MOTION, FORCE, MATTER 315 



Change. It seems clear, moreover, that motion is a change 

 of some kind. The definition of the concept of change is a 

 task of some difficulty, and can hardly be undertaken here. 

 Reference may be made to the preceding chapter where a 

 brief analysis of the notion was made in connection with the 

 empirical foundation of time. It was there suggested that 

 change always involves something coming into being, some- 

 thing passing out of being, and a permanent background 

 within which these events occur. An alternative description 

 is that of Russell, who defines change as "the difference in 

 respect of truth or falsehood, between a proposition con- 

 cerning an entity and a time T and a proposition concerning 

 the same entity and another -time T', provided that the two 

 propositions differ only by the fact that T occurs in the one 

 where T' occurs in the other." 1 For example, if of the two 

 propositions, "x is white at time T," and " x is white at time 

 T"," one is t rue an d the other is false, then x may be said 

 to have changed. This is to define "change'' in terms of 

 "truth" and "falsity " — a procedure which may involve one 

 in further difficulties when the definitions of these latter con- 

 cepts become necessary. The point is, however, that motion 

 is change. Rut it is a kind of change. An object may be said 

 to move when its spatial relation to another object passes 

 out of being, another spatial relation comes into being, and 

 there remains an identical feature which is the objects them- 

 selves. Or, in Russell's terms, motion arises when the com- 

 mon feature of the two propositions is a spatial relation, 

 e.g., if "x is five miles northeast of y at time T" is true (or 

 false), and "x is five miles northeast of y at time T"' is false 

 (or true), then x and y may be said to have moved relatively 

 to one another. 



Of these two formulations of the concept of change, the 

 former has an advantage from the empirical point of view, 

 for it permits the description of motion as taking place, 

 while the latter, without the addition of further propositions 

 about the continuity of T and T', describes only the fact of 



1 Principles of Mathematics, p. 469. 



