PHYSIOLOGICAL PARADOXES. 



Since the swift, however, do sometimes pass 

 the slow in a handicap, there must, as the 

 mathematician has demonstrated, be some very 

 definite fallacy, though he could not discover 

 it, in the argument which would make out 

 that this never could happen. 



The difficulty in finding it is due to the fact 

 that it is not a mere verbal or syllogistic fallacy 

 which could be excluded by careful adherence 

 to the rules of logic, but consists in the applica- 

 tion of one of the most radical conceptions of 

 the human mind, which, nevertheless, we may 

 find it necessary to revise, that of the continuity 

 of motion and space. 



Our persuasion that there is continuity in 

 sounds heard and in things seen or touched is 

 equally deep-rooted, but we have already 

 learned that this persuasion cannot stand against 

 a close observation of the facts. It may prove 

 to be equally unreal in the case of motion and 

 space. 



Now, the argument against Achilles winning 

 depends upon the assumption of this continuity, 

 or,^to put it in another way, upon the assump- 

 tion of the infinite divisibility of motion and 

 space. We say, at a certain point in the argu- 

 ment, however small the distance between 

 the competitors, while Achilles is traversing 

 that distance the tortoise can be going a still 

 smaller distance in advance. Perhaps this is 

 not true. Perhaps there is a limit to the 



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