ch. in.] THE TEST OF TRUTH. 61 



validity whatever, some further explanation is desirable. It 

 must not be supposed that, in erecting such a canon of truth, 

 we arc imitating those high a priori metaphysicians, who 

 regard all their cherished traditional notions as infallible in- 

 tuitions, because of their professed inability to disbelieve them. 

 This is a confusion of which Mr. Mill has not succeeded in 

 keeping clear, and which has led him unintentionally to mis- 

 represent the position taken by Mr. Spencer and Mr. Lewes. 

 The confusion arises from the double sense of the word belief* 

 and the accompanying ambiguous use of the term inconceiv- 

 able. By a singular freak of language we use the word belief 

 to designate both the least persistent and the most persistent 

 coherence among our states of consciousness, — to describe our' 

 state of mind with reference both to those propositions of the 

 truth of which we are least certain, and to those of the truth 

 of which we are most certain. We apply it to states of mind 

 which have nothing in common, except that they cannot be 

 justified by a chain of logical proofs. For example, you believe, 

 perhaps, that all crows are black, but being unable to furnish 

 absolutely convincing demonstration of the proposition, you 

 say that you believe it, not that you know it. You also 

 believe in your own personal existence, of which, however, 

 you can furnish no logical demonstration, simply because it 

 is an ultimate fact in your consciousness which underlies 

 and precedes all demonstration. So with the axioms of 

 geometry. If asked what are our grounds for believing that 

 two straight lines cannot enclose a space, we can only reply 

 that the counter-proposition is inconceivable; that we cannot 

 frame the conception of two straight lines enclosing a space ; 

 mat in any attempt to do so, the conception of straight lines 

 disappears and is replaced by the conception of bent lines. 

 We believe the axiom simply because we must believe it. 



4 The source of this confusion is the failure to distinguish between the 

 kind uf belief which remains after " the reduction of inferences to sensa- 

 tions," and that which is founded in a "reliance on unverified inferences."— 

 Be* Lewis, Problems of Life and Mind, vol. i. p. 369. 



