84 MYSTICISM AND LOGIC 



moves, it is in a state of motion. This is now known to 

 be a mistake. When a body moves, all that can be said 

 is that it is in one place at one time and in another at 

 another. We must not say that it ^\^ill be in a neighbour- 

 ing place at the next instant, since there is no next 

 instant. Philosophers often tell us that when a body is 

 in motion, it changes its position within the instant. To 

 this view Zeno long ago made the fatal retort that every 

 body always is where it is ; but a retort so simple and 

 brief was not of the kind to which philosophers are accus- 

 tomed to give weight, and they have continued down to 

 our own day to repeat the same phrases which roused the 

 Eleatic's destructive ardour. It was only recently that 

 it became possible to explain motion in detail in accord- 

 ance with Zeno's platitude, and in opposition to the 

 philosopher's paradox. We may now at last indulge the 

 comfortable belief that a body in motion is just as truly 

 where it is as a body at rest. Motion consists merely in 

 the fact that bodies are sometimes in one place and some- 

 times in another, and that they are at intermediate places 

 at intermediate times. Only those who have waded 

 through the quagmire of philosophic speculation on this 

 subject can reahse what a liberation from antique pre- 

 judices is involved in this simple and straightforward 

 commonplace. 



The philosophy of the infinitesimal, as we have just 

 seen, is mainly negative. People used to believe in it, 

 and now they have found out their mistake. The philo- 

 sophy of the infinite, on the other hand, is wholly positive. 

 It was formerly supposed that infinite numbers, and the 

 mathematical infinite generally, were self-contradictory. 

 But as it was obvious that there were infinities ^for 

 example, the number of numbers ^the contradictions of 

 mfinity seemed unavoidable, and philosophy seemed to 



