Points and Spaces

Abstract

The gradual disengagement of mathematics from logic. Beginning with a historical review of the development of mathematical thought, we have to consider successively (cf. 10, pp. 139-140):(1) The observational period. For some familiar regularities of (outer or inner) experience of time and space, which, to any attainable degree of approximation, seemed invariable, absolute and sure invariability was postulated. These regularities were called axioms and were put into language. Thereupon extensive systems of properties were developed from the linguistic substratum of the axioms by means of reasoning, guided by experience but linguistically following and using the principles of classical logic. This logic was considered autonomous, and mathematics was considered more or less dependent on logic.