'HE METAPHYSICAL CONTRADICTIONS OF INFINITY. 253 



I 



^Ho define off the existent against the non-existent. 

 ^^But this condition cannot be satisfied in the case of 

 ^^n infinite, which can never be completed by succes- 

 ^^kive synthesis, and never therefore be grasped 

 ^■together as a whole. We may generalize the case 

 ^^of the infinite quantity (§ 4), and say that an in- 

 j^»finite whole is, like a bottomless pit, a contradiction 

 ^Bin terms, in which the infinity negates the whole 

 ^Band the whole excludes infinity. We must aban- 

 don, therefore, either the conception of a totality or 

 that of the infinity of the world. If the world is a 

 whole, it is not infinite, if it is infinite, it is not a 

 whole, i.e.^ not a world at all. 



And there is a parallel contradiction between 

 the conception of infinity and of a process. It w^as 

 shown in chapter vii. § 20 that a process is necessarily 

 and essentially finite, and limited by the two points 

 between which the process lies. Unless it were 

 finite, it would be a mere wavering and fluctuating 

 Becoming, void of Being, and as such unknowable. 

 The Becoming, therefore, of reality must be en- 

 closed within the limits of a conception, which 

 enables us to define it as having Being relatively to 

 one point and Not- Being relatively to another. To 

 apply to the world the conception of a process is to 

 imply that its Becoming is definite and finite. If, 

 therefore, we wish to assert that the world has a real 

 history, that its Evolution is a fact and that our 



(formulas of Evolution are true, we must think the 

 world as finite in Space and Time. 

 Lastly, the belief in infinity conflicts with the 

 most indispensable organon of all knowledge and 

 all science, the conception of causation (cp. ch. iii. 

 § II s.f.). For a chain of causation depends on the 



