§ 1. polemical discussion is foreign to the plan of this work. but an opinion which stands in need of much illustration, can often receive it most effectually, and least tediously, in the form of a defence against objections. and on subjects concerning which speculative minds are still divided, a writer does but half his duty by stating his own doctrine, if he does not also examine, and to the best of his ability judge, those of other thinkers.
in the dissertation which mr. herbert spencer has prefixed to his, in many respects, highly philosophical treatise on the mind,[39] he criticises some of the doctrines of the two preceding chapters, and propounds a theory of his own on the subject of first principles. mr. spencer agrees with me in considering axioms to be "simply our earliest inductions from experience." but he differs from me "widely as to the worth of the test of inconceivableness." he thinks that it is the ultimate test of all beliefs. he arrives at this conclusion by two steps. first, we never can have any stronger ground for believing anything, than that the belief of it "invariably exists." whenever any fact or proposition is invariably believed; that is, if i understand mr. spencer rightly, believed by all persons, and by oneself 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 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 [pg 295]or not." "for our primary beliefs, the fact of invariable existence, tested by an abortive effort to cause their non-existence, is the only reason assignable." he thinks this the sole ground of our belief in our own sensations. if i believe that i feel cold, i only receive this as true because i cannot conceive that i am not feeling cold. "while the proposition remains true, the negation of it remains inconceivable." there are numerous other beliefs which mr. spencer considers to rest on the same basis; being chiefly those, or a part of those, which the metaphysicians of the reid and stewart school consider as truths of immediate intuition. that there exists a material world; that this is the very world which we directly and immediately perceive, and not merely the hidden cause of our perceptions; that space, time, force, extension, figure, are not modes of our consciousness, but objective realities; are regarded by mr. spencer as truths known by the inconceivableness of their negatives. we cannot, he says, by any effort, conceive these objects of thought as mere states of our mind; as not having an existence external to us. their real existence is, therefore, as certain as our sensations themselves. the truths which are the subject of direct knowledge, being, according to this doctrine, known to be truths only by the inconceivability of their negation; and the truths which are not the object of direct knowledge, being known as inferences from those which are; and those inferences being believed to follow from the premises, 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 philosophers 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 any fault in the test itself, but because "men have mistaken for inconceivable things, some things which were not inconceivable." and he himself, in this very book, denies not a few propositions usually regarded as among the most marked examples [pg 296]of truths whose negations are inconceivable. but occasional failure, he says, is incident 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.
§ 2. the doctrine, that "a belief 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.
the positive argument is, that every such belief represents the aggregate of all past experience. "conceding the entire truth of" the "position, that during any phase of human progress, the ability or inability to form a specific conception wholly depends on the experiences men have had; and that, by a widening of their experiences, they may, by and by, be 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 [pg 297]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 must, absolute uniformities in our experience; and if ... these absolute uniformities in our experience disable us from conceiving the negations of them; then answering to each absolute uniformity in nature which we can cognize, 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 experience 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: even if it were true that inconceivableness represents "the net result" of all past experience, why should we stop at the representative when we can get at the thing represented? if our incapacity to conceive the negation of a given supposition is proof of its truth, because proving that our experience [pg 298]has hitherto been uniform in its favour, the real evidence for the supposition is not the inconceivableness, 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 experience is in favour of a belief, let 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 experience does amount to the strongest possible proof, as with such propositions as these, two straight lines cannot inclose a space, every event has a cause, it is not because their negations 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 phenomenon, often suffices to make every other mode appear inconceivable. whatever connects two ideas by a strong association may, and continually does, render their separation in thought impossible; as mr. spencer, in other parts of his speculations, frequently recognises. it was not for want of experience that the cartesians were unable to conceive [pg 299]that one body could produce motion in another without contact. they had as much experience of other modes of producing motion, as they had of that mode. the planets had revolved, and heavy bodies had fallen, every hour of their lives. but they fancied these phenomena to be produced by a hidden machinery which they did not see, because without it they were unable to conceive what they did see. the inconceivableness, instead of representing their experience, dominated and overrode their experience. it is needless to dwell farther on what i have termed the positive argument of mr. spencer in support of his criterion of truth. i pass to his negative argument, on which he lays more stress.
§ 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 systematization 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 similarly tested; or we synthetically ascend from such axiom or truth by such steps. in either case we connect some isolated belief, with a belief which invariably exists, by a series of intermediate beliefs which invariably exist." the following passage sums up the whole theory: "when we perceive that the negation of the belief is inconceivable, we have all possible warrant for asserting the invariability of its existence: and in asserting this, we express alike our logical justification of it, and the inexorable necessity we are under of holding it.... we have seen that this is the assumption on which every conclusion whatever ultimately rests. we have no other guarantee [pg 300]for the reality of consciousness, of sensations, of personal existence; we have no other guarantee for any axiom; we have no other guarantee for any step in a demonstration. hence, as being taken for granted in every act of the understanding, it must be regarded as the universal postulate." but as this postulate which we are under an "inexorable necessity" of holding true, is sometimes 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.
