130 SCIENTIFIC METHOD IN PHILOSOPHY 



But even when points and instants, as independent 

 entities, are discarded, as they were by the theory 

 advocated in our last lecture, the problems of continuity, 

 as I shall try to show presently, remain, in a practically 

 unchanged form. Let us therefore, to begin with, admit 

 points and instants, and consider the problems in con- 

 nection with this simpler or at least more familiar 

 hypothesis. 



The argument against continuity, in so far as it rests 

 upon the supposed difficulties of infinite numbers, has 

 been disposed of by the positive theory of the infinite, 

 which will be considered in Lecture VII. But there 

 remains a feeling of the kind that led Zeno to the 

 contention that the arrow in its flight is at rest which 

 suggests that points and instants, even if they are 

 infinitely numerous, can only give a jerky motion, a 

 succession of different immobilities, not the smooth 

 transitions with which the senses have made us familiar. 

 This feeling is due, I believe, to a failure to realise 

 imaginatively, as well as abstractly, the nature of con- 

 tinuous series as they appear in mathematics. When a 

 theory has been apprehended logically, there is often a 

 long and serious labour still required in order to feel it : 

 it is necessary to dwell upon it, to thrust out from the 

 mind, one by one, the misleading suggestions of false but 

 more familiar theories, to acquire the kind of intimacy 

 which, in the case of a foreign language, would enable 

 us to think and dream in it, not merely to construct labori- 

 ous sentences by the help of grammar and dictionary. 

 It is, I believe, the absence of this kind of intimacy 

 which makes many philosophers regard the mathematical 

 doctrine of continuity as an inadequate explanation of the 

 continuity which we experience in the world of sense. 



In the present lecture, I shall first try to explain in 



