cluded if we find, and in proportion as we find, the assumptions to be truemay be performed once for all, and the results held ready to be employed as the occasions turn up for use. We thus do all beforehand that can be so done, and leave the least possible work to be performed when cases arise and press for a decision. This inquiry into the inferences which can be drawn from assumptions is what properly constitutes Demonstrative Science. It is of course quite as practicable to arrive at new conclusions from facts assumed, as from facts observed; from fictitious, as from real, inductions. Deduction, as we have seen, consists of a series of inferences in this form--a is a mark of b, b of c, c of d, therefore a is a mark of d, which last may be a truth inaccessible to direct observation. In like manner it is allowable to say, suppose that a were a mark of b, b of c, and c of d, a would be a mark of d, which last conclusion was not thought of by those who laid down the premises. A system of propositions as complicated as geometry might be deduced from assumptions which are false; as was done by Ptolemy, Descartes, and others, in their attempts to explain synthetically the phenomena of the solar system on the supposition that the apparent motions of the heavenly bodies were the real motions, or were produced in some way inore or less different from the true one. Some times the same thing is knowingly done for the purpose of showing the falsity of the assumption; which is called a reductio ad absurdum. In such cases the reasoning is as follows a is a mark of b, and b of c; now if c were also a mark of d, a would be a mark of d; but d is known to be a mark of the absence of a; consequently a would be a mark of its own absence, which is a contradiction; therefore c is not a mark of d. § 5. It has even been held by some writers that all ratiocination rests in the last resort on a reductio ad ab surdum, since the way to enforce assent to it, in case of obscurity, would be to show that if the conclusion be denied we must deny some one at least of the premises, which, as they are all supposed true, would be a contradiction. And in accordance with this, many have thought that the peculiar nature of the evidence of ratiocination consisted in the impossibility of admitting the premises and rejecting the conclusion without a contradiction in terms. This theory, however, is admissible as an explanation of the grounds on which ratiocination itself rests. If any one denies the conclusion notwithstanding his admission of the premises, he is not involved in any direct and express contradiction until he is compelled to deny some premise; and he can only be forced to do this by a reductio ad absurdum, that is, by another ratiocination: now, if he denies the validity of the reasoning process itself, he can no more be forced to assent to the second syllogism than to the first. In truth, therefore, no one is ever forced to a contradiction in terms: he can only be forced to a contradiction (or rather an infringement) of the funda mental maxim of ratiocination, namely, that whatever has a mark, has what it is a mark of; or, (in the case of universal propositions,) that whatever is a mark of anything, is a mark of whatever else that thing is a mark of. For in the case of every correct argument, as soon as thrown into the syllogistic form, it is evident without the aid of any other syllogism, that he who, admitting the premises, fails to draw the conclusion, does not conform to the above axiom. We have now proceeded as far in the theory of Deduction as we can advance in the present stage of our inquiry. Any further insight into the subject requires that the foundation shall have been laid of the philosophic theory of Induction itself; in which theory that of Deduction, as a mode of Induction, which we have now shown it to be, will assume spontane ously the place which belongs to it, and will receive its share of whatever light may be thrown upon the great intellectual operation of which it forms so important a part. CHAPTER VII. believed to be true is our inability to conceive it as false. "The inconceivability of its negation is the test by which we ascertain whether a given belief invariably exists or not." "For our primary beliefs, the fact of invariable existence, tested by an abortive effort to cause their nonexistence, is the only reason assignable." He thinks this the sole ground EXAMINATION OF SOME OPINIONS OP- of our belief in our own sensations. POSED TO THE PRECEDING DOC- If I believe that I feel cold, I only receive this as true because I cannot § 1. POLEMICAL discussion is foreign conceive that I am not feeling cold. to the plan of this work. But an "While the proposition remains true, opinion which stands in need of much the negation of it remains inconceivillustration can often receive it most able." There are numerous other beeffectually, and least tediously, in the liefs which Mr. Spencer considers to form of a defence against objections. rest on the same basis, being chiefly And on subjects concerning which those, or a part of those, which the speculative minds are still divided, a metaphysicians of the Reid and writer does but half his duty by Stewart school consider as truths of stating his own doctrine, if he does not immediate intuition. That there exalso examine, and to the best of his ists a material world; that this is the ability judge, those of other thinkers. very world which we directly and imIn the dissertation which Mr. mediately perceive, and not merely the Herbert Spencer has prefixed to his, hidden cause of our perceptions; that in many respects, highly philosophical Space, Time, Force, Extension, Figure, treatise on the mind,* he criticises are not modes of our consciousness, some of the doctrines of the two pre- but objective realities; are regarded ceding chapters, and propounds a by Mr. Spencer as truths known by theory of his own on the subject of the inconceivableness of their negafirst principles. Mr. Spencer agrees tives. We cannot, he says, by any with me in considering axioms to be effort, conceive these objects of thought 'simply our earliest inductions from as mere states of our mind; as not experience." But he differs from me having an existence external to us. widely as to the worth of the test of Their real existence is, therefore, as inconceivableness." He thinks