur much in direct inductions, since the things
themselves are there present to the senses or memory; but chiefly, in
Ratiocination, where we are deciphering our own or others' notes. The
ambiguity arises very often from assuming that a word corresponds
precisely in meaning with the root itself (e.g. _representative_), or
with cognate words from the same root, called _paronymous_ words (as,
_artful_, with _art_). Other examples of ambiguities are; 'Money,'
which, meaning both the currency and also capital seeking investment, is
often thought to be scarce in the former sense, because scarce in the
latter; 'Influence of Property,' which, signifying equally the influence
of respect for the power for good, and of fear of the power for evil,
which is possessed by the rich, is represented as being assailed under
its former form when attacked really only under the latter; 'Theory,'
which, because applied popularly to the accounting for an effect apart
from facts, is ridiculed, even when expressing, as it properly does, the
result of philosophical induction from experience; 'The Church,' which
refers (as in the question of the inviolability of _Church_ property)
sometimes to the clergy alone, sometimes to all its members; 'Good,' in
the Stoic argument that virtue, as alone _good_ (in the Stoic sense),
must therefore include freedom and beauty, because these are _good_ (in
the popular sense). So, the meaning of 'I' shifts from _the laws of my
nature_ to _my will_, in Descartes' _à priori_ argument for the being of
a God, viz. that there must be an external archetype whence I got the
conception, for if _I_ (i.e. _the laws of my nature_) made it, _I_ (i.e.
_my will_, and not, as it should consistently be, _the laws of my
nature_) could unmake it; but _I_ (i.e. _my will_) cannot. In the
Free-Will controversy, 'I' is used ambiguously for volitions, actions,
and mental dispositions, and 'Necessity' both for _Certainty_ and for
_Compulsion_. From the application of 'same,' 'one,' 'identical,' which
primarily refer to a single object, to several objects because
_similar_, grew up (for the purpose of accounting for the supposed
_oneness_ in things said to have the _same_ nature or qualities) both
the Platonic _Ideas_, and also the _Substantial Forms_ and _Second
Substances_ of the Aristotelians, even though the latter did see the
distinction between things differing both _specie_ and _numero_, and
those differing _numero_ only. And thence, too, sprang Berkeley's proof
of the existence of a Universal Mind from the supposed need of such a
Being to harbour, in the interval, the idea, which, one and the same
(really, only two _similar_ ideas), a man's mind has entertained at two
distinct times. The difficulty in _Achilles and the Tortoise_ arises
from the use of _infinity_, or, _for ever_, in the premisses, to
signify a finite time which is infinitely divisible, and, in the
conclusion, to signify an infinite time. Thus, again, 'right' is used to
express, both what others have no right to stop a man from doing, and
also what it is not against his own duty to do; both what people are
entitled to expect from, and also what they may enforce from others. The
Fallacy of Composition and Division, i.e. the use of the same term in a
syllogism, at one time in a collective, at another in a distributive
sense, is one of the Fallacies of Ambiguous Terms. Examples of it are
the arguments, that _great men_ (collectively) could be dispensed with,
because the place of any particular great man might have been supplied
(i.e., in fact, by some other great man); and, that a high prize in a
lottery may be reasonably expected (by _a certain individual_, viz.
oneself), because a high prize is commonly gained (_by some one or

