134 SCIENTIFIC METHOD IN PHILOSOPHY 



the one to the other, but will pass through an infinite 



numb : other pos ons on the way. Ever] distance, 



however small, ; .s traversed by passing through .ill the 



infinite series of :ions between the two ends of the 



sl i ice. 



But at this point imagination sv.cc^sts that we may 

 describe the continuity of motion bj saying that the speck 



alwavs p.-.sscs From one position at one instant to the wexi 

 position at the I tistant As soon as we say this or 



imagine it, we fall into error, because there is no next 



point or next instant. If there were, we should rind 

 Zeno's paradoxes, in some form, unavoidable, as will 

 .r in our next lecture. One simple paradox may 

 serve as an illustration. If our speck is in motion along 

 the scale throughout the whole of a certain time, it cannot 

 be at the same point at two consecutive instants. But it 

 cannot, from one instant to the next, travel further than 

 from one point to the next, for if it did, there would be 

 no instant at which it was in the positions intermedi/uc 

 between that at the first instant and that at the next, and 

 igreed that the continuity of motion excludes the 

 possibility of such sudden jumps. It follows thai our 

 speck must, so long as it moves, pass from one point at 

 one instant to the next point at the next instant. Thus 

 there will be just one perfectly definite velocity with 

 which all motions must take place : no motion can be 

 faster than this, and no motion can be slower. Since this 

 conclusion is false, we must re : ect the hvpothesis upon 

 which it is based, namely that there are consecutive points 

 and instants. 1 Heuce the continuity of motion must not 

 be supposed to consist in a body's occupying consecutive 

 positions at consecutive times. 



1 The above paradox is essentially the same as Zeno"s argument of the 

 it^i ..- ill be ;c..s:dered in our next lecture. 



