ii USELESS KNOWLEDGE 33 



the eternal truths of mathematics and the like one may 

 surely affirm that they necessarily exist for all intelli 

 gences ? 



Even this is more than I can grant you. 



How so ? 



They seem to me to be also relative to us ; nay, 

 human institutions of the plainest kind. 



Is it not self-evident and absolutely certain that the 

 straight line is the shortest between two points ? 



That is our definition of distance. It will do in the 

 sense in which you use it, if I may add, &quot; for one living 

 in a spatial world which behaves like ours, and apparently 

 yours, once he has succeeded in postulating a system of 

 geometry which suits his world.&quot; 



I really do not understand you. 



I fear I have not the space to explain myself, and to 

 show you the practical aim of our assumptions concerning 

 &quot; Space,&quot; even if I dared to discuss the foundations of 

 geometry in the presence of Plato. But it really does 

 not affect my point. What I desire to maintain is that 

 the eternal truths are at bottom postulates, demands we 

 make upon our experience because we need them in order 

 that it may become a cosmos fit to live in. 



But I do not find myself postulating them at all. 

 They are plainly self-evident and axiomatic. 



That is only because your axioms are postulates so 

 ancient and so firmly rooted that no one now thinks of 

 disputing them. 



Your doctrine seems as monstrous as it is unfamiliar. 



I can neither help that nor establish it fully at this 

 juncture. Perhaps, if the gods are willing, I shall find 

 another occasion l to expound to you the proofs of this 

 doctrine, and even, if the gods are gracious, to convince 

 you. For it seems to me that in a manner you already 

 admit the principle of my doctrine. 



It would greatly surprise me if I did. 



You contend, do you not, that concerning ethical 

 matters it is impossible to have the right opinion without, 



1 See Axioms as Postulates. 