2. In Petitio Principii, the premisses are not even verbally sufficient
for the conclusion, since one premiss is either clearly the same as the
conclusion, or actually proved from it, or not susceptible of any other
proof. Men commonly fall into it, through believing that the premiss
_was_ verified, though they have forgotten how. But the variety, termed
Reasoning in a Circle, implies a conscious attempt to prove two
propositions reciprocally from each other. This formal proof is not
often attempted, except under the pressure of controversy; but, from
mistaking mutual coherency for truth, propositions, which cannot be
proved except from each other, are often _admitted_, when expressed in
different language, without other proof. Frequently a proposition is
presented in abstract terms as a proof of the same in concrete, as, in
Molière's parody, 'L'opium endormit parcequ'il a une vertu soporifique.'
So, some qualities of a thing selected arbitrarily are termed its nature
or essence, and then reasoned from as though not able to be counteracted
by any of the rest. 'Question-begging appellatives,' particularly, are
cases of Petitio Principii, e.g. the styling any reform an _innovation_,
which it really is, only that _innovation_ conveys, besides its
dictionary meaning, a covert sense of something extreme. Thus, in
Cicero's De Finibus, 'Cupiditas,' which usually implies vice, is used to
express certain desires the moral character of which is the point in
question. Again, the infinite divisibility of matter was assumed by the
argument which was used to prove it, viz. that the least portion of
matter must have both an upper and an under surface (which, as every
other Fallacy of Confusion, when cleared up, appears as a fallacy of a
different sort, under shelter of which, as indeed in ratiocinative
fallacies generally, the mere verbal juggle at first escapes detection).
Such, again, was Euler's argument, that _minus_ multiplied by _minus_
gives _plus_, _because_ it could not give the same as _minus_ multiplied
by _plus_, which gives _minus_. So, some ethical writers begin by
assuming, that certain general sentiments are the _natural_ sentiments
of mankind, and thence argue that any which differ are morbid and
_unnatural_. Thus, lastly, Hobbes and Rousseau rested the existence of
government and law on a supposed social compact, and not on men's
perception of the interests of society, which, however, could be the
only ground for their abiding by such compact if a fact.

3. In Ignoratio Elenchi, or, the Fallacy of Irrelevant Conclusion, the
error lies not either in mistaking the import of the premisses, or in
forgetting what they are, but in mistaking what is the conclusion to be
proved. Sometimes, a particular is substituted for the universal as the
proposition needing proof, and sometimes, a proposition with different
terms. Under this fallacy come the cases, not only of proving what was
not denied, but of disproving what was not asserted; e.g. the argument
used against Malthus (whose own position was, that population increases
only _in so far as not kept down_ by prudence, or by poverty and
disease), that, at times, population has been nearly stationary; or
again, that, in some country or other, population and comfort are
increasing together, Malthus himself having asserted that this might be
so, if capital has increased. Similarly, even Reid, Stewart, and Brown
(not merely Dr. Johnson) urged that Berkeley ought, if consistent, to
have run his head against a post, as though the non-recognition of an
occult _cause_ of sensations implies disbelief in any _fixed order among





Many complex problems have been resolved through the use of the
Scientific Methods, and thus only. The most complex of all problems are
the problems relating to Man himself; and of them those concerned with
the Mind and Society have never been scientifically resolved. They can
be rescued from empiricism, if at all, only by being submitted to some
of the methods already characterised as applicable to science in
general. Which of these methods must be selected, and why; what are the
causes of previous failures; and what degree of success now is possible
or probable, will be considered in this book, when a preliminary
objection (_based on the theory of free will_), that men's actions are
not, like other natural events, subject to invariable laws, has been
first removed.



The theory of _free will_, viz. that the will is determined by itself,
and not by antecedents, was invented as being more in accordance with
the dignity of human nature and our consciousness of freedom, than
_philosophical necessity_. The latter doctrine, in laying down simply
that our volitions and actions are invariable consequents of our
antecedent states of mind, and that, given our motives, character, and
disposition, other men could predict our conduct as certainly as any
physical event, states indeed nothing which is in itself either
contradicted by our consciousness, or degrading; yet the doctrine of
causation, as applied to volition, is supposed, from the natural
tendency of the mind to imagine falsely that a mysterious constraint is
exercised by _any_ antecedent over the consequent, to imply some state
of dependence which our consciousness does contradict. Moreover, the
erroneous notion that something more than uniformity of order and
capability of being predicted is meant, has been favoured by the use of
the ambiguous term _necessity_ (which, it is true, commonly implies
irresistibleness), to signify simply that the given cause will be
followed by the effect subject to all possibilities of counteraction by
other causes. Most necessarians have been themselves deceived by the
expression: they are apt to be partially fatalists as to their own
actions, with a weaker spirit of self-culture than the believers in
free-will, and to fail to see that the fact of their character being
formed _for_ them, that is, by their circumstances, including their own
organisation, is consistent with its being formed _by_ themselves, as
intermediate agents, moulding it in any particular way which they may
_wish_. The belief that the _wishing_ is excited by external causes,
e.g. by education, casual aspirations, and experience of ills resulting
from our previous character, can be of no practical harm, and does not
conflict with our feeling of moral freedom, that is, of power, _if we
wish_, to modify or conquer our own character.

