79 



functions of fixed structures that have become moulded into 

 correspondence with fixed outer relations." "Certain primary 

 space relations are presented to consciousness under the form 

 of necessary relations." "The truth that a straight line is the 

 shortest line between two points, lies latent in the structures 

 of the eyes and the nervous centres which receive and co- 

 ordinate visual impressions, We cannot think otherwise, 

 because, during the adjustment between the organism and the 

 environment which evolution has established, the inner re- 

 lations have been so moulded upon the outer relations that 

 they cannot, by any effort, be made not to fit them." In fact, 

 "just as it has become impossible for the hand to grasp by 

 bending the fingers outwards instead of inwards, so it has be- 

 come impossible for those nervous actions by which we appre- 

 hend primary space relations, to be reversed so as to enable 

 us to think of those relations otherwise than we do." 1 



Our experience, as it has been seen, is a register of objective 

 facts; and the inconceivableness of a thing implies that it is 

 wholly at variance with the register. While many of the facts 

 impressed upon us are occasional, and while others are more 

 general, some are universal and unchanging. These universal 

 and unchanging facts are certain to establish beliefs of which 

 the negations are inconceivable. "Subjective inconceivable- 

 ness corresponds to objective impossibility. Throughout the 

 great body of our consciousness, consisting as it does of things 

 presented from moment to moment under definite relations 

 of space, time, and number, the test of inconceivableness is 

 valid. Perpetually-repeated experiences have generated in us 

 cognitions of logical relations, mathematical relations, and 

 some simple physical relations, for the necessity of which the 

 inconceivableness of their negations is a guarantee unhesi- 

 tatingly accepted." 2 "Reasoning itself can be trusted only on 

 the assumption that absolute uniformities of Thought corre- 

 spond to absolute uniformities of Things." 3 



To conclude this short synopsis of Spencer's doctrine of the 

 necessary relations upon which mathematics is founded, the 

 following statement from his 'Principles of Ethics' will afford 

 us a brief expression of his whole standpoint on this subject. 

 In dealing with the axiom that "two straight lines cannot 

 enclose a space" Spencer states: "Unquestionably on the 

 Evolution-hypothesis this fixed intuition must have been 

 established by that intercourse with things which, throughout 

 an enormous past, has, directly or indirectly, determined the 



K).C. 332. 

 2O.C. 430. 

 3 O.C. 433. 



