THEORIES CONCERNING AXIOMS. 197 



§ 3. The negative argument is, that, whether inconceivability be good 

 evidence or bad, no stronger evidence is to be obtained. That what is in- 

 conceivable can not 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 demon- 

 stration. Logic is simply a systematization of the process by which we in- 

 dii-ectly obtain this warrant for beliefs that do not directly possess it. To 

 gain the strongest conviction possible respecting any complex fact, we ei- 

 ther analytically descend from it by successive steps, each of which we un- 

 consciously 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 theory : " When we perceive that the negation of the belief is in- 

 conceivable, we have all possible warrant for asserting the invariability of 

 its existence : and in asserting this, we exjjress alike our logical justifica- 

 tion of it, and the inexorable necessity we are under of holding it 



We have seen that this is the assumption on which every conclusion what- 

 ever ultimately rests. We have no other guarantee for the reality of con- 

 sciousness, of sensations, of personal existence ; we have no other guaran- 

 tee for any axiom ; we have no other guarantee for any step in a demon- 

 stration. Hence, as being taken for granted in every act of the under- 

 standing, it must be regarded as the Universal Postulate," But as this 

 postulate, which we are under an " inexorable necessity " of holding true, i^ 

 sometimes false; as "beliefs that once were shown by the inconceivable- 

 ness 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 recognized as valid except because we can hot conceive the conclu- 

 sion not to follow from the premises. 



It will be convenient to take the last part of this argument first. In ev- 

 ery 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 can not conceive it not to follow. Consequently if the postulate is fal- 

 lible, the conclusions of reasoning are more vitiated by that uncertainty 

 tlian 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 

 I single step, which would be represented by one syllogism. This argu- 

 nent does rest on an assumption, and we have seen in the preceding chap- 

 ers what the assumption is. It is, that whatever has a mark, has what it 

 s a mark of. The evidence of this axiom I shall not consider at present ;* 



* Mr. Spencer is mistaken in supposing me to claim any peculiar " necessity " for this ax- 

 om as compared with others. I have corrected the expressions which led him into that mis- 

 pprehension of my meaning. 



