Substance and Function, and Einstein's Theory of Relativity (Classic Reprint)

Excerpt from Substance and Function, and Einstein's Theory of Relativity

The investigations contained in this volume were first prompted by studies in the philosophy of mathematics. In the course of an attempt to comprehend the fundamental conceptions of mathematics from the point of view of logic, it became necessary to analyse more closely the function of the concept itself and to trace it back to its presuppositions. Here, however, a peculiar difficulty arose: the traditional logic of the concept, in its well-known features, proved inadequate even to characterize the problems to which the theory of the principles of mathematics led. It became increasingly evident that exact science had here reached questions for which there existed no precise correlate in the traditional language of formal logic. The content of mathematical knowledge pointed back to a fundamental form of the concept not clearly defined and recognized within logic itself. In particular, investigations concerning the concepts of the series and of the limit, the special results of which, however, could not be included in the general exposition of this book, confirmed this view and led to a renewed analysis of the principles of the construction of concepts in general.

The problem thus defined gained more general meaning when it became clear that it was in no way limited to the field of mathematics, but extended over the whole field of exact science. The systematic structure of the exact sciences assumes different forms according as it is regarded in different logical perspectives. Thus an attempt had to be made to advance from this general point of view to the forms of conceptual construction of the special disciplines, - of arithmetic, geometry, physics and chemistry. It did not accord with the general purpose of the enquiry to collect special examples from the particular sciences for the support of the logical theory, but it was necessary to make an attempt to trace their systemati…