it will be convenient to take the last part of this argument first. in every reasoning, according to mr. spencer, the assumption of the postulate is renewed at every step. at each inference we judge that the conclusion follows from the premises, our sole warrant for that judgment being that we cannot conceive it not to follow. consequently if the postulate is fallible, the conclusions of reasoning are more vitiated by that uncertainty than direct intuitions; and the disproportion is greater, the more numerous the steps of the argument.
to test this doctrine, let us first suppose an argument consisting only of a single step, which would be represented by one syllogism. this argument does rest on an assumption, and we have seen in the preceding chapters what the assumption is. it is, that whatever has a mark, has what it is a mark of. the evidence of this axiom i shall not consider at [pg 301]present;[40] let us suppose it (with mr. spencer) to be the inconceivableness of its reverse.
let us now add a second step to the argument: we require, what? another assumption? no: the same assumption a second time; and so on to a third, and a fourth. i confess i do not see how, on mr. spencer's own principles, the repetition of the assumption at all weakens the force of the argument. if it were necessary the second time to assume some other axiom, the argument would no doubt be weakened, since it would be necessary to its validity that both axioms should be true, and it might happen that one was true and not the other: making two chances of error instead of one. but since it is the same axiom, if it is true once it is true every time; and if the argument, being of a hundred links, assumed the axiom a hundred times, these hundred assumptions would make but one chance of error among them all. it is satisfactory that we are not obliged to suppose the deductions of pure mathematics to be among the most uncertain of argumentative processes, which on mr. spencer's theory they could hardly fail to be, since they are the longest. but the number of steps in an argument does not subtract from its reliableness, if no new premises, of an uncertain character, are taken up by the way.
to speak next of the premises. our assurance of their truth, whether they be generalities or individual facts, is grounded, in mr. spencer's opinion, on the inconceivableness of their being false. it is necessary to advert to a double meaning of the word inconceivable, which mr. spencer is aware of, and would sincerely disclaim founding an argument upon, but from which his case derives no little advantage notwithstanding. by inconceivableness is sometimes meant, inability to form or get rid of an idea; sometimes, inability to form or get rid of a belief. the former meaning is the most conformable to the analogy of language; for a conception [pg 302]always means an idea, and never a belief. the wrong meaning of "inconceivable" is, however, fully as frequent in philosophical discussion as the right meaning, and the intuitive school of metaphysicians could not well do without either. to illustrate the difference, we will take two contrasted examples. the early physical speculators considered antipodes incredible, because inconceivable. but antipodes were not inconceivable in the primitive sense of the word. an idea of them could be formed without difficulty: they could be completely pictured to the mental eye. what was difficult, and as it then seemed, impossible, was to apprehend them as believable. the idea could be put together, of men sticking on by their feet to the under side of the earth; but the belief would follow, that they must fall off. antipodes were not unimaginable, but they were unbelievable.
on the other hand, when i endeavour to conceive an end to extension, the two ideas refuse to come together. when i attempt to form a conception of the last point of space, i cannot help figuring to myself a vast space beyond that last point. the combination is, under the conditions of our experience, unimaginable. this double meaning of inconceivable it is very important to bear in mind, for the argument from inconceivableness almost always turns on the alternate substitution of each of those meanings for the other.
in which of these two senses does mr. spencer employ the term, when he makes it a test of the truth of a proposition that its negation is inconceivable? until mr. spencer expressly stated the contrary, i inferred from the course of his argument, that he meant unbelievable. he has, however, in a paper published in the fifth number of the fortnightly review, disclaimed this meaning, and declared that by an inconceivable proposition he means, now and always, "one of which the terms cannot, by any effort, be brought before consciousness in that relation which the proposition asserts between them—a proposition of which the subject and predicate offer an insurmountable resistance to union in thought." we now, therefore, know positively that mr. spencer always endeavours to use the word inconceivable in this, its proper, sense: but it may yet be questioned whether his endeavour is [pg 303]always successful; whether the other, and popular use of the word does not sometimes creep in with its associations, and prevent him from maintaining a clear separation between the two. when, for example, he says, that when i feel cold, i cannot conceive that i am not feeling cold, this expression cannot be translated into, "i cannot conceive myself not feeling cold," for it is evident that i can: the word conceive, therefore, is here used to express the recognition of a matter of fact—the perception of truth or falsehood; which i apprehend to be exactly the meaning of an act of belief, as distinguished from simple conception. again, mr. spencer calls the attempt to conceive something which is inconceivable, "an abortive effort to cause the non-existence" not of a conception or mental representation, but of a belief. there is need, therefore, to revise a considerable part of mr. spencer's language, if it is to be kept always consistent with his definition of inconceivability. but in truth the point is of little importance; since inconceivability, in mr. spencer's theory, is only a test of truth, inasmuch as it is a test of believability. the inconceivableness of a supposition is the extreme case of its unbelievability. this is the very foundation of mr. spencer's doctrine. the invariability of the belief is with him the real guarantee. the attempt to conceive the negative, is made in order to test the inevitableness of the belief. it should be called, an attempt to believe the negative. when mr. spencer says that while looking at the sun a man cannot conceive that he is looking into darkness, he should have said that a man cannot believe that he is doing so. for it is surely possible, in broad daylight, to imagine oneself looking into darkness.[41] as mr. spencer himself says, speaking of the belief of our own existence: "that he might not exist, he can conceive well enough; but that he does not exist, he finds it impossible to conceive," i.e. [pg 304]to believe. so that the statement resolves itself into this: that i exist, and that i have sensations, i believe, because i cannot believe otherwise. and in this case every one will admit that the necessity is real. any one's present sensations, or other states of subjective consciousness, that one person inevitably believes. they are facts known per se: it is impossible to ascend beyond them. their negative is really unbelievable, and therefore there is never any question about believing it. mr. spencer's theory is not needed for these truths.
