INFINITY A FALSE ABSTRACTION. 25 I 



contradicts some of the chief conceptions of our 

 thought, and that of Time even contradicts itself 

 (ch. iii. § 6). The infinity of Space conflicts with the 

 conception of the world as a whole, the infinity of 

 Time with that of the world as a process, and as has 

 been already shown (ch. vii. §§ 3, 20), all evolutionist 

 or historic methods imply that Time is limited and 

 that the world had a beginning. Lastly, the in- 

 finity of the world involves a reductio ad absurdum 

 of the category of causation. 



And, of course, these metaphysical difficulties 

 about the infinity of Space and Time reappear in 

 science, and generate conflicts between the principal 

 and most approved scientific doctrines and this 

 alleged infinity. It is not merely that science knows 

 nothing of anything infinite, but that it is in various 

 ways compelled to assert that infinity is directly 

 incompatible with verified knowledge. It is neces- 

 sary, therefore, to give a sketch of these objections. 



§ 7. We are too apt, in the first place, to forget 

 that " Space " and '* Time " are mere abstractions. 

 We speak as though things were plunged in Space 

 and Time, and as if Space and Time could exist 

 without them. But as a matter of fact Space and 

 Time are constituted by things, and are only two 

 prominent aspects of their interaction. It is as the 

 result of the attractions and repulsions of things 

 that they constitute certain spaces between one 

 another. Empty Space and empty Time are bogies 

 which we have no business to conjure up out of the 

 limbo of vain imaginings. Hence there is no real 

 difficulty in conceiving (with Aristotle) that Space 

 should be limited by the spatially-extended, i.e. 

 bodies, seeing that the conception has no meaning 

 except in connection with bodies : where bodies 



