Analysis of Mr. Mill's System of Logic Part 1

a.n.a.lysis of Mr. Mill's System of Logic.

by William Stebbing.

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 ill.u.s.trations by which they are supported; and these conclusions may be adequately, and, it is believed, with much practical utility, embodied in an epitome. The processes of reasoning on which they depend, can, on the other hand, be represented in outline only. But it is hoped that the substance of every paragraph, necessary for the due comprehension of the several steps by which the results have been reached, will be here found at all events suggested.

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

LONDON: _Dec. 21, 1865_.

INTRODUCTION.

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 a.n.a.lysis 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 a.s.sertions 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 cla.s.sification, 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 Cla.s.sification.

Conception, Memory, and other like faculties, are not treated by it; but it presupposes them. Our object, therefore, must be to a.n.a.lyse the process of inference and the subsidiary operations, besides framing canons to test any given evidence. We need not, however, carry the a.n.a.lysis beyond what is necessary for the practical uses of Logic; for one step in a.n.a.lysis is good without a second, and our purpose is simply to see the difference between good and ill processes of inference.

Minuter a.n.a.lysis 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 a.n.a.lYSIS 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 a.s.sumes 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 cla.s.sifications of things as shown by names, correcting them as we proceed.

CHAPTER II.

NAMES.

Hobbes's a.s.sertion 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 cla.s.sification. 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 distinguis.h.i.+ng 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, G.o.d, 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 a.n.a.lysis, 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 cla.s.s.

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

Some make a _sixth_ division, viz. Univocals, i.e. names predicated of different individuals in the same sense, and aequivocals, i.e. names predicated of different individuals in different senses. But these are not two kinds of names, but only two modes of using them; for an aequivocal name is two names accidentally coinciding in sound. An intermediate case is that of a name used a.n.a.logically 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 a.s.sert 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 a.s.serted, be predicable of everything. His, however, is a rude catalogue, without philosophical a.n.a.lysis of the rationale even of familiar distinctions. For instance, his Relation properly includes Action, Pa.s.sivity, and Local Situation, and also the two categories of Position [Greek: pote] and [Greek: pou], while the difference between [Greek: pou] and [Greek: keisthai] is only verbal, and [Greek: echein] is not a _summum genus_ at all. Besides--only substantives and attributes being there considered--there is no category for sensation and other mental states, since, though these may rightly be placed, so far as they express their relation, if active, to their objects, if pa.s.sive to their causes, in the Categories of Actio and Pa.s.sio, 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, _ent.i.ty_, was made into a concrete, equivalent to _being_. Yet even _ent.i.ty_ 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 a.s.sociation 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 pa.s.sive, 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 pa.s.sive _states_. Enough for us now that they are all states of the mind.

II. Substances.--Logicians think they have defined substance and attribute, when they have shown merely what difference the use of them respectively makes in the grammar of a sentence. They say an attribute must be an attribute _of_ something, but that a substance is self-existent (being followed, if a relative, by _of_, not _qua_ substance, but _qua_ the relation). But this _of_, as distinguis.h.i.+ng 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 a.s.sociated 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. Noumena, 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 cla.s.s 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 ent.i.ty _per se_, called quality, is a relic of the scholastic _occult causes_; the only intelligible cause of sensation being the presence of the a.s.semblage 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 cla.s.s 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 a.n.a.lysed, 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 a.n.a.lysed 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 a.n.a.logy), we simply a.s.sert resemblance between the facts const.i.tuting 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 quant.i.ty, is often called ident.i.ty.

The _third_ species of attributes is Quant.i.ty. The a.s.sertion of likeness or unlikeness in quant.i.ty, 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.