Analysis of Mr. Mill's system of logic

Front matter

ANALYSIS

WORKS BY JOIN STUART MILL, M.P. FOR WESTMINSTER.

A SYSTEM of LOGIC, RATIOCINATIVE and INDUC-

Preface

TO

THE SECOND EDITION.

The author’s aim has been to produce such a con¬ densation of the original work as may recall its con¬ tents 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 substan¬ tive 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

UBRAR'ES

VI

PREFACE, 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.

Definition.

Book II. Reasoning

I.

Inference, or Eeasoning in General .

. 35

II.

Eatiocination, or Syllogism .

. 36

III.

The Functions and Logical Value of the Syllogism

. 39'

IV.

Trains of Eeasoning, and Deductive Sciences

. 43

V. & VI.

. 46

Vlll

CONTENTS.

Book III. Induction

CHAP. PAGE

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

X. Plurality of Causes, and intermixture of Effects . 7 3

XI. The Deductive Method.76

XII. & XIII. The Explanation and Examples of the Ex¬ planation 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 Causa¬ tion . 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

CONTENTS.

IX CHAP ’ . . t PAGE

III. Naming as Subsidiary to Induction . . . .Ill

IV. The Requisites of a Philosophical Language, and the

Principles of Definition . . . , .112

V. The Natural History of the Variation in the Meaning

VI. Terminology and Nomenclature . . . .117

VII. Classification, as Subsidiary to Induction . . .121

VHI. 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 Cha¬

VI. General Considerations on the Social Science . . 155

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

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

ANALYSIS

OF

MILL’S LOGIC.

Introduction

u 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 , how¬ ever, is not wide enough. Reasoning means either syllogising, or (and this is its truer sense) the draw¬ ing inferences from assertions already admitted. But the Aristotelian or Scholastic logicians included in Logic terms and propositions, and the Port Eoyal logicians spoke of it as equivalent to the art of think¬ ing. Even popularly, accuracy of classification, and the extent of command over premisses, are thought clearer signs of logical powers than accuracy of de-, duction. On the other hand, the definition of logic as a f science treating of the operations of the un¬ derstanding 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

B

INTRODUCTION.

wliat 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 in¬ ference, the fields of Logic and of Knowledge coincide; but the two differ in so far that Logic does not find evidence, but only j udges of it. All science is com¬ posed of data, and conclusions thence: Logic shows what relations must subsist between them. All in¬ ferential 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 evi¬ dence. It includes not only the process of proceeding from the known to the unknown, but, as auxiliary thereto, Naming, Definition, and Classification. Con¬ ception, 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

CHAPTEB I.

ON TEE NECESSITY OP COMMENCING WITH AN ANALYSIS OP 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 para¬ mount reason why we must, as a preliminary, con¬ sider 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.

CHAPTEE 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

It 2

NAMES AND PROPOSITIONS.

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 attri¬ butes 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 4 generally, since every one of them, if it signifies anything at all, must imply an attribute.

. The third division is into Connotative and Nonconnotative (the latter being wrongly called Abso¬ lute). 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,de¬ noted receives a common name (e.g snow is named white) from the attribute connoted. Even some ab¬ stracts are connotative, for attributes may have attri-

NiMES.

butes asQribed 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, inde¬ pendent 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 gene¬ ralisation 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

NAMES AND PROPOSITIONS.

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 inde¬ terminate 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. . Corre¬ latives, 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.

THE THINGS DENOTED BY NAMES.

Some make a sixth division, viz. Univocals, i.e, names predicated of different individuals in the same sense, and iEquivocals, i.e. names predicated of differ¬ ent individuals in different senses. But these are not two kinds of names, but only two modes of using them; for an equivocal name is two names acciden¬ tally 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.

CHAPTEE III.

THE THINGS DENOTED BY NAMES.

Logic is the theory of Proof, and everything prov¬ able 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 predi¬ cate. It was with this object that Aristotle formed his Categories, i.e. an attempted enumeration of all nameable things by the summa geneva 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,

NAMES AND PROPOSITIONS.

his Relation properly includes Action, Passivity, and Local Situation, and also the two categories of Position ttots and 7ro £, while the difference between 7 rod and tcsicrOai is only verbal, and Sxsiv n °t 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 ob¬ stacle to renewing Aristotle’s attempt. The words used for the purpose commonly denote substances only, though attributes and feelings are equally ex¬ istences. Even being is inadequate, since it denotes only some existences, being used by custom as sy¬ nonymous with substance , both material and spiritual. That is, it is applied to what excites feelings and has attributes, but not to feelings and attributes them¬ selves ; and if we called extension, virtue, &e., beings , we should be accused of believing in the Platonic seif-existing ideas, or Epicurus’s sensible forms — : m 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 exist¬ ence, gradually enlarges its connotation to mean separate existence, i.e. existence freed from the con¬ dition of belonging to a substance, so as to exclude

THE THINGS DENOTED BY NAMES.

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 am¬ biguous : 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 sen¬ sations and emotions, or to the emotions alone; but it is properly a genus, having for species, Sensation, Emotion, Thought, and Volition. Bv 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 sensa¬ tion 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 x of the feelings into bodily and mental. But really there is no such di¬ vision, even sensations being states of the sentient

NAMES AND PROPOSITIONS.

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 wbat 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 sub¬ stance is self-existent (being followed, if a relative, by o/, not qua substance, but qua the relation). But this o/, as distinguishing attributes, itself needs ex¬ planation : besides, we can no more conceive a sub¬ stance 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 sen¬ sations. 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

THE THINGS DENOTED BY NAMES.

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 uni¬ form order of sensations implies an external cause determining the law of the order; and that the attri¬ butes inhere in this external cause or substratum, viz. matter. But at last it was seen that the exist¬ ence 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 in¬ tuitive 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. Noiimena, as contrasted with the mental repre¬ sentation 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 Keid referred to as proving that some qualities must exist, not in the sensations, but

NAMES AND PROPOSITIONS.

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 sub¬ stance, is the unknown recipient both of the sensa¬ tions and of all the other feelings. Though I call a something myself , as distinct from the series of feelings, the 6 thread of consciousness,’ yet this self shows itself only through its capacity of feeling or being con¬ scious ; and I can, with my present faculties, conceive the gaining no new information but about as yet un¬ known 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. Seem¬ ingly, this doctrine arises only from the tendency to

THE THINGS DENOTED BY NAMES.

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 9 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 ques¬ tion belongs to metaphysics; and it suits this doc¬ trine, 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 rela¬ tions 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, like-

NAMES AND PROPOSITIONS.

wise, with the relations of likeness and unlikeness. The feeling of these sometimes cannot he 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 un¬ likeness between states of our own or some other mind; and this, whether the feeling of the resem¬ blance or dissimilarity relate to bodies or to attri¬ butes, 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 qriality, is always founded on a likeness or unlikeness in the sensations excited. What the difference is all who have bad 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

THE THINGS DENOTED BY NAMES.

sensations. So, Relation generally is but the power which an object has of joining its correlative in pro¬ ducing 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 re¬ lations 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 pro¬ ducing 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 con-

NAMES AND PROPOSITIONS.

Vey 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 (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 ean be described. Q3) Relations also, with four ex¬ ceptions, are based on some fact, i.e. a series of states of consciousness, (y) 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 popu¬ larly (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.