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ANALYSIS

OF

MR. MILL'S SYSTEM OF LOGIC.

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

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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.

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 Æquivocals, i.e. names predicated of different individuals in different senses. But these are not two kinds of names, but only two modes of using them; for an æquivocal name is two names accidentally coinciding in sound. An intermediate case is that of a name used analogically or metaphorically, that is, in two senses, one its primary, the other its secondary sense. The not perceiving that such a word is really two has produced many 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 ποτἑ [Greek: pote] and ποὑ [Greek: pou], while the difference between ποὑ [Greek: pou] and κεἱσθαι [Greek: keisthai] is only verbal, and ἑχειν [Greek: echein] is not a summum genus at all. Besides—only substantives and attributes being there considered—there is no category for sensation and other mental states, since, though these may rightly be placed, so far as they express their relation, if active, to their objects, if passive to their causes, in the Categories of Actio and Passio, the things, viz., the mental states, do not belong there.

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

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

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

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

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

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

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

The general result is, that there are three chief kinds of nameable things:—1. Feelings distinct from the objects exciting and the organs supposed to convey them, and divisible into four classes, perceptions being only a particular case of belief, which is itself a sort of thought, while actions are only volitions followed by an effect. 2. Substances, i.e. the unknown cause and the unknown recipient of our sensations. 3. Attributes, subdivisible into Quality, Relation, Quantity. Of these α ([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. β ([Greek: b]) Relations also, with four exceptions, are based on some fact, i.e. a series of states of consciousness. γ ([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. Cæsar may be dead, may properly be rendered, I am not sure that he is alive.

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

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

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 ὑστερον πρὁτερον [Greek: hysteron proteron]: it explains the cause by the effect, since the predicate cannot be known for a class name which includes the subject, till several propositions having it for predicate have been first assented to. This doctrine seems to suppose all individuals to have been made into parcels, with the common name outside; so that, to know if a general name can be predicated correctly of the subject, we need only search the roll so entitled. But the truth is, that general names are marks put, not upon definite objects, but upon collections of objects ever fluctuating. We may frame a class without knowing a single individual belonging to it: the individual is placed in the class because the proposition is true; the proposition is not made true by the individual being placed there.

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

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

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

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 mediæval Realists) from seeing that the only difference between altering a non-essential (or accidental) property, which, he says, makes the thing ἁλλοἱον [Greek: alloion], and altering an essential one, which makes it ἁλλο [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 prædicabilis and also subjicibilis), whose common properties must include all the common properties of every other real kind to which the individual can be referred.

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

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 differentiæ leading to the most interesting propria. The enquiry into the more hidden agreement on which these obvious agreements depend, often itself arises under the guise of enquiries into the definition of a name.

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 suprà, p. 26) propositions (and, of course, all combinations of them) be regarded, not speculatively, as portions of our knowledge of nature, but as memoranda for practical guidance, to enable us, when we know that a thing has one of two attributes, to infer it has the other, these two axioms may be translated into one, viz. Whatever has any mark has that which it is a mark of; or, if both premisses are universal, Whatever is a mark of any mark, is a mark of that of which this last is a mark.

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 bonâ fide inference, though not an inference from the general proposition. The general proposition (i.e. in the first figure, the major premiss) contains not only a record of many particular facts which we have observed or inferred, but also instructions for making inferences in unforeseen cases. Thus the inference is completed in the major premiss; and the rest of the syllogism serves only to decipher, as it were, our own notes.

