HIS PHILOSOPHICAL POSITION 



or intelligence. It is not necessary to establish a 

 harmony between local visual signs and certain corre- 

 sponding positions in space, but there is a harmony 

 between the laws of representation and of thinking 

 and those of the outer world. 



Among the elementary propositions of geometry 

 there are some that are held not to require proof. 

 There are the axioms, such as, (i) if the shortest 

 line drawn between two points is called straight, 

 there can be only one straight line ; (2) through 

 any three points in space, not lying in a straight 

 line, a plane may be drawn, that is, a surface which 

 will include every straight line joining any two of 

 its points ; and (3) through a point lying without 

 a straight line only one straight line can be drawn 

 parallel to the first ; so that two straight lines that 

 lie in the same plane and never meet, however far 

 they may be produced, are called parallel. Again 

 there are such propositions as that a solid is bounded 

 by a surface, a surface by a line, and a line by a 

 point ; that the point is indivisible, that by the 

 movement of a point a line is described, by that of 

 a line a line or a surface, by that of a surface a 

 surface or a solid, and by the movement of a solid 

 a solid and nothing else is described. 1 The question 

 arises, how far results of experience have become mixed 

 up with logical processes ? Now, in problems of geo- 

 metrical construction, these axioms are true in all 



1 Mind, vol. i., p. 302. 

 26l 



