AND ITS SELF-CONSEKVATION. 113 



Here, indeed, the fallacy is not so very deeply hidden 

 as has been sometimes supposed. Space is assumed to 

 be infinitely divisible. Then a finite space is assumed to 

 be actually divided to infinity. Then one of these " in- 

 finitely small " divisions is assumed to have absolutely no 

 dimensions at all. That is, an " infinitely small " portion 

 or extent of space is assumed to be identical with the 

 point which, so far from being a space, even an "infi- 

 nitely small " space, is just the absolute negation of space. 



On the contrary, no matter how far the division of 

 space may be considered to have been carried, even though 

 it be to "infinity," yet will the smallest actual division 

 still be space, and will thus have actual dimensions. So 

 that, each extending over a definite part of the distance, 

 there will be but a finite number of spaces to pass 

 through. 



But, again, as Aristotle did not fail to observe, time 

 is infinitely divisible, as well as space. And, hence, a 

 portion of time, however small, may be stretched out to 

 infinity by the same process, and thus a fictitious infinite 

 time produced to render the passage of the arrow through 

 the assumed fictitious infinity of space reasonably suc- 

 cessful and prompt. 



Nay, let the same mode of proof be applied to the 

 arrow itself (since matter is also infinitely divisible), and 

 it will be found that the arrow consists of an infinite 

 number of parts, each of which has a certain extent. 

 Whence the arrow, as a whole, has infinite dimensions, 

 and thus offers a solid bridge whereon one may safely pass 

 from the earth to the remotest star in space I For thus, 

 evidently, the arrow itself is already the star and the 

 earth, and all things else extended. Hence, too, it is 