The ambiguity of the word _motive_ has also caused confusion. A motive,
when used to signify that which determines the will, means not always or
only the anticipation of a pleasure or a pain, but often the desire of
the action itself. The action having finally become by association in
itself desirable, we may get the habit of willing it (that is, get a
_purpose_) without reference to its being pleasurable. We are then said
to have a confirmed character.



Any facts may be a subject of science, if they follow one another
according to constant laws; and this, whether, although the ultimate
laws are known, yet, of the derivative laws on which a phenomenon
directly depends, either _none_, as in Meteorology, or, as in Tidology,
_only_ the laws of the greater causes on which the chief part of a
phenomenon directly depends, have been ascertained, and not those of all
the minor modifying causes; or, as in Astronomy (which is therefore
called an _exact_ science), both the ultimate laws are known, and also
the derivative laws as well of the greater as of all the minor causes.
The science of Human Nature cannot be exact, the causes of human conduct
being only approximately known. Hence it is impossible to predict _with
scientific accuracy_ any one man's acts, resulting as they do partly
from his circumstances, which, in the future, cannot be precisely
foreseen, and, partly, from his character, which can never be exactly
calculated, because the causes which have determined it are sure, in the
aggregate, not to be entirely like those which have determined any other
man's. But approximate generalisations, though only probably true as to
the acts and characters of individuals, will be certainly true as to
those of masses, whose conduct is determined by general causes chiefly;
and they are therefore sufficient for political and social science. They
must, however, be connected deductively with the universal laws of human
nature on which they rest, or they will be only low empirical laws. This
is the text of the next two chapters.



By the laws of mind (i.e. as considered in this treatise, the laws of
mental phenomena) are meant the laws according to which one state of
mind is produced by another. If M. Comte and others be right in saying
that, in like manner with the mental phenomena called sensations, all
the other states of mind have for their proximate causes nervous states,
there would be no original laws of mind, and Psychology would be a mere
branch of Physiology. But at present, this tenet is not proved, however
highly probable; and, at all events, the characteristics of those
nervous states are quite unknown; consequently the uniformities of
succession among the mental phenomena, which undoubtedly do exist, and
which are not proved to result from more general laws, must be
considered as the subject of a distinct science called Psychology. We
can ascertain only by experiment the simple laws of Mind, such as--1.
That a state of consciousness can be reproduced in the absence of the
cause which first excited it (i.e. that every mental impression has its
idea), and--2. That these secondary mental states themselves are
produced according to the three laws of ideas. But the complex laws are
got from these simple laws, according either to the Composition of
Causes, when the complex idea is said to _consist of_ the Simple Ideas,
or to chemical combination, when it is said to be _generated by_ them.
Hartley and Mr. James Mill indeed hold _all_ the mental phenomena to be
generated by chemical combination from simple ideas of _sensation_,
however unlike to the alleged results; but even though they had proved
their theory, employing the Method of Difference, and not only the
Method of Agreement (which latter itself they have used only partially),
we should still have to study the complex ideas themselves inductively,
before we could ascertain their sequences.

The analytical enquiry (neglected alike by the German metaphysical
school, and by M. Comte) into the general laws of mind, will show that
the mental differences of individuals are not ultimate facts, but may be
referred generally to their particular mental history, their education
and circumstances, but sometimes also to organic differences influencing
the mental phenomena, not directly, but through the medium of the
psychological causes of the latter. Men's animal instincts, however, are
probably, equally with the mere sensations, connected directly with
physical conditions of the brain and nerves. Whether or not there be any
direct relation between organic causes and any other mental phenomena,
Physiology is likely in time to show; but at least Phrenology does not
embody the principles of the relation.



