ON THE THEORY OF SCIENCE 341 



not applicable (for the omission of certain parts and the concentra- 

 tion upon others which is characteristic of these is excluded by the 

 nature of the task), yet in a given case usually the necessity of bringing 

 in various pure sciences for the purpose of explanation is evident. 



Astronomy is one of these applied sciences. Primarily it rests upon 

 mechanics, and in its instrumental portion, upon optics; in its 

 present development on the spectroscopic side, however, it borrows 

 considerably of chemistry. In like manner history is applied sociology 

 and psychology. Medicine makes use of all the sciences before men- 

 tioned, up to psychology, etc. 



It is important to get clearly in mind the nature of these sciences, 

 since, on account of their compound nature, they resist arrangement 

 amongst the pure sciences, while, on account of their practical 

 significance, they still demand consideration. The latter fact gives 

 them also a sort of arbitrary or accidental character, since their 

 development is largely conditioned by the special needs of the time. 

 Their number, speaking in general, is very large, since each pure 

 science may be turned into an applied science in various ways; and 

 since in addition we have combinations of two, three, or more sciences. 

 Moreover, the method of procedure in the applied sciences is funda- 

 mentally different from that in the pure sciences. In the first it is 

 a question of the greatest possible analysis of a single given complex 

 into its scientifically comprehensible parts; while pure science, on 

 the other hand, considers many complexes together in order to 

 separate out from them their common element, but expressly dis- 

 claims the complete analysis of a single complex. 



In scientific work, as it appears in practice, pure and applied 

 science are by no means sharply separated. On the one hand the 

 auxiliaries of investigations, such as apparatus, books, etc., demand 

 of the pure investigator knowledge and application in applied science; 

 and, on the other hand, the applied scientist is frequently unable to 

 accomplish his task unless he himself becomes for the time being 

 a pure investigator and ascertains or discovers the missing general 

 relationships which he needs for his task. A separation and differentia- 

 tion of the two forms of science was necessary, however, since the 

 method and the aim of each present essential differences. 



In order to consider the method of procedure of pure science more 

 carefully, let us turn back to the table on pages 339, 340, and attend to 

 the single sciences separately. The theory of arrangement was men- 

 tioned first, although this place is usually assigned to mathematics. 

 However, mathematics has to do with the concepts of number and 

 magnitude as fundamentals, while the theory of arrangement does 

 not make use of these. Here the fundamental concept is rather the 

 thing or object of which nothing more is demanded or considered 

 than that it is a fragment of our experience which can be isolated and 



