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ANALYSIS OF MR. MILL'S SYSTEM OF LOGIC.
* * * * *
WORKS BY JOHN STUART MILL, M.P. FOR WESTMINSTER.
A SYSTEM of LOGIC, RATIOCINATIVE and INDUCTIVE. Sixth Edition. 2
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ANALYSIS OF MR. MILL'S SYSTEM OF LOGIC.
BY
W. STEBBING, M.A.
FELLOW OF WORCESTER COLLEGE, OXFORD.
_NEW EDITION._
LONDON:
LONGMANS, GREEN, AND CO.
1867.
LONDON
PRINTED BY SPOTTISWOODE AND CO.
NEW-STREET SQUARE
PREFACE TO THE SECOND EDITION.
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_.
CONTENTS.
PAGE
INTRODUCTION 1
BOOK I.
NAMES AND PROPOSITIONS.
CHAP.
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
BOOK II.
REASONING.
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
BOOK III.
INDUCTION.
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
BOOK IV.
OPERATIONS SUBSIDIARY TO INDUCTION.
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
BOOK V.
FALLACIES.
I. Fallacies in general 127
II. Classification of Fallacies 128
III. Fallacies of Simple Inspection; or, a priori Fallacies 130
IV. Fallacies of Observation 134
V. Fallacies of Generalisation 137
VI. Fallacies of Ratiocination 141
VII. Fallacies of Confusion 143
BOOK VI.
ON THE LOGIC OF THE MORAL SCIENCES.
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
ANALYSIS OF MILL'S LOGIC.
INTRODUCTION.
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.
BOOK I
NAMES AND PROPOSITIONS.
CHAPTER I.
ON THE NECESSITY OF COMMENCING WITH AN ANALYSIS OF LANGUAGE IN 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
proceed.
CHAPTER II.
NAMES.
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
attribute.
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 AEquivocals, 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
aequivocal 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
fallacies.
CHAPTER III.
THE THINGS DENOTED BY NAMES.
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 _qua_
substance, but _qua_ 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. Nouemena, 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.
CHAPTER IV.
PROPOSITIONS.
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. Caesar _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.
CHAPTER V.
THE IMPORT OF PROPOSITIONS.
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 (_nouemena_) 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 nouemena; and, moreover, in affirming the existence of a nouemenon,
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.
CHAPTER VI.
PROPOSITIONS MERELY VERBAL.
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 mediaeval 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.
CHAPTER VII.
THE NATURE OF CLASSIFICATION, AND THE FIVE PREDICABLES.
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
praedicabilis_ 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 Linnaean 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).
CHAPTER VIII.
DEFINITION.
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
differentiae 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.
BOOK II.
REASONING.
CHAPTER I.
INFERENCE, OR REASONING IN GENERAL.
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.
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.
CHAPTER II.
RATIOCINATION, OR SYLLOGISM.
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 _supra_, 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.
CHAPTER III.
THE FUNCTIONS AND LOGICAL VALUE OF THE SYLLOGISM.
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 _bona
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 formulae 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
died.
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.'
CHAPTER IV.
TRAINS OF REASONING, AND DEDUCTIVE SCIENCES.
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
formulae. This need of several formulae arises merely from the fact that
the marks by which we perceive that an inference can be drawn (and of
which marks the formulae 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 formulae) 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
each.
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
properties.
CHAPTERS V. AND VI.
DEMONSTRATION AND NECESSARY TRUTHS.
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 _a priori_ by the constitution of the mind as soon as the
meaning of the proposition is understood. But this assumption of an _a
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 _a
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.
BOOK III.
INDUCTION.
CHAPTER I.
PRELIMINARY OBSERVATIONS ON INDUCTION IN GENERAL.
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.