when 35 and 9 are really called up 66 As now limited by Mr. Spencer, before it; but this is not done. And the ultimate cognitions fit to be subnot only schoolboys, but men and mitted to his test are only those of so thinkers, do not always distinctly universal and elementary a character translate into their equivalent states as to be represented in the earliest of consciousness the words they use." and most unvarying experience, or It is but just to give Mr. Spencer's apparent experience, of all mankind. doctrine the benefit of the limitation In such cases the inconceivability of he claims, viz. that it is only applicable the negative, if real, is accounted for to propositions which are assented to by the experience: and why (I have on simple inspection, without any in- asked) should the truth be tested by tervening media of proof. But this the inconceivability, when we can go limitation does not exclude some of farther back for proof-namely, to the most marked instances of proposi- the experience itself? To this Mr. tions now known to be false or ground- Spencer answers, that the experiences less, but whose negative was once cannot be all recalled to mind, and if found inconceivable: such as, that in recalled, would be of unmanageable sunrise and sunset it is the sun which multitude. To test a proposition by moves; that gravitation may exist experience seems to him to inean that without an intervening mediumn; and "before accepting as certain the proeven the case of antipodes. The dis- position that any rectilineal figure tinction drawn by Mr. Spencer is real; must have as many angles as it has but, in the case of the propositions sides," I have "to think of every classed by him as complex, conscious- triangle, square, pentagon, hexagon, ness, until the media of proof are &c., which I have ever seen, and to supplied, gives no verdict at all: it verify the asserted relation in each neither declares the equality of the case. I can only say, with surprise, square of the hypothenuse with the that I do not understand this to be sum of the squares of the sides to be the meaning of an appeal to experiinconceivable, nor their inequality to ence. It is enough to know that one be inconceivable. But in all the three has been seeing the fact all one's life, cases which I have just cited, the in- and has never remarked any instance conceivability seems to be apprehended to the contrary, and that other people, directly; no train of argument was with every opportunity of observation, needed, as in the case of the square of the hypothenuse, to obtain the verdict my private opinion would be that he mis. took the nature of conception. Conception of consciousness on the point. Neither implies representation. Here the elements is any of the three a case like that of of the representation are the two bodies the schoolboy's mistake, in which the and an agency by which either affects the other. To conceive this agency is to remind was never really brought into present it in some terms derived from our contact with the proposition. They experiences-that is, from our sensations. are cases in which one of two opposite As this agency gives us no sensations, we predicates, mero adspectu, seemed to are obliged (if we try to conceive it) to use symbols idealised from our sensationsbe incompatible with the subject, and imponderable units forming a medium." the other, therefore, to be proved always to exist with it.* If Mr. Spencer means that the action of gravitation gives us no sensations, the assertion is one than which I have not seen, in the writings of philosophers, many more startling. What other sensation do we need than the sensation of one body moving towards another? "The elements of the are not two bodies and an agency, but two bodies and an effect, viz. the fact of their approaching one another. If we are able to conceive a vacuum, is there any difficulty in conceiving a body falling to the earth through it? * In one of the three cases, Mr. Spencer, to my no small surprise, thinks that the belief of mankind "cannot be rightly said to have undergone" the change I allege.representation Mr. Spencer himself still thinks we are unable to conceive gravitation acting through empty space. "If an astronomer vowed that he could conceive gravitative force as exercised through space absolutely void, " unanimously declare the same thing. | ceive A as not being C. After It is true, even this experience may assenting, with full understanding, be insufficient, and so it might be to the Copernican proof that it is the even if I could recall to mind every earth and not the sun that moves, I instance of it but its insufficiency, not only can conceive, or represent to instead of being brought to light, is myself, sunset as a motion of the sun, disguised, if, instead of sifting the but almost every one finds this conexperience itself, I appeal to a test ception of sunset easier to form than which bears no relation to the suffi- that which they nevertheless know to ciency of the experience, but, at the be the true one. most, only to its familiarity. These remarks do not lose their force even if we believe, with Mr. Spencer, that mental tendencies originally derived from experience impress themselves permanently on the cerebral structure and are transmitted by inheritance, so that modes of thinking which are acquired by the race become innate and à priori in the individual, thus representing, in Mr. Spencer's opinion, the experience of his progenitors, in addition to his own. All that would follow from this is, that a conviction might be really innate, i.e. prior to individual experience, and yet not be true, since the