that certain as our sensations themselves. it is the ultimate test of all beliefs. The truths which are the subject of He arrives at this conclusion by two direct knowledge, being, according to steps. First, we never can have any this doctrine, known to be truths only stronger ground for believing anything by the inconceivability of their negathan that the belief of it "invariably tion, and the truths which are not exists." Whenever any fact or pro- the object of direct knowledge, being position is invariably believed that known as inferences from those which is, if I understand Mr. Spencer rightly, are: and those inferences being bebelieved by all persons, and by one-lieved to follow from the premises self at all times it is entitled to be received as one of the primitive truths or original premises of our knowledge. Secondly, the criterion by which we decide whether anything is invariably 66 66 *Principles of Psychology. only because we cannot conceive them not to follow, inconceivability is thus the ultimate ground of all assured beliefs. Thus far there is no very wide difference between Mr. Spencer's doctrine and the ordinary one of philo. A which is proved by the inconceivableness of its negation to invariably exist is true," Mr. Spencer enforces by two arguments, one of which may be distinguished as positive, and the other as negative. sophers of the intuitive school, from Descartes to Dr. Whewell; but at this point Mr. Spencer diverges from them. For he does not, like them, set up the test of inconceivability as infallible. On the contrary, he holds that it may be fallacious, not from The positive argument is, that every any fault in the test itself, but because such belief represents the aggregate "men have mistaken for inconceivable of all past experience. Conceding things some things which were not the entire truth of" the "position, inconceivable." And he himself, in that during any phase of human prothis very book, denies not a few pro- gress, the ability or inability to form positions usually regarded as among a specific conception wholly depends the most marked examples of truths on the experiences men have had; whose negations are inconceivable. and that, by a widening of their exBut occasional failure, he says, is in-periences, they may, by and by, be cident to all tests. If such failure vitiates "the test of inconceivableness," it "must similarly vitiate all tests whatever. We consider an inference logically drawn from established premises to be true. Yet in millions of cases men have been wrong in the inferences they have thought thus drawn. Do we therefore argue that it is absurd to consider an inference true on no other ground than that it is logically drawn from established premises? No: we say that though men may have taken for logical inferences inferences that were not logical, there nevertheless are logical inferences, and that we are justified in assuming the truth of what seem to us such, until better instructed. Similarly, though men may have thought some things inconceivable which were not so, there may still be inconceivable things; and the inability to conceive the negation of a thing may still be our best warrant for believing it. Though occasionally it may prove an imperfect test, yet, as our most certain beliefs are capable of no better, to doubt any one belief because we have no higher guarantee for it is really to doubt all beliefs." Mr. Spencer's doctrine, therefore, does not erect the curable, but only the incurable limitations of the human conceptive faculty into laws of the outward universe. enabled to conceive things before inconceivable to them, it may still be argued that as, at any time, the best warrant men can have for a belief is the perfect agreement of all pre-existing experience in support of it, it follows that, at any time, the inconceivableness of its negation is the deepest test any belief admits of. . . Objective facts are ever impressing themselves upon us; our experience is a register of these objective facts; and the inconceivableness of a thing implies that it is wholly at variance with the register. Even were this all, it is not clear how, if every truth is primarily inductive, any better test of truth could exist. But it must be remembered that whilst many of these facts impressing themselves upon us are occasional, whilst others again are very general, some are universal and unchanging. These universal and unchanging facts are, by the hypothesis, certain to establish beliefs of which the negations are inconceivable; whilst the others are not certain to do this; and if they do, subsequent facts will reverse their action. Hence if, after an immense accumulation of experiences, there remain beliefs of which the negations are still inconceivable, most, if not all of them, must correspond to universal objective facts. If there be . . . certain absolute uniformities in nature; if these uniformities produce, as they § 2. The doctrine that "a belief must, absolute uniformities in our ex truth, because proving that our experience has hitherto been uniform in its favour, the real evidence for the supposition is not the inconceivable. ness, but the uniformity of experience. Now this, which is the substantial and only proof, is directly accessible. We are not obliged to presume it from an incidental consequence. If all past perience; and if . . . these absolute of a given supposition is proof of its uniformities in our experience disable us from conceiving the negations of them; then answering to each absolute uniformity in nature which we can cognise, there must exist in us a belief of which the negation is inconceivable, and which is absolutely true. In this wide range of cases subjective inconceivableness must correspond to objective impossibility. Further ex-experience is in favour of a belief, let perience will produce correspondence where it may not yet exist; and we may expect the correspondence to become ultimately complete. In nearly all cases this test of inconceivableness must be valid now "-(I wish I could think we were so nearly arrived at omniscience)" and where it is not, it still expresses the net result of our experience up to the present time; which is the most that any test can do." To this I answer, first, that it is by no means true that the inconceivability, by us, of the negative of a proposition proves all, or