248 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



between time, space, and force remain in science even 

 though they are all "reduced' to measured values. Similar 

 considerations apply to that high abstraction of numbers 

 which generalizes them into meaningless marks manipulated 

 according to arbitrary rules. 



In the second place, one must recognize the difficulties 

 which arise in the attempt to clarify the meanings of the 

 concepts and assumptions, even from the point of view of 

 the way in which they function in the science. Attention 

 has already been called to the fact that they are often im- 

 plicitly rather than explicitly present, and hence may never 

 have been consciously clarified even by the scientist himself. 

 In addition there are difficulties due to the technical char- 

 acter of the terminology which is often employed in the 

 definitions of these notions. But most important is the 

 recognition of what is involved finally in the very method 

 of definition itself. A definition is a statement of equivalence 

 between two symbols, one of which is better understood 

 than the other; hence definition involves the reduction of 

 an obscure symbol to a clear one. "Now, obviously the 

 process of definition can not be led back ad infinitum. It 

 must terminate in the undefined, or indefinable. Any dis- 

 cussion must begin with certain primitive concepts from 

 which it proceeds in an orderly way. Psychologically, it 

 would always be best to take as undefined those concepts 

 which are most clearly understood; but logically, such a 

 procedure might be very limiting indeed, being confined by 

 the circumference of the understanding to which we appeal. 

 What is best taken as primitive (or undefined) may there- 

 fore be some extremely complex idea, so far as understand- 

 ing is concerned. A glance at any mathematical system 

 easily convinces us that this is the case." : Thus definition 

 is not usually a reduction to the psychologically primitive 

 but to the logically primitive, as Russell uses these terms 

 in the quotation given on page 238. Broad points out that 

 what is logically most primitive in nature is not what is 



1 R. M. Eaton, General Logic (New York: Scribners, 1931), p. 298.- 



