146 SCIENTIFIC METHOD IN PHILOSOPHY 



questions to be distinguished. There is the question of 

 absolute or relative space and time, and there is the 

 question whether what occupies space and time must 

 be composed of elements which have no extension or 

 duration. And each of these questions in turn may 

 take two forms, namely : (a) is the hypothesis consistent 

 with the facts and with logic ? (/3) is it necessitated by the 

 facts or by logic ? I wish to answer, in each case, yes to 

 the first form of the question, and no to the second. 

 But in any case the mathematical account of motion will 

 not be fictitious, provided a right interpretation is given 

 to the words " point " and " instant." A few words on 

 each alternative will serve to make this clear. 



Formally, mathematics adopts an absolute theory of 

 space and time, i.e. it assumes that, besides the things 

 which are in space and time, there are also entities, called 

 "points' and "instants," which are occupied by things. 

 This view, however, though advocated by Newton, has 

 long been regarded by mathematicians as merely a 

 convenient fiction. There is, so far as I can see, no 

 conceivable evidence either for or against it. It is 

 logically possible, and it is consistent with the facts. But 

 the facts are also consistent with the denial of spatial and 

 temporal entities over and above things with spatial and 

 temporal relations. Hence, in accordance with Occam's 

 razor, we shall do well to abstain from either assuming 

 or denying points and instants. This means, so far as 

 practical working out is concerned, that we adopt the 

 relational theory ; for in practice the refusal to assume 

 points and instants has the same effect as the denial of 

 them. But in strict theory the two are quite different, 

 since the denial introduces an element of unverifiable 

 dogma which is wholly absent when we merely refrain 

 from the assertion. Thus, although we shall derive 