Till the Empirical laws of Mind, i.e. the truths of common experience,
are _explained_ by being resolved into the causal laws (the subject of
the last chapter), they are mere approximate generalisations which
cannot be safely applied beyond the limits in which they were collected
by observation. But this does not prove aught against the universality
and simplicity of the ultimate mental laws; for the same is the case
with the empirical laws even in astronomy, where each effect results
from but few causes; _à fortiori_, therefore, will it be so in regard to
man's character, which is influenced by each of his circumstances, which
differ in the case of each nation, generation, and individual. But
though mankind have not one universal character, yet there exist
universal laws of the formation of character. These universal laws
cannot be discovered experimentally, i.e. either by artificial
experiment, since we can seldom vary the experiment sufficiently, and
exclude all but known circumstances, or by observation, since, even in
the most favourable instances for the latter, viz. National acts, only
the Method of Agreement can be applied. Observation has its uses in
relation to this subject; but only as verification of the results
arrived at by the Deductive Method. The Deductive Method must be
employed to obtain the laws of the formation of character. They are got
by supposing any given circumstances, and then considering how these
will, according to the general laws of mind, influence the formation of
character. So, contrary to Bacon's rule, laid down wrongly as universal,
for the discovery of principles, the highest generalisations must be
first ascertained by the experimental science of Psychology; and then
will come what is in fact a system of corollaries from the latter
science, viz. Ethology, i.e. (as dealing only with tendencies) the
_exact_ science of human character, or of education both national and
individual, and which has for its principles the middle principles
(_axiomata media_) of mental science. It does not yet, but it will soon,
exist as a science. Its object must be to determine, from the general
laws of mind, combined with man's general position in the universe, what
circumstances will aid or check the growth of good or bad qualities, so
that the Art of Education will be merely the transformation of these
middle principles into precepts and their adaptation to the special
cases. But at every step these middle principles, got by deduction, must
be verified _à posteriori_ by empirical laws, and by specific experience
respecting the assumed circumstances.



Political and social phenomena have been thought too complex for
scientific treatment. Practitioners hitherto have been the only
students; and so, as in medicine, before the rise of Physiology and
Natural History, _experimenta fructifera_, and not _lucifera_, have been
sought. The scheme of such a science has even been thought quackery,
through the vain attempts of some theorists to frame universal precepts,
as though their failure (arising from the variety of human
circumstances) proved that the phenomena do not conform to universal
laws. Social phenomena, however, being phenomena of human nature in
masses, must, as human nature is itself subject to fixed laws, obey
fixed laws resulting from the fixed laws of human nature. The number and
changefulness of the data (unlike those of Astronomy) will prevent our
ever predicting the far future of society. But, when general laws have
been ascertained, an application of them to the individual circumstances
of a given age and country will show us the causes and tendencies of,
and the means of modifying, its actual condition. A consideration of two
methods, erroneously used for this science, viz. the Experimental or
Chemical, and the Abstract or Geometrical, will introduce us to the true



The followers of this method do not recognise the laws of social
phenomena as merely a composition of the laws of individual human
nature. They demand specific experience in all cases; and they attempt
to make effects, which depend on the greatest possible complication of
causes, the subject of induction by observation and experiment. The
attempt must fail; for, we can neither get by experiment appropriate
_artificial_ instances, nor, by observation, _spontaneous_ instances
(from history), with the circumstances enough varied for a true
induction. Neither the _direct_ nor the _indirect_ Method of Difference
can be applied, for we cannot find either two single instances differing
in nothing but the presence or absence of a given circumstance (the
_direct_), or two classes respectively agreeing in nothing but the
presence of a circumstance on one side and its absence on the other (the
_indirect_). Then, again, the Method of Agreement is of small value,
because social phenomena admit the widest plurality of causes; and so
also is that of Concomitant Variations, on account of the mutual action
of the coexisting elements of society being such that what affects one
affects all. The Method of Residues is better suited to social enquiries
than the other three. But _it_ is not a method of pure observation and
experiment. It presupposes that we know, by previous deduction from
principles of human nature, the causes of part of the effect. But if
thus part of the truths are, why may not all be, ascertained by
Deduction, and the experimental argument be confined to the verifying of
the deductions?



