their composite nature renders it impossible to classify them among the pure sciences, though, because of their practical importance, they demand consideration. The latter characteristic gives them to a certain extent an arbitrary or accidental character since their development 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 individual 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 knowledge 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 himself 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 indiscriminate fraction, for such a one could have but a momentary duration; 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 concerning such uncertain things, one will find that the relations of
