THEORIES OF SCIENTIFIC CONCEPTS 149 



the end-result, and that their meanings are a function of 

 two factors — the data and the knowing activities. Using 

 S to designate any scientific symbol such as a concept or 

 law, D to designate the data, and to designate the know- 

 ing operations, the dependence of the symbol upon these 

 two factors may be represented, 



S=f(D,0). 



Now the first problem is to determine the character of 

 this functional relation. To what extent is the meaning of the 

 symbol a function of the data, and to what extent is it a func- 

 tion of the knowing operations? Positivism insists that it is 

 primarily a function of the data, and only incidentally a 

 function of the operations; hence the operations may be 

 neglected or relegated to a position of unimportance. All 

 modified positivisms and all realisms insist that the meaning 

 of a symbol is at least as significantly a function of the 

 operations as it is of the data; hence the operations may 

 not be neglected. All rationalisms insist that the meaning 

 of a symbol is primarily a function of the operations, and 

 only incidentally a function of the data ; hence the data may 

 be neglected. It is interesting to note that theories of science 

 rarely take rationalistic form; they are, almost without 

 exception, either positivistic in the extreme or modified 

 form, or else realistic. Hence there will be no further occasion 

 to refer to rationalistic positions. 



But there is another problem. Though the ascertainment 

 of the importance of the operation serves to differentiate 

 pure positivisms, on the one hand, from modified positivisms 

 and realisms, on the other, an additional consideration is 

 required to distinguish modified positivisms from realisms. 

 Both of these positions insist on the importance of the 

 operations. But whereas modified positivisms insist that the 

 operations are essentially inventive, and hence result in sym- 

 bols for entities which are not presumed to exist, realisms insist 

 that the operations are essentially exploratory, and hence result 

 in symbols for entities which are presumed to exist. 



