176 SCIENTIFIC METHOD IN PHILOSOPHY 



assumption which is false. For instance (so runs the 

 argument), let A A ... be the stationary bodies of equal 

 size, B B . . . the bodies, equal in number and in size 

 to A A . . ., originally occupying the half of the course 

 from the starting-post to the middle of the A's, and 

 C C . . . those originally occupying the other half from 

 the goal to the middle of the A's, equal in number, size, 

 and velocity, to B B . . . Then three consequences follow. 

 First, as the B's and C's pass one another, the first B 

 reaches the last C at the same moment at which the first 

 C reaches the last B. Secondly, at this moment the first 

 C has passed all the A's, whereas the first B has passed 

 only half the A's and has consequently occupied only 

 half the time occupied by the first C, since each of the 

 two occupies an equal time in passing each A. Thirdly, 

 at the same moment all the B's have passed all the C's : 

 for the first C and the first B will simultaneously reach 

 the opposite ends of the course, since (so says Zeno) the 

 time occupied by the first C in passing each of the B's is 

 equal to that occupied by it in passing each of the A's, 

 because an equal time is occupied by both the first B and 

 the first C in passing all the A's. This is the argument : 

 but it presupposes the aforesaid fallacious assumption." 



This argument is not quite easy to follow, and it is 

 only valid as against the assumption that a finite time 



consists of a finite 



First Position. Second Position. , f . 



B B , B B B / B number of instants. 



We may re-state it 

 ^ pj A" A A' A" in different language. 



Let us suppose three 

 C C C" C C r C" drill-sergeants, A, A', 



****** 



and A , standing in a 

 row, while the two files of soldiers march past them in 

 opposite directions. At the first moment which we con- 