The Methods of Elementary Chemistry are applied to social phenomena from
carelessness as to, or ignorance of, any of the higher physical
sciences: the Geometrical Method, from the belief that Geometry, that
is, a science of coexistent, not successive facts, where there are no
conflicting forces, is, and that the now deductive physical sciences of
Causation, where there are conflicting forces, are _not_, the type of
deductive science. Thus, it seems to have been supposed by many
philosophers, that each social phenomenon results from only one force,
one single property of human nature. For instance, Hobbes assumed (eking
out his assumption by the fiction of an original contract), that
government is founded on fear. Even the scientific Bentham School based
a general theory on one premiss, viz. that men's actions are always
determined by their interests, meaning probably thereby, that the bulk
of the conduct of any succession, or of the majority of any body of men,
is determined by their private or worldly interests. They inferred
thence, that those rulers alone will govern according to the interest of
the governed, whose selfish interests are identified with it (forgetting
that, apart from the philanthropy and sense of duty of many, the
conduct of _all_ rulers must be influenced by the habits of mind, both
of the whole community, and also of their own class in it, and by the
maxims of their predecessors). Lastly, they laid down that this sense of
identity of interest with the governed is producible only by
responsibility (whereas the personal interest of rulers often prompts
them to acts, e.g. for the suppression of anarchy, which are also for
the interest of the governed). In fact, this school was pleading for
parliamentary reform, and saw truly, that it is against the selfish
interests of rulers that constitutional checks are needed, and that, in
modern Europe, a feeling in the governors of identity of interest, when
not active enough, can be roused only by responsibility to the governed.
Their mistake was, that they based on just these few premisses a general
theory of government, in forgetfulness that such should proceed by
deduction from _the whole_ of the laws of human nature, since each
effect is an aggregate result of many causes operating now through the
same ones, now through different ones, of these laws.



The complexity in social effects arises from the number, not of the
laws, but of the data. Therefore, Sociology, i.e. Social Science, must
use the Concrete Deductive Method, compounding with one another the laws
of all the causes on which any one effect depends, and inferring its law
from them all. As in the easiest case to which the Method of Deduction
applies, so in this, the most difficult, the conclusions of
ratiocination must be _verified_ by collation with the concrete
phenomena, or, if possible, with their empirical laws; and then the only
effect of an increase in the complication of the subject will be a
tendency to a disturbance, and sometimes even to an inversion (which,
indeed, M. Comte thinks inseparable from all Sociological enquiries) in
the order of the two processes, obliging us, first, to conjecture the
conclusions by specific experience, and then verify them by _à priori_
reasonings showing their connection with the principles of human nature.

Sociology is a system not of positive predictions, but of tendencies. Of
tendencies themselves, not many can be laid down as true of all
societies alike. Even in the case of any single feature of society, the
_consensus_ which exists in the body politic, as in the body natural,
makes it uncertain whether a cause with a special tendency in one age or
country will have quite the same in another. General propositions,
therefore, in this deductive science, as, to be true, they must be
hypothetical, and state the operation of a given cause in _given
circumstances_, so, to be of any utility, should be limited to those
classes of facts, which, though influenced by all sociological agents,
are yet influenced _immediately_ by a few only, certain fixed
combinations of which are likely to recur often. Thus, Political
Economy, taking the one psychological law that men prefer a greater gain
to a smaller, and ignoring every other motive, except what are
perpetually adverse principles to this, viz. men's aversion to labour
and desire of present costly pleasures, assumes, in enquiring what acts
this desire of gain will produce, that, within the department of human
affairs, where it is actually the main end, it is the _sole_ end. Yet
its general propositions are of great practical use, even though it thus
provisionally overlooks as well miscellaneous concurrent causes (with
some exceptions, as e.g. the principle of population), as also the fact
of the non-existence elsewhere of the conditions of any one particular
country (e.g. the peculiarly British mode of distribution of the produce
of industry among three classes). Another hypothetical or abstract
science, which can be carved out of Sociology, is the as yet unexplored
Political Ethology, i.e. the theory of the causes which determine a
people's, or age's, type of character, which collective character,
besides being the most interesting phenomenon in the particular state of
society, is the _main_ cause of the social state which follows, and
moulds _entirely_ customs and laws. The neglect of national diversities
sometimes (as e.g. the assumption by our political economists, that in
commercial populations everywhere, equally as in Great Britain and
America, all motives yield to the desire of gain) vitiates only the
practical application of a proposition; but when the national character
is mixed up at every step with the phenomena (as is the case in
questions respecting the tendencies of forms of government), the
phenomena cannot properly be insulated in a separate branch of