even any, "pre-existing experience to be in favour of the affirmative. There may have been no such pre-existing experiences, but only a mistaken supposition of experience. How did the inconceivability of antipodes prove that experience had given any testimony against their possibility? How did the incapacity men felt of conceiving sunset otherwise than as a motion of the sun, represent any "net result of experience in support of its being the sun and not the earth that moves? It is not experience that is represented, it is only a superficial resemblance of experience. The only thing proved with regard to real experience is the negative fact that men have not had it of the kind which would have made the inconceivable proposition conceivable. Next Even if it were true that inconceivableness represents the net result of all pastexperience, why should we stop at the representative when we can get at the thing represented? If our incapacity to conceive the negation this be stated, and the belief openly rested on that ground: after which the question arises, what that fact may be worth as evidence of its truth? For uniformity of experience is evidence in very different degrees: in some cases it is strong evidence, in others weak, in others it scarcely amounts to evidence at all. That all metals sink in water, was an uniform experience, from the origin of the human race to the discovery of potassium in the present century by Sir Humphry Davy. That all swans are white, was an uniform experience down to the discovery of Australia. In the few cases in which uniformity of ex. perience does amount to the strongest possible proof, as with such propositions as these, Two straight lines cannot enclose a space, Every event has a cause, it is not because their nega tions are inconceivable, which is not always the fact, but because the experience, which has been thus uniform, pervades all nature. It will be shown in the following Book that none of the conclusions either of induction or of deduction can be considered certain, except as far as their truth is shown to be inseparably bound up with truths of this class. I maintain then, first, that uniformity of past experience is very far from being universally a criterion of truth. But, secondly, inconceivableness is still farther from being a test even of that test. Uniformity of contrary experience is only one of many causes of inconceivability. Tradition handed down from a period of more limited knowledge is one of the commonest. The mere familiarity of one mode of production of a pheno- | similarly tested; or we synthetically menon often suffices to make every ascend from such axiom or truth by other mode appear inconceivable. such steps. In either case we connect Whatever connects two ideas by a some isolated belief with a belief strong association may, and conti- which invariably exists by a series of nually does, render their separation intermediate beliefs which invariably in thought impossible; as Mr. Spencer exist.' The following passage sums in other parts of his speculations fre- up the theory: "When we perceive quently recognises. It was not for that the negation of the belief is inconwant of experience that the Cartesians ceivable, we have all possible warrant were unable to conceive that one body for asserting the invariability of its could produce motion in another with- existence; and in asserting this, we out contact. They had as much ex- express alike our logical justification perience of other modes of producing of it, and the inexorable necessity we motion as they had of that mode. are under of holding it. . . . . We The planets had revolved, and heavy have seen that this is the assumption bodies had fallen, every hour of their on which every conclusion whatever lives. But they fancied these pheno- ultimately rests. We have no other mena to be produced by a hidden guarantee for the reality of consciousmachinery which they did not see, ness, of sensations, of personal existbecause without it they were unable ence; we have no other guarantee for to conceive what they did see. The any axiom; we have no other guarinconceivableness, instead of represent- antee for any step in a demonstration. ing their experience, dominated and Hence, as being taken for granted in overrode their experience. Without every act of the understanding, it dwelling further on what I have must be regarded as the Universal termed the positive argument of Mr. Postulate." But as this postulate Spencer in support of his criterion of which we are under an "inexorable truth, I pass to his negative argument, necessity" of holding true, is someon which he lays more stress. times false; as "beliefs that once were shown by the inconceivableness of their negations to invariably exist have since been found untrue," and as "beliefs that now possess this character may some day share the same fate; the canon of belief laid down by Mr. Spencer, is, that "the most certain conclusion" is that "which involves the postulate the fewest times." Reasoning, therefore, never ought to prevail against one of the immediate beliefs, (the belief in Matter, in the outward reality of Extension, Space, and the like,) because each of these involves the postulate only once; while an argument, besides involving it in the premises, involves it again in every step of the ratiocination, no one of the successive acts of inference being recognised as valid except because we cannot conceive the conclusion not to follow from the premises. § 3. The negative argument is, that, whether inconceivability be good evidence or bad, no stronger evidence is to be obtained. That what is inconceivable cannot be true is postulated in every act of thought. It is the foundation of all our original premises. Still more it is assumed in all conclusions from those premises. The invariability of belief, tested by the inconceivableness of its negation, "is our sole warrant for every demonstration. Logic is simply a systematisation of the process by which we indirectly obtain this warrant for beliefs that do not directly possess it. To gain the strongest conviction possible respecting any complex fact, we either analytically descend from it by successive steps, each of which we unconsciously test by the inconceivableness of its negation, until we reach some axiom or truth which we have It will be convenient to take the |