but according to mr. spencer there are other beliefs, relating to other things than our own subjective feelings, for which we have the same guarantee—which are, in a similar manner, invariable and necessary. with regard to these other beliefs, they cannot be necessary, since they do not always exist. there have been, and are, many persons who do not believe the reality of an external world, still less the reality of extension and figure as the forms of that external world; who do not believe that space and time have an existence independent of the mind—nor any other of mr. spencer's objective intuitions. the negations of these alleged invariable beliefs are not unbelievable, for they are believed. it may be maintained, without obvious error, that we cannot imagine tangible objects as mere states of our own and other people's consciousness; that the perception of them irresistibly suggests to us the idea of something external to ourselves: and i am not in a condition to say that this is not the fact (though i do not think any one is entitled to affirm it of any person besides himself). but many thinkers have believed, whether they could conceive it or not, that what we represent to ourselves as material objects, are mere modifications of consciousness; complex feelings of touch and of muscular action. mr. spencer may think the inference correct from the unimaginable to the unbelievable, because he holds that belief itself is but the persistence of an idea, and that what we can succeed in imagining, we cannot at the moment help apprehending as believable. but of what consequence is it what we apprehend at the moment, if the moment is in contradiction to the permanent state of our mind? a person who has been frightened when [pg 305]an infant by stories of ghosts, though he disbelieves them in after years (and perhaps disbelieved them at first), may be unable all his life to be in a dark place, in circumstances stimulating to the imagination, without mental discomposure. the idea of ghosts, with all its attendant terrors, is irresistibly called up in his mind by the outward circumstances. mr. spencer may say, that while he is under the influence of this terror he does not disbelieve in ghosts, but has a temporary and uncontrollable belief in them. be it so; but allowing it to be so, which would it be truest to say of this man on the whole—that he believes in ghosts, or that he does not believe in them? assuredly that he does not believe in them. the case is similar with those who disbelieve a material world. though they cannot get rid of the idea; though while looking at a solid object they cannot help having the conception, and therefore, according to mr. spencer's metaphysics, the momentary belief, of its externality; even at that moment they would sincerely deny holding that belief: and it would be incorrect to call them other than disbelievers of the doctrine. the belief therefore is not invariable; and the test of inconceivableness fails in the only cases to which there could ever be any occasion to apply it.
that a thing may be perfectly believable, and yet may not have become conceivable, and that we may habitually believe one side of an alternative, and conceive only in the other, is familiarly exemplified in the state of mind of educated persons respecting sunrise and sunset. all educated persons either know by investigation, or believe on the authority of science, that it is the earth and not the sun which moves: but there are probably few who habitually conceive the phenomenon otherwise than as the ascent or descent of the sun. assuredly no one can do so without a prolonged trial; and it is probably not easier now than in the first generation after copernicus. mr. spencer does not say, "in looking at sunrise it is impossible not to conceive that it is the sun which moves, therefore this is what everybody believes, and we have all the evidence for it that we can have for any truth." yet [pg 306]this would be an exact parallel to his doctrine about the belief in matter.
the existence of matter, and other noumena, as distinguished from the phenomenal world, remains a question of argument, as it was before; and the very general, but neither necessary nor universal, belief in them, stands as a psychological phenomenon to be explained, either on the hypothesis of its truth, or on some other. the belief is not a conclusive proof of its own truth, unless there are no such things as idola trib?s; but, being a fact, it calls on antagonists to show, from what except the real existence of the thing believed, so general and apparently spontaneous a belief can have originated. and its opponents have never hesitated to accept this challenge.[42] the amount of their success in meeting it will probably determine the ultimate verdict of philosophers on the question.
§ 4. 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 to conceive its possibility." "things there are which may, nay must, be true, of which the understanding is wholly unable to construe to itself the possibility."[43] 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 [pg 307]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, 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 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 phraseology 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 generalizations from experience. the original foundation [pg 308]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 generalization 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.[44] in the second place, though matter, considered as the occult cause of our sensations, do really exist, [pg 309]yet what we call divisibility may be an attribute only of our sensations of sight and touch, and not of their uncognizable 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 together; while to think of the non-existence 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 generalization 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."[45]
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.