inherited tendency to accept it may have been originally the result of other causes than its truth. Mr. Spencer would have a much stronger case if he could really show that the evidence of Reasoning rests on the Postulate, or, in other words, that we believe that a conclusion follows from premises only because we cannot conceive it not to follow. But this statement seems to me to be of the same kind as one I have previously commented on, viz. that I believe I see light, because I cannot, while the sensation remains, conceive that I am looking into darkness. Both these statements seem to me incompatible with the meaning (as very rightly limited by Mr. Spencer) of the verb to conceive. To say that when I apprehend that A is B and that B is C, I cannot conceive that A is not C, is to my mind merely to say that I am compelled to believe that A is C. If to conceive be taken in its proper meaning, viz. to form a mental representation, I may be able to con § 5. Sir William Hamilton holds as I do, that inconceivability is no criterion of impossibility. There is no ground for inferring a certain fact to be impossible, merely from our inability toconceive its possibility." "Things there are which may, nay must, be true, of which the understanding is wholly unable to construe to itself the possibility.' Sir William Hamilton is, however, a firm believer in the à priori character of many axioms, and of the sciences deduced from them; and is so far from considering those axioms to rest on the evidence of experience, that he declares certain of them to be true even of Noumena-of the Unconditioned-of which it is one of the principal aims of his philosophy to prove that the nature of our faculties debars us from having any knowledge. The axioms to which he attributes this exceptional emancipation from the limits which confine all our other possibilities of knowledge; the chinks through which, as he represents, one ray of light finds its way to us from behind the curtain which veils from us the mysterious world of Things in themselves,-are the two principles which he terms, after the schoolmen, the Principle of Contradiction and the Principle of Excluded Middle: the first, that two contradictory propositions cannot both be true; the second, that they cannot both be false. Armed with these logical weapons, we may boldly face Things in themselves, and tender to them the double alternative, sure that they must absolutely elect one or the other side, * Discussions, &c., 2d ed. p. 624. though we may be for ever precluded from discovering which. To take his favourite example, we cannot conceive the infinite divisibility of matter, and we cannot conceive a minimum, or end to divisibility: yet one or the other must be true. As I have hitherto said nothing of the two axioms in question, those of Contradiction and of Excluded Middle, it is not unseasonable to consider them here. The former asserts that an affirmative proposition and the corresponding negative proposition cannot both be true; which has generally been held to be intuitively evident. Sir William Hamilton and the Germans consider it to be the statement in words of a form or law of our thinking faculty. Other philosophers, not less deserving of consideration, deem it to be an identical proposition, an assertion involved in the meaning of the terms; a mode of defining Negation, and the word Not. I am able to go one step with these last. An affirmative assertion and its negative are not two independent assertions, connected with each other only as mutually incompatible. That if the negative be true, the affirmative must be false, really is a mere identical proposition; for the negative proposition asserts nothing but the falsity of the affirmative, and has no other sense or meaning whatever. The Principium Contradictionis should therefore put off the ambitious phrase ology which gives it the air of a fundamental antithesis pervading nature, and should be enunciated in the simpler form, that the same proposition cannot at the same time be false and true. But I can go no farther with the Nominalists; for I cannot look upon this last as a merely verbal proposition. I consider it to be, like other axioms, one of our first and most familiar generalisations from experi ence. The original foundation of it I take to be, that Belief and Disbelief are two different mental states, excluding one another. This we know by the simplest observation of our own minds. And if we carry our observation outwards, we also find that light and darkness, sound and silence, motion and quiescence, equality and inequality, preceding and following, succession and simultaneousness, any positive phenomenon whatever and its negative, are distinct phenomena, pointedly contrasted, and the one always absent where the other is present. I consider the maxim in question to be a generalisation from all these facts. In like manner as the Principle of Contradiction (that one of two contradictories must be false) means that an assertion cannot be both true and false, so the Principle of Excluded Middle, or that one of two contradictories must be true, means that an assertion must be either true or false: either the affirmative is true, or otherwise the negative is true, which means that the affirmative is false. I cannot help thinking this principle a surprising specimen of a so called necessity of Thought, since it is not even true, unless with a large qualification. A proposition must be either true or false, provided that the predicate be one which can in any intelligible sense be attributed to the subject (and as this is always assumed to be the case in treatises on logic, the axiom