last part of this argument first. In factory that we are not obliged to every reasoning, according to Mr. suppose the deductions of pure matheSpencer, the assumption of the postu-matics to be among the most uncertain late is renewed at every step. At of argumentative processes, which on 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 present; let us suppose it (with Mr. Spencer) to be the inconceivableness of its reverse.

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.*

* Mr. Spencer, in recently returning to the subject, (Principles of Psychology, new edition, ch. xii., "The Test of Relative ceding remarks. One is : Validity,") makes two answers to the pre

"Were an argument formed by repeating it would be true that any intrinsic falli the same proposition over and over again, bility of the postulate would not make the conclusion more untrustworthy than the first step. But an argument consists of unlike propositions. Now since Mr. Mill's in some cases, which he names, it has proved to be an untrustworthy test, it follows that in any argument consisting of heterogeneous propositions, there is a risk, increasing as the number of propositions increases, that some one of them belongs to this class of cases, and is wrongly accepted because of the inconceivableness of its negation."

criticism on the Universal Postulate is that

No doubt: but this supposes new premises to be taken in. The point we are discussing is the fallibility not of the premises, but of premises. Now the validity of the reasonthe reasoning, as distinguished from the

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, therepetition of the assump-ing depends always upon the same axiom, tion 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 satis

* Mr. Spencer is mistaken in supposing me to claim any peculiar "necessity" for this axiom as compared with others. I have corrected the expressions which led him into that misapprehension of my meaning.

repeated (in thought) "over and over again," viz. that whatever has a mark, has what it is a mark of. Even, therefore, on the assumption that this axiom rests ultimately on the Universal Postulate, and that, the Postulate not being wholly trustof its failure; all the risk there is of this worthy, the axiom may be one of the cases is incurred at the very first step of the reasoning, and is not added to, however long may be the series of subsequent steps. I am here arguing, of course, from Mr. Spencer's point of view. From my own the case is still clearer; for, in my view, the truth that whatever has a mark has what it is a mark of, is wholly trustworthy, and derives none of its evidence from so very untrustworthy a test as the inconceivability of the negative.

Mr. Spencer's second answer is valid up to a certain point; it is, that every prolongation of the process involves additional chances of casual error, from carelessness in the reasoning operation. This is an important consideration in the private specu lations of an individual reasoner; and even with respect to mankind at large, it must

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.

To speak next of the premises. under side of the earth; but the Our assurance of their truth, whether belief would follow that they must they be generalities or individual fall off. Antipodes were not unimafacts, is grounded, in Mr. Spencer's ginable, but they were unbelievable. 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 always means an idea, never a belief. The wrong meaning of "inconceivable" is, In which of these two senses does however, fully as frequent in philo- Mr. Spencer employ the term, when sophical discussion as the right mean- he makes it a test of the truth of a ing, and the intuitive school of meta-proposition that its negation is inconphysicians could not well do without ceivable? Until Mr. Spencer exeither. To illustrate the difference, pressly stated the contrary, I inferred we will take two contrasted examples. from the course of his argument that The early physical speculators con- he meant unbelievable. He has, howsidered antipodes incredible, because ever, in a paper published in the fifth inconceivable. But antipodes were number of the Fortnightly Review, disnot inconceivable in the primitive claimed this meaning, and declared sense of the word. An idea of them that by an inconceivable proposition could be formed without difficulty: he means now and always, 66 one of they could be completely pictured to which the terms cannot, by any effort, the mental eye. What was difficult, be brought before consciousness in that and as it then seemed impossible, relation which the proposition asserts was to apprehend them as believable. between them--a proposition of which The idea could be put together of the subject and predicate offer an inmen sticking on by their feet to the surmountable resistance to union in be admitted that, though mere oversights thought." We now, therefore, know in the syllogistic process, like errors of positively that Mr. Spencer always addition in an account, are special to the endeavours to use the word inconceivindividual, and seldom escape detection, able in this, its proper sense: but it confusion of thought produced (for example) by ambiguous terms has led whole may yet be questioned whether his nations or ages to accept fallacious reason endeavour is always successful; wheing as valid. But this very fact points to ther the other, and popular use of the causes of error so much more dangerous word does not sometimes creep in than the mere length of the process, as quite to vitiate the doctrine that the "test with its associations, and prevent him of the relative validities of conflicting con- from maintaining a clear separation clusions" is the number of times the funda- between the two. When, for example, mental postulate is involved. On the contrary, the subject on which the trains of he says, that when I feel cold I canreasoning are longest, and the assumption not conceive that I am not feeling therefore, oftenest repeated, are in general cold, this expression cannot be transthose which are best fortified against the really formidable causes of fallacy; as in lated into "I cannot conceive myself the example already given of mathematics.not feeling cold," for it is evident that

M

I can the word conceive, therefore, this case every one will admit that is here used to express the recognition the impossibility is real. Any one's of a matter of fact-the perception of present sensations, or other states of truth or falsehood; which I apprehend subjective consciousness, that one perto be exactly the meaning of an act of son inevitably believes. They are belief, as distinguished from simple facts known per se: it is impossible conception. Again, Mr. Spencer calls to ascend beyond them. Their negathe attempt to conceive something tive is really unbelievable, and therewhich is inconceivable "an abortive fore there is never any question about effort to cause the non-existence" not believing it. Mr. Spencer's theory is of a conception or mental representa- not needed for these truths. tion, 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.* 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., 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 *Mr. Spencer makes a distinction between conceiving myself looking into darkness, and conceiving that I am then and there looking into darkness. To me it seems that this change of the expression to the form I am, just marks the transition from conception to belief, and that the phrase "to conceive that I am," or "that anything is," is not consistent with using the word "conceive" in its rigorous sense.

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 apprehend