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

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

All reasoning, then, is induction: but the difficulties in sciences often lie (as, e.g. in geometry, where the inductions are the simple ones of which the axioms and a few definitions are the formulæ) not at all in the inductions, but only in the formation of trains of reasoning to prove the minors; that is, in so combining a few simple inductions as to bring a new case, by means of one induction within which it evidently falls, within others in which it cannot be directly seen to be included. In proportion as this is more or less completely effected (that is, in proportion as we are able to discover marks of marks), a science, though always remaining inductive, tends to become also deductive, and, to the same extent, to cease to be one of the experimental sciences, in which, as still in chemistry, though no longer in mechanics, optics, hydrostatics, acoustics, thermology, and astronomy, each generalisation rests on a special induction, and the reasonings consist but of one step 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 à priori by the constitution of the mind as soon as the meaning of the proposition is understood. But this assumption of an à priori recognition is gratuitous. It has never been shown that there is anything in the facts inconsistent with the view that the recognition of the truth of the axioms, however exceptionally complete and instant, originates simply in experience, equally with the recognition of ordinary physical generalisations. Thus, that we see a property of geometrical forms to be true, without inspection of the material forms, is fully explained by the capacity of geometrical forms of being painted in the imagination with a distinctness equal to reality, and by the fact that experience has informed us of that capacity; so that a conclusion on the faith of the imaginary forms is really an induction from observation. Then, again, there is nothing inconsistent with the theory that we learn by experience the truth of the axioms, in the fact that they are conceived by the mind as universally and necessarily true, that is, that we cannot figure them to ourselves as being false. Our capacity or incapacity of conceiving depends on our associations. Educated minds can break up their associations more easily than the uneducated; but even the former not entirely at will, even when, as is proved later, they are erroneous. The Greeks, from ignorance of foreign languages, believed in an inherent connection between names and things. Even Newton imagined the existence of a subtle ether between the sun and bodies on which it acts, because, like his rivals the Cartesians, he could not conceive a body acting where it is not. Indeed, inconceivableness depends so completely on the accident of our mental habits, that it is the essence of scientific triumphs to make the contraries of once inconceivable views themselves appear inconceivable. For instance, suppositions opposed even to laws so recently discovered as those of chemical composition appear to Dr. Whewell himself to be inconceivable. What wonder, then, that an acquired incapacity should be mistaken for a natural one, when not merely (as in the attempt to conceive space or time as finite) does experience afford no model on which to shape an opposed conception, but when, as in geometry, we are unable even to call up the geometrical ideas (which, being impressions of form, exactly resemble, as has been already remarked, their prototypes), e.g. of two straight lines, in order to try to conceive them inclosing a space, without, by the very act, repeating the scientific experiment which establishes the contrary.

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

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

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

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

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.

CHAPTER II.

INDUCTIONS IMPROPERLY SO CALLED.

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

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

CHAPTER III.

THE GROUND OF INDUCTION.

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

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

CHAPTER IV.

LAWS OF NATURE.

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

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

CHAPTER V.

THE LAW OF UNIVERSAL CAUSATION.

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

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

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

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

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

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

CHAPTER VI.

THE COMPOSITION OF CAUSES.

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

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

CHAPTER VII.

OBSERVATION AND EXPERIMENT.

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

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

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

CHAPTER VIII. and Note to CHAPTER IX.[1]

THE FOUR METHODS OF EXPERIMENTAL ENQUIRY.

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

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

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

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

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

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

FOOTNOTE:

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

CHAPTER X.

PLURALITY OF CAUSES, AND INTERMIXTURE OF EFFECTS.

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

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

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

CHAPTER XI.

THE DEDUCTIVE METHOD.

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

CHAPTERS XII. AND XIII.

THE EXPLANATION AND EXAMPLES OF THE EXPLANATION OF LAWS OF NATURE.

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

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

FOOTNOTE:

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

CHAPTER XIV.

THE LIMITS TO THE EXPLANATION OF LAWS OF NATURE. HYPOTHESES.

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

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

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

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

CHAPTER XV.

PROGRESSIVE EFFECTS, AND CONTINUED ACTION OF CAUSES.

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

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

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

CHAPTER XVI.

EMPIRICAL LAWS.

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

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

CHAPTER XVII.

CHANCE, AND ITS ELIMINATION.

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

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

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

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

CHAPTER XVIII.

THE CALCULATION OF CHANCES.

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

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

CHAPTER XIX.

THE EXTENSION OF DERIVATIVE LAWS TO ADJACENT CASES.

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

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

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

CHAPTER XX.

ANALOGY.

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

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

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

CHAPTER XXI.

THE EVIDENCE OF THE LAW OF UNIVERSAL CAUSATION.

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

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

CHAPTER XXII.

UNIFORMITIES OF COEXISTENCE NOT DEPENDENT ON CAUSATION.

Besides uniformities of succession, which always depend on causation, there are uniformities of coexistence. These also, whenever the coexisting phenomena are effects of causes, whether of one common cause or of several different causes, depend on the laws of their cause or causes; and, till resolved into these laws, are mere empirical laws. But there are some uniformities of coexistence, viz. those between the ultimate properties of kinds, which do not depend on causation, and therefore seem entitled to be classed as a peculiar sort of laws of nature. As, however, the presumption always is (except in the case of those kinds which are called simple substances or elementary natural agents), that a thing's properties really depend on causes though not traced, and we never can be certain that they do not; we cannot safely claim (though it may be an ultimate truth) higher certainty than that of an empirical law for any generalisation about coexistence, that is to say (since kinds are known to us only by their properties, and, consequently, all assertions about them are assertions about the coexistence of something with those properties), about the properties of kinds.

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

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

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

CHAPTER XXIII.

APPROXIMATE GENERALISATIONS, AND PROBABLE EVIDENCE.

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

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

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