THE THEORY OF CONTINUITY 147 



points and instants from things, we shall leave the bare 

 possibility open that they may also have an independent 

 existence as simple entities. 



We come now to the question whether the things in 

 space and time are to be conceived as composed of 

 elements without extension or duration, i.e. of elements 

 which only occupy a point and an instant. Physics, 

 formally, assumes in its differential equations that things 

 consist of elements which occupy only a point at each 

 instant, but persist throughout time. For reasons ex- 

 plained in Lecture IV., the persistence of things through 

 time is to be regarded as the formal result of a logical 

 construction, not as necessarily implying any actual per- 

 sistence. The same motives, in fact, which lead to the 

 division of things into point-particles, ought presumably 

 to lead to their division into instant-particles, so that the 

 ultimate formal constituent of the matter in physics will be 

 a point-instant-particle. But such objects, as well as the 

 particles of physics, are not data. The same economy of 

 hypothesis, which dictates the practical adoption of a 

 relative rather than an absolute space and time, also 

 dictates the practical adoption of material elements which 

 have a finite extension and duration. Since, as we saw 

 in Lecture IV., points and instants can be constructed as 

 logical functions of such elements, the mathematical 

 account of motion, in which a particle passes continuously 

 through a continuous series of points, can be interpreted 

 in a form which assumes only elements which agree with 

 our actual data in having a finite extension and duration. 

 Thus, so far as the use of points and instants is concerned, 

 the mathematical account of motion can be freed from 

 the charge of employing fictions. 



(d) But we must now face the question : Is there, in 

 actual empirical fact, any sufficient reason to. believe the 



