OF SPACE. 65 



the world can be limited. For it is equally difficult 

 to treat of '' Space " apart from that which fills it, i.e. 

 Matter, and to neglect this distinction. If Space = 

 the spatially-extended, then the infinite extent and 

 divisibility of Space must apply to Matter, i.e. atoms 

 and limits of the material universe are Impossible. 

 If, on the other hand, Space is distinguished from 

 that which fills it, we not only seem to be making a 

 false abstraction, inasmuch as Space is never pre- 

 sented to us except as filled by Matter, but to com- 

 mit ourselves to the existence of the Void or empty 

 space, existing certainly between the interstices of 

 the atoms, and probably beyond the limits of the 

 universe. But empty Space, possessing no qualities 

 by which it could possibly be cognizable, is a thing 

 in no way distinguishable from nothing, i.e. a non- 

 entity. And further, if Space be not identified 

 with the spatially extended, how do we know that 

 the properties of Space hold good of the spatially- 

 extended, i.e. that bodies obey the laws prescribed 

 for them by mathematics } 



And even when Space has been distinguished 

 from that which fills it, it seems necessary to dis- 

 tinguish afresh between real Space which we per- 

 ceive and ideal or conceptual Space, about which 

 we reason in mathematics. For they differ on the 

 important point of infinity : real Space is not in- 

 finite, for nothing infinite can be perceived. In- 

 finity, on the other hand, is the most prominent 

 attribute of Ideal Space. And so their other pro- 

 perties also might be different, e.g. all the lines drawn 

 in real Space might really be closed curves, owing 

 to an inherent curvature of Space, etc. If, then, 

 ideal Space and real Space are different, a serious 

 difficulty arises for mathematics, for they deal with 



R. ofS. 