As in Ethology and other deductive sciences, so in Statistics and
History there are empirical laws. The immediate causes of social facts
are often not open to direct observation; and the deductive science can
determine only what causes produce a given effect, and not the frequency
and quantities of them; in such cases, the empirical law of the causes
(which, however, can be applied to new cases only if we know that the
remoter causes, on which these latter causes depend, remain unchanged)
must be found through that of the effects, the Deductive Science relying
then for its data on indirect observation. But, in the separate branches
of Sociology, we cannot obtain empirical laws by specific experience. It
is so particularly (on account both of the number of the causes, and
also the fewness of the instances to be compared with the one in point)
when the effect of any one (e.g. Corn Laws) of many simultaneous social
causes has to be determined. We can, however, in such cases, verify
_indirectly_ a theory as to the influence of a particular cause in given
circumstances, by seeing if the same theory accounts for the _existing_
state of actual social facts which that cause has a tendency to



The _general_ Science of Society, as contrasted with the branches,
shows, not what effect will follow from a given cause under given
circumstances, but what are the causes and characteristic phenomena of
States of Society generally. A _State of Society_ is the simultaneous
state of all the chief social facts (e.g. employments, beliefs, laws).
It is a condition of the whole organism; and, when analysed, it
exhibits uniformities of coexistence between its different elements.
But, as this correlation between the phenomena is itself a law resulting
from the laws which regulate the succession between one state of society
and another, the fundamental problem of Social Science is to find these
latter laws. The form of this succession, by which (on account of the
exceptionally constant reaction, in social facts, of the effects, i.e.
human character, on their causes, i.e. human circumstances) one social
state is ever in process of changing into a different one, is now
allowed to be, not, as in the solar system, a cycle, but a _progress_
(by which is not here _necessarily_ meant _improvement_, whatever the
fact may be). In France it has been thought, that a law of progress, to
be found by an analysis of the course of history, would enable us to
predict the whole future. But such a law would be empirical, and not
true beyond its own facts; for the succession of mental and social
states cannot have an independent law. Empirical laws must indeed be
found; or a _general_ Science of Society would be impossible: for, the
character of any one generation is so much the result of the characters
of all prior ones, that _men_ could not compute so long a series from
the elementary laws producing it. But the empirical laws, when found (as
they can be, since the series of the effects as a whole is ever growing
in uniformity), must be shown by deductions to be, if not the only
possible, or even the most probable, at least possible, consequences of
the laws of human nature.

The empirical laws of society are uniformities, either of coexistence,
or of succession. The former are ascertained and verified by Social
Statics (which is the theory of the _consensus_, i.e. the mutual actions
and reactions, of contemporaneous social elements); the latter, by
Social Dynamics (the theory of Society considered as in a state of
progress). As to Social Statics--there is, M. Comte thinks, a perpetual
reciprocity of influence between all aspects of the same organism, and
to such an extent, that the condition of any one which we cannot
directly observe can be estimated by that of another which we can. There
is, he considers, such an interdependence, not only between the
different sciences and arts among themselves, but between the sciences
in general and the arts in general, even between the condition of
different nations of the same age, and between a form of government and
the civilisation of the period. Social Statics will ascertain for us the
requisites of stable political union: it will enquire what special
circumstances have always attended on such union, increasing and
decreasing in proportion to its completeness; and will then verify these
facts as requisites by deducing them from general laws of human nature.
Thus, history indicates as such requisites and conditions of free
political union: 1. A system of educational discipline checking man's
tendency to anarchy; 2. Loyalty, i.e. a feeling of there being
something, whether persons, institutions, or individual freedom and
political and social equality, which is not to be, at least in practice,
called in question; 3. That which the Roman Empire, notwithstanding all
its tyranny, established, viz. a strong sense of common interest among
fellow-citizens (a very different feeling, by the bye, to mere
antipathy to foreigners).

