1906] 



ROYCE— PRINCIPLES OF THEORETICAL SCIENCE. 93 



of the mind, a fashion of reacting to our environment. And no 

 simple introspection can tell what such a way of behavior involves. 

 For just as personal character cannot be discovered by looking with- 

 in, but must express itself in a long and active life, before it can be 

 fathomed, so with the forms of thought. They are methods of ac- 

 tivity. A direct reflection does not discover their constitution and 

 relations. These must be judged through an examination of con- 

 sequences, and through a development of extensive thinking proc- 

 esses. For instance, if you ask a plain man how he gets the idea 

 of number, he will reply, by counting. And he supposes that he 

 knows by direct introspection what counting is. A psychological 

 analysis made under experimental conditions may in many ways fur- 

 ther dissect the mental processes which go on when we count. But 

 how remote any such analysis is from a logical comprehension of the 

 form of thought used in counting will become evident only after one 

 has read such discussions as those of Dedekind in his famous essay 

 on whole numbers, or such as Russell's and Whitehead's recent anal- 

 yses of the relation between the cardinal and ordinal numbers. 

 The relation between the number concept and the concept of quan- 

 tity is again wholly inaccessible to direct introspection or to psycho- 

 logical experiment. Only an elaborate process of what one might 

 call logic experimentation brings out the relation between the two 

 concepts. The analysis of Peano, or the recent papers of my col- 

 league, Professor Huntington, are instances of such logical experi- 

 mentation. The process of experimentation in question consists 

 of undertaking to discover what assumptions, or what various sets 

 of assumptions, are sufficient, or are both necessary and sufficient, in 

 order that one may be able to deduce from them the consequences 

 which are already known to be characteristic of whatever concept 

 one happens to be analyzing. Only by such experimentation can 

 one dissect the thought form with which one is dealing. 



It follows from our inability to detect by any direct mental in- 

 spection what ones of our concepts are the fundamental ones, it 

 follows, I say, that the older philosophers, including Aristotle, were 

 indeed frequently very profound and as far as they went accurate 

 in some of their logical analyses, but could never be exhaustive, in 

 their account of the first principles of our theoretical thinking. 



