62 COSMIC PIIILOSOrHY. [pt. i. 



It is o*ily in tins latter sense that the word "belief is em- 

 ployed in the canon of truth above stated, and when Mr. 

 Spencer says that a given proposition is inconceivable, he 

 means that it is one of which the subject and predicate can 

 by no amount of effort be united in consciousness. Thus 

 (to take Mr. Spencer's illustration), that a cannon-ball fired 

 from England will reach America is a proposition which, 

 though utterly incredible, is not inconceivable, — since it is 

 quite possible to imagine the projectile power of cannons 

 increased four-hundredfold, or one-thousandfold, were the 

 requisite conditions at hand; but that a certain triangle is 

 round is an inconceivable proposition, for the conceptions of 

 roundness and triangularity will destroy each other sooner 

 than be united in consciousness. And manifestly we can 

 have no deeper warrant for the truth of a proposition than 

 that the counter-proposition is one which the mind is incom- 

 petent to frame. Such a state of things implies that the 

 entire intercourse of the mind with the environment is 

 witness in favour of the proposition and against its negation. 

 It is indeed a popular misconception, — a misconception 

 which lies at the bottom of that manner of philosophizing 

 which is called Empiricism, — that nothing can be known to be 

 true which cannot be demonstrated. To be convinced that this 

 is a misconception, we need but to recollect what a demonstra- 

 tion is. Every demonstration consists, in the first place, of a 

 series of steps in each of which the group of relations expressed 

 in a proposition is included in some other and wider group of 

 relations, — is seen to be like some other group previously 

 constituted. Now if this process of inclusion is not to be 

 carried on for ever, we must come at last to some widest 

 group, — to some generalization which cannot be included in 

 any wider generalization, and of which we can only say that 

 the truth which it expresses is so completely abstracted from 

 perturbing conditions that it can be recognized by a simple 

 act of consciousness as self-evident. If, for example, "we 



