II. Foundations of Geometry

Abstract

An overview of the very extensive field which we now enter is afforded by the Enzyklopädie report by Federigo Enriques entitled Prinzipien der Geometrie (Enz. III A. B. 1). Investigations in the foundations of geometry often approach very closely the interests of the theory of knowledge and of psychology, which, from their viewpoints, study the origin of space intuition and the justification of treating it by mathematical methods. We shall touch these questions very superficially, of course, and we shall treat essentially the mathematical side of the problem, assuming that space intuition is to be taken for granted. We must also pass over the question that is so important in pedagogy, as to how space intuition develops in the individual to the precise form to which we, as mathematicians, are accustomed.