Social Dynamics regards sequences. But the _consensus_ in social facts
prevents our tracing the leading facts in one generation to separate
causes in a prior one. Therefore, we must find the law of the
correspondence not only between the simultaneous states, but between the
simultaneous changes of the elements of society. To find this law,
which, when duly verified, will be the scientific derivative law of the
development of humanity, we must combine the statical view of the
phenomena with the dynamical. Fortunately, the state of mankind's
speculative faculties and beliefs, being the prime agent of the social
movement, furnishes a clue in the maze of social elements, since the
order of human progression in all respects will mainly depend on the
order of progression of this prime agent. That the other dispositions
which aid in social progress (e.g. the desire for increased material
comfort) owe their means of working to this (however relatively weak a
propensity it may be) is a conclusion from the laws of human nature; and
this conclusion is in accordance also with the course of history, in
which internal social changes have ever been preceded by proportionate
intellectual changes. To determine the law of the successive
transformations of opinions all past time must be searched, since such
changes appear definitely only at long intervals. M. Comte alone has
followed out this conception of the Historical Method; and his
generalisation, to the effect that speculation has, on all subjects,
three successive stages, has high scientific value.

The Historical Method will trace the derivative laws of social order
and progress. It will enable us both to predict the future, and (thus
founding the noblest part of the Political Art) partly to shape it. At
present, both the Science and the Art are in the rudiments; but they are



Practical Ethics, i.e. Morality, is an art; and therefore its Method
must be that of Art in general. Now, Art from the major premiss,
supplied by itself, viz. that the end is desirable, and from the
theorem, lent by Science, of the combinations of circumstances by which
the end can be reached, concludes that to secure this combination of
circumstances is desirable; if it also appear practicable, it turns the
theorem into a rule. Unless Science's report as to the circumstances is
a full one, the rule may fail; and as, in any case, rules of conduct
cannot comprise more than the ordinary conditions of the effect (or they
would be too cumbrous for use), they must, at least in moral subjects,
be considered, till confronted with the theorems, which are the reasons
of them, provisional only. Practical maxims, therefore, till so
confronted, are not universally true even for a given end, much less for
conduct generally, and must not be used, as they are by the
_geometrical_ school, as ultimate premisses.

Any particular art consists of its rules, _together with_ the theorems
on which they depend; and Art in general consists of the truths of
Science; only these must be arranged in the order most convenient, not,
as in Science (which is an enquiry into the course of nature), for
thought, but for practice. Intermediate scientific truths must be framed
to serve as first principles of the various arts: and through them the
end or purpose of an art will be connected with the means for realising
the conditions of its attainment. The end itself, however, is defined by
the art, not by the science. Each art has one first principle or major
premiss which does not, as the propositions of Science, assert that a
thing _is_ or _will be_, but recommends it as what _ought to be_. A
scientific theory, however complete, of the history and tendencies of
society does not show us (without Teleology, i.e. the Doctrine of Ends)
what are the preferable ends. Art itself has its Philosophia Prima, for
ascertaining the standard of ends. There can be but one such standard or
general principle to which all rules of practice should conform; for, if
there were several, a higher yet would be needed, as umpire when they
disagreed. In Morality the felt need of a standard has been sometimes
supplied by the hypothesis of intuitive moral principles: but a standard
would still be wanted for the other two branches of the Art of Life,
viz. Prudence or Policy, and Taste; and _their_ standard when found
would serve for Morality as well. The true standard, or general
principle, is, _the promotion of the happiness of_ ALL _sentient
beings_. This is not the _sole_ end; for instance, ideal nobleness of
will or conduct should be pursued in preference to the _specific_
pursuit of happiness; but all ends whatsoever must be justified and
should be controlled by it.


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