MOTION, FORCE, MATTER 323 



through any formal techniques, there is no longer any 

 reason to suppose that it functions in science in any sig- 

 nificant way. It must therefore be replaced by a more fruit- 

 ful notion, viz., that of relative motion. This becomes the 

 foundation for relativity mechanics just as the Newtonian 

 conception became the foundation for the classical mechan- 

 ics. The complications which are introduced when general- 

 ization is made to accelerated and rotational motions in- 

 volve extension to the general theory of relativity and are 

 too great to be discussed here. 



Hence, in summary of the concept of motion, one may 

 say that at the empirical level it designates a quantitatively 

 variable change in the spatial relations holding between two 

 events. But at the scientific level, it designates a certain 

 correlation between points of space and instants of time, 

 accomplished through the medium of a particle, and ex- 

 pressible in terms of measured values; for the absolute 

 theory this correlation is between an absolute space and an 

 absolute time, and hence determines an absolute motion; 

 but for a relative theory the correlation is recognized as being 

 relevant always to coordinate systems, and hence as in 

 some sense arbitrary. Since motion is defined in terms of 

 space and time, the operational derivation of scientific 

 motion from its empirical foundation is such as is involved in 

 the passage from empirical space and time to scientific space 

 and time. 



FORCE : EMPIRICAL^ FOUNDATION 



The confusion which is to be found in recent literature 

 with reference to the concept of force makes a satisfactory * 

 discussion of it impossible. The obscurity bears not only on 

 the empirical notion, but on the scientific concept, and, 

 as a result, on the operational derivation as well. That there 

 is empirically revealed some such thing as force seems hard 

 to deny, in spite of Russell's statement that "force is a 

 mathematical fiction, not a physical entity." l Yet, on the 



1 Principles of Mathematics, p. 482. 



