198 REASONING. 



let us suppose it (with Mr. Spencer) to be the inconceivableness of its re- 

 verse. 



Let us now add a second step to the argument : we require, what ? An- 

 other 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 ax* 

 iom, the argument would no doubt be weakened, since it would be necessary 

 to its vaUdity 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 sup- 

 pose 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 ste2:)s in 

 an argument does not subtract from its reliableness, if no new pr6w^^ses, of 

 an uncertain character, are taken uj) 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 opin- 

 ion, 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 



* Mr. Spencer, in recently returning to the subject (Principles of Psychology, new edition, 

 chap. xii. : " The Test of lielative Validity"), makes two answers to the preceding remarks. 

 One is : 



"Were an argument formed by repeating the same proposition over and over again, it 

 would be true that any intrinsic fallibility 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 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 heterogeneous propositions, there is a risk, increasing as the number of propositions in- 

 creases, 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 premises to be taken in. The point we are discussing is 

 the fallibility not of the premises, but of tiie reasoning, as distinguished from the premises. 

 Now the validity of the reasoning 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, on the assumption that tliis axiom rests ultimately on the Universal Postulate, and 

 that, the Postulate not being wholly trustworthy, 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 

 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 speculations of an individual 

 reasoner ; and even witli respect to mankind at large, it must be admitted that, though mere 

 oversights in the syllogistic process, like errors of addition in an account, are special to the 

 individual, and seldom escape detection, confusion of thought produced (for example) by am- 

 biguous terms has led whole nations or ages to accept fallacious reasoning as valid. But this 

 very fact points to causes of error so much more dangerous than the mere length of the proc- 

 ess, as quite to vitiate the doctrine that the "test of the relative validities of conflicting con- 

 clusions " is the number of times the fundamental postulate is involved. On the contrary, the 

 subjects on which the trains of reasoning are longest, and the assumption, therefore, oftenest 

 lepeated, are in general those which are best fortified against the really formidable causes of 

 fallacy ; as in the example already given of mathematics. 



