FALLACIES OF CONFUSION. 453 



The argument is, let Achilles run ten times as fast 

 as the tortoise, yet if the tortoise has the start, 

 Achilles will ne\ 7 er overtake him. For suppose them 

 to be at first separated by an interval of a thousand 

 feet: when Achilles has run these thousand feet, the 

 tortoise will have got on a hundred; when Achilles 

 has run those hundred, the tortoise will have run ten, 

 and so on for ever: therefore Achilles may run for 

 ever without overtaking the tortoise. 



Now, the " for ever" in the conclusion, means, for 

 any length of time that can be supposed ; but in the 

 premisses " ever" does not mean any length of time : 

 it means any number of subdivisions of time. It means 

 that we may divide a thousand feet by ten, and that 

 quotient again by ten, and so on as often as we 

 please; that there never needs be an end to the subdi- 

 visions of the distance, nor consequently to those of 

 the time in which it is performed. But an unlimited 

 number of subdivisions may be made of that which is 

 itself limited. The argument proves no other infinity 

 of duration than may be embraced within five minutes. 

 As long as the five minutes are not expired, what 

 remains of them may be divided by ten, and again by 

 ten, as often as we like, which is perfectly compatible 

 with their being only five minutes altogether. It 

 proves, in short, that to pass through this finite space 

 requires a time which is infinitely divisible, but not 

 an infinite time ; the confounding of which distinction 

 Hobbes had already seen to be the gist of the fallacy. 



The following ambiguities of the word right (in 

 addition to the obvious and familiar one of a right and 

 the adjective right) are abstracted from a forgotten 

 paper of my own, in a periodical work: 



" Speaking morally, you are said to have a right 

 to do a thing, if all persons are morally bound not to 