is always laid down there as of absolute truth). "Abracadabra is a second intention" is neither true nor false. Between the true and the false there is a third possibility, the Unmeaning; and this alternative is fatal to Sir William Hamilton's extension of the maxim to Noumena. That Matter must either have a minimum of divisibility or be infinitely divisible, is more than we can ever know. For in the first place, Matter, in any other than the phenomenal sense of the term, may not exist; and it will scarcely be said that a non-entity must be either infinitely or finitely divisible. In the second place, though matter, considered as the occult cause of our sensations, do really exist, yet what we call divisibility may be an attri bute only of our sensations of sight and touch, and not of their uncognisable cause. Divisibility may not be predicable at all, in any intelligible sense, of Things in Themselves, nor therefore of Matter in itself; and the assumed necessity of being either infinitely or finitely divisible may be an inapplicable alternative. On this question I am happy to have the full concurrence of Mr. Herbert Spencer, from whose paper in the Fortnightly Review I extract the following passage. The germ of an idea identical with that of Mr. Spencer may be found in the present chapter, about a page back, but in Mr. Spencer it is not an undeveloped thought, but a philosophical theory. "When remembering a certain thing as in a certain place, the place and the thing are mentally represented toge ther; while to think of the non-exis tence of the thing in that place implies a consciousness in which the place is represented, but not the thing. Similarly, if instead of thinking of an object as colourless, we think of its having colour, the change consists in the addition to the concept of an element that was before absent from it-the object cannot be thought of first as red and then as not red, without one component of the thought being totally expelled from the mind by another. The law of the Excluded Middle, then, is simply a generalisation of the universal experience that some mental states are directly destructive of other states. It formulates a certain absolutely constant law, that the appearance of any positive mode of consciousness cannot occur without excluding a correlative negative mode; and that the negative mode cannot occur without excluding the correlative positive mode, the antithesis of positive and negative being, indeed, merely an expression of this experience. Hence it follows that if consciousness is not in one of the two modes it must be in the other.' I must here close this supplementary chapter, and with it the Second Book. The Theory of Induction, in the most comprehensive sense of the term, will form the subject of the Third. Professor Bain (Logic, i. 16) identifies the Principle of Contradiction with his Law of Relativity, viz. that "everything that can be thought of, every affirmation that can be made, has an opposite or a propocounter notion or affirmation; sition which is one of the general results of the whole body of human experience. For further considerations respecting the axioms of Contradiction and Excluded An Examination of Sir William Hamilton's Middle, see the twenty-first chapter of Philosophy. BOOK III. OF INDUCTION. "According to the doctrine now stated, the highest, or rather the only proper object of physics, is to ascertain those established conjunctions of successive events, which constitute the order of the universe; to record the phenomena which it exhibits to our observation or which it discloses to our experiments; and to refer these phenomena to their general laws."-D. STEWART, Elements of the Philosophy of the Human Mind, vol. ii. chap. iv. sect. 1. CHAPTER I. PRELIMINARY OBSERVATIONS ON INDUCTION IN GENERAL. SI. THE portion of the present inquiry upon which we are now about to enter may be considered as the principal, both from its surpassing in intricacy all the other branches, and because it relates to a process which has been shown in the preceding Book to be that in which the investigation of nature essentially consists. We have found that all Inference, consequently all Proof, and all discovery of truths not self-evident, consists of inductions, and the interpretation of inductions; that all our knowledge, not intuitive, comes to us exclusively from that source. What Induction is, therefore, and what conditions render it legitimate, cannot but be deemed the main question of the science of logic-the question which includes all others. It is, however, one which professed writers on logic have almost entirely passed The generalities of the subject Over. have not been altogether neglected by metaphysicians; but, for want of sufficient acquaintance with the processes by which science has actually succeeded in establishing general truths, their analysis of the inductive operation, even when unexceptionable as to correctness, has not been specific enough to be made the foundation of practical rules, which might be for induction itself what the rules of the syllogism are for the interpretation of induction; while those by whom physical science has been carried to its present state of improvementand who, to arrive at a complete theory of the process, needed only to generalise, and adapt to all varieties of problems, the methods which they themselves employed in their habitual pursuits-never until very lately made any serious attempt to philosophise on the subject, nor regarded the mode in which they arrived at their conclusions as deserving of study, independently of the conclusions themselves. § 2. For the purposes of the present |