PHYSIOLOGICAL PARADOXES. 



the tortoise gets one-tenth of that distance in 

 advance of D. 



But let us suppose that there are no smaller 

 distances than T D. How this could come 

 about we will consider afterwards. For the 

 present we will reflect that though we can con- 

 ceive of half or quarter of the distance TD, 

 many things are conceivable which do not 

 actually exist or happen. It is quite conceiv- 

 able that a pound of lead might become a 

 pound of gold. It is conceivable that a gold 

 sovereign, shut up in the purse, might become 

 two sovereigns ; or even that we might hear of 

 a rich relative having died in Australia and 

 left us heir to half a million sovereigns. But it 

 does not follow, because a thing is conceivable, 

 that it is true, or even possible. And so it may 

 be that there is in nature a limit to the possible 

 smallness of things, spaces, and movements. 



If, then, T D is the smallest possible or 

 existing space, it follows that the tortoise can- 

 not travel one-tenth, one-half, or any other 

 fraction of T D. His next stage must be equal 

 to T D, namely D C. But while the tortoise 

 travels from D to C, Achilles goes ten times 

 that distance namely, T D, DC, and eight 

 other spaces each equal to D C. He thus gets 

 eight such stages in advance of the tortoise. 



Thus with the postulate that space is not 

 infinitely divisible, we can not only explain in 

 detail exactly where the error is in the argu- 



274 



