THE PROBLEM OF INFINITY 175 



The fourth and last of Zeno's arguments is 1 the argu- 

 ment of the stadium. 



The argument as stated by Burnet is as follows : 



First Position. Second Position. 



x~V x\. 



O -D 



\^ V*> 



" Half the time may be equal to double the time. 

 Let us suppose three rows of bodies, one of which (A) 

 is at rest while the other two (B, C) are moving with 

 equal velocity in opposite directions. By the time they 

 are all in the same part of the course, B will have passed 

 twice as many of the bodies in C as in A. Therefore the 

 time which it takes to pass C is twice as long as the time 

 it takes to pass A. But the time which B and C take to 

 reach the position of A is the same. Therefore double 

 the time is equal to the half." 



Gave 2 devoted an interesting article to the interpreta- 

 tion of this argument. His translation of Aristotle's 

 statement is as follows : 



" The fourth argument is that concerning the two 

 rows of bodies, each row being composed of an equal 

 number of bodies of equal size, passing each other on a 

 race-course as they proceed with equal velocity in opposite 

 directions, the one row originally occupying the space 

 between the goal and the middle point of the course, and 

 the other that between the middle point and the starting- 

 post. This, he thinks, involves the conclusion that half 

 a given time is equal to double the time. The fallacy of 

 the reasoning lies in the assumption that a body occupies 

 an equal time in passing with equal velocity a body that 

 is in motion and a body of equal size that is at rest, an 



1 P/rys., vi. 9. 239B (R.P. 139). 2 Loc. cit. 



