ACHILLES AND THE TORTOISE. 



of the intermediate positions during the inter- 

 vening time. 



Now we, who have seen in detail the working 

 of the boards which cover the ground, know that 

 his impressions are wrong in two respects. 



In the first place, it is not true that any 

 object has moved from A I, where he first saw 

 the red spot, to U Y or any more distant posi- 

 tion. All the boards which he first saw at 

 A I, with their red sides up, are still there, 

 with their green sides up. And when he sees 

 the red object at U Y, there is not anything 

 there, as he imagines, which has come from A I. 



Secondly, the motion of colour which he 

 has seen take place from A I to J R, and from 

 J R to U Y, has not been, as he imagines, a 

 continuous motion. When it advanced be- 

 yond G H I it never occupied half, or quarter, 

 of J K L, for there are no half or quarter 

 boards. Each board turns over as a whole. 



Thus we see that the continuity and even 

 the reality of the movement of objects may be 

 entirely deceptive. 



To the latter point we will return a little 

 later. At present we will consider how this 

 illustration helps to apply the principle on 

 which we criticise the argument against Achilles 

 beating the tortoise the principle that space 

 is not infinitely divisible. 



In the field which we have described above 

 let there be two red spots moved by two 



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