MOTION, FORCE, MATTER 321 



at instants that are also still nearer together. The moving 

 body never jumps from one position to another, but always 

 passes by a gradual transition through an infinite number 

 of intermediaries." * The second feature of the definition 

 is that both motion and rest require the notion of "interval" 

 for definition. There is no such thing as motion or rest 

 at an instant; in order to ascertain what the particle is doing 

 at an instant one must know something as to what it was 

 doing before that instant or what it will be doing after that 

 instant. Motion and rest require comparison of the positions 

 of a particle at two instants; if the particle is at the same 

 position at the two instants, it is at rest; but if it is at dif- 

 ferent positions at the two instants, it is in motion. If one 

 has given only one instant, no such comparison is possible. 

 The importance of the notion of interval in the definition of 

 motion and rest is obvious in the ease with which it enables 

 one to avoid Zeno's paradoxes. 



motion: operational derivation 



The operational passage from empirical motion to scien- 

 tific motion is essentially that involved in the transition 

 from empirical space and time to the space and time of the 

 classical physics. Empirical motion is an aspect of empirical 

 space and time in much the same way that scientific motion 

 is an aspect of scientific space and time. However, the degree 

 of abstraction is not quite so great. Whereas scientific space 

 and time are empty, scientific motion retains the notion of 

 particle; hence although for science space and time need not 

 be occupied, motion demands occupants, i.e., motion and 

 rest would be meaningless in an empty world. To be sure, 

 in the scientific concept of motion there is an element of 

 abstraction, for reference to specific spatial frames has been 

 lost. Nevertheless, there is a general frame. The fact that 

 even this general frame of reference tends to take material 

 form in the "body Alpha," one of the fixed stars, or the 

 ether, suggests the abstractness of the conception and the 



1 Bertrand Russell, Our Knowledge of the External World, pp. 135-136. 



