CAN THE WORLD-PROCESS FAIL ? 453 



an asymptote, always approaching the state of Per- 

 fect Beinor and never attaininof it. 



But here again our fears would be unfounded. 

 In thought, indeed, any process is infinitely divis- 

 ible into infinite gradations, but in reality this is not 

 the case. It is a natural error to suppose that 

 because the infinitesimal can be thought it can also 

 be felt, but were it true, all sorts of absurdities would 

 follow. 



Thus, e.g., Zeno would be right in asserting that 

 Achilles would never catch up the Tortoise, if the 

 Tortoise had a start. The demonstration of this 

 most ancient and ingenious fallacy is quite irresist- 

 ible, if we admit that the endless divisibility of 

 Space and Time can be applied also to the experi- 

 ence of Space and Time. If Achilles could run first 

 ten yards, then one, then one-tenth, then one- 

 hundredth, and so on indefinitely, and be conscious 

 of each step and each moment he required to tra- 

 verse it, he really would require an infinite time to 

 catch the Tortoise. For he would be conscious of 

 an infinite series of events before he caught it, snb- 

 jectively at least he would never complete the 

 infinity of infinitesimal steps required {cp. ch. ii. § 6). 

 Really, of course, real Space and Time are not 

 infinitely divisible (ix. § 9), Achilles would soon come 

 to a minimum step no longer capable of subdivision, 

 and he would require a minimum time to traverse it. 



And so in the case proposed ; the approximations 

 to perfection could not go on indefinitely : they 

 would sooner or later approach so nearly to per- 

 fection, that the discrepancy between the real and 

 the ideal would be too minute to enter into con- 

 sciousness. A precisely similar instance, moreover, 

 of this impossibility of endless approximation in 



