1^6 



REASONING. 



last part of this argument first. In 

 every reasoning, according to Mr. 

 Spencer, the assumption of the postu- 

 late is renewed at every step. At 

 each inference we judge that the con- 

 clusion follows from the premises, our 

 sole warrant for that judgment being 

 that we cannot conceive it not to follow. 

 Consequently if the postulate is fal- 

 lible, the conclusions of reasoning are 

 more vitiated by that uncertainty 

 than direct intuitions ; and the dispro- 

 portion 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 repre- 

 sented by one syllogism. This argu- 

 ment 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. 



Let us now add a second step to the 

 argument: we require, what? Another 

 assumption ? No : the same assump- 

 tion 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- 

 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 neces- 

 sary 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 assump- 

 tions 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 



factory that we are not obliged to 

 suppose the deductions of pure mathe- 

 matics 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.* 



* Mr. Spencer, in recently returning to 

 the subject, (Principles of Psychology, new 

 edition, ch. xiL, "The Test of Relative 

 Validity,") makes two answers to the pre- 

 ceding remarks. One is : 



" Were an argument formed by repeating 

 the same proposition over and over again, 

 it would be true that any intrinsic falli- 

 bility of the postulate would not make the 

 conclusion more untrustworthy than tho 

 first step. But an argument consists of un- 

 like propositions. Now since Mr. Mill's 

 criticism on the Universal Postulate is that 

 in some cases, which he names, it has proved 

 to be an untrustworthy test, it follows 

 that in any argument consisting of hete- 

 rogeneous propositions, there is a risk, in- 

 creasing 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." 



No doubt : but this supposes new premise 

 to be taken in. The point we are discussing 

 is the fallibility not of the premises, but of 

 the reasoning, as distinguished from the 

 premises. Now the validity of the reason- 

 ing depends always upon the same axiom, 

 repeated (in thought) " over and over 

 again," viz. that whatever has a mark, has 

 what it is a mark of. Even, therefore, ou 

 the assumption that this axiom rests ulti- 

 mately on the Universal Postulate, and 

 that, the Postulate not being wholly trust- 

 worthy, the axiom may be one of the cases 

 of its failure ; all the risk there is of this 

 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 inconceiv- 

 ability of the negative. 



Mr. Spencer's second answer is valid up 

 to a certain point ; it is, that every pro- 

 longation of the process involves additional 

 chances of casual error, fiom carelessness 

 in the reasoning operation. This is an im- 

 portant consideration in the private specu- 

 lations of an individual reasouer ; and even 

 with respect to mankind at large, it must 



