FOR THE LOGIf (»F Ml ri\E8. 7 



It follows from what has been said that for every pro] sitton in geom«n v then is 

 a proposition in the pure logic of relatives. But the method of working \ th I :ica) 

 algebra which is founded on this principle seems to be of little us. On the ot r 

 hand, the fact promises to throw some light upon the phil< ophy of -pace* 





Properties of Partutlar Bsuxivg Terms 



Classification of Shu pie Relative. 



Any particular property which any class of relative terms may have may be ittted 

 in the form of an equation, and affords us another premise for the solution of problems 



in which such terms occur. A good classification of relatives is, therefore, a great aid 



in the use of this notation, as the notation is also an aid in forming luch i\ Has ii- 

 cation. 



The first division of relatives is, of course, into simple relatifii and conjugatifw 

 The most fundamental divisions of simple relative are based on the distinction 



Kpioe* Vqt them 





lines 



:ed, 



supposition are inconsistent with supposing space to retain its present nature and the properties nly of the thinge in i 

 to change. For example, in Lobatchewsky's geometry a star at an infinite distance has a finite parallax. But rap]*** 

 space to have its present properties, and suppose that there were one point in the universe towards which anything being 

 moved should expand, and away from which being moved should contract. Then this expansion and contraction m 



tuber 



it distance. I have not seen Beltrami's investigations, 

 possible. Tim, it may be that, make what iq>p<*itioi 



you 



present 



tradictions. If this is so, — and whether it is or not is a completely open question 



» 



the principles of geometry 

 ondi tii of cogni »n in 



general. In speaking 



psycholog 



distinction between principles which, if the facts should present a sufficient difficulty, I may alway. logically <lo« aod 



continue 



to be supposed in all logical procedure. 



spies 



uaUy believed to be axiomatkai is conceivably false. That f 

 does not destroy all important practical distinction between 



t« ki„d S of necessity. It .nay be said that if Lobatcbewsk/s geometry k the true on,, .ben -pace «*. - -^ 



constant, trbicb value cannot be given a priori. Tbi, -V be i bn. k n»y be .ba. ,be genera p**.* +*-* 

 tbe „„„a, ft* .Hat. ,.,,ee» i. S „cb a constant, are . prion, .bile .be value of «bo consUn. ,. only etnptncHy denned. 



K 



osophy of space, which is a logical 

 logic of relatives. 



