CONTRIBUTION TO THE THEORY OF SCIENCE 227 



their composite nature renders it impossible to classify them among the 

 pure sciences, though, because of their practical importance, they de- 

 mand consideration. The latter characteristic gives them to a cer- 

 tain extent an arbitrary or accidental character since their develop- 

 ment depends upon the particular requirements of the times. Their 

 number, broadly speaking, is very great because every pure science may 

 be changed to an applied one in many ways and may be combined for 

 this purpose with one or more other sciences. Furthermore, the 

 method of applied science is fundamentally different from that of pure 

 science inasmuch as the former seeks to analyze any given complex 

 into its scientifically manageable parts, whereas conversely the latter 

 considers many complexes in order to extract from them their common 

 feature and explicitly refrains from the complete analysis of each in- 

 dividual complex. 



In scientific work, as carried out in practise, pure and applied 

 science are by no means always to be sharply separated. On the one 

 hand, the means of research, apparatus, books, etc., demand the knowl- 

 edge and the practise of applied science even by the ' pure ' investigator. 

 On the other hand, the ' applied ' investigator is often able to solve his 

 problem only by becoming temporarily a ' pure ' investigator and him- 

 self ferreting out or discovering the universal relations which he needs 

 for the solution of his problem. The separation and differentiation of 

 these two kinds of science was, however, necessary, because each employs 

 quite different methods and pursues essentially different ends. 



In order that we may attain a clear understanding of the method 

 of pure science, we will turn to the table on page 225 and consider 

 the individual sciences separately. The first place is ordinarily 

 given to mathematics as to the science of quantity. However, 

 mathematics deals with number and size as its fundamental concepts, 

 while the science of assemblages does not as yet use them. Moreover, 

 in the latter, the fundamental concept is the thing or object of which 

 no more is required than merely that it be a fraction of our experience 

 capable of being isolated and remaining so. It may not be any in- 

 discriminate fraction, for such a one could have but a momentary dura- 

 tion; and the aim of science, to discover the unknown from what is 

 given, could not be accomplished with it. This part of experience must 

 rather be of such a nature that it may be distinguished and recognized, 

 that is to say, it must already be of the nature of a concept. Only 

 those parts of our experience which are capable of repetition (for these 

 alone can form the subject-matter of science) can be called things or 

 objects. This statement, however, includes everything that is required 

 of them. Otherwise they may differ as much as is conceivable. 



If it be asked what scientific statements it is possible to make con- 

 cerning such uncertain things, one will find that the relations of 



