Abstract

The aim of this paper is a partial axiomatic reconstruction of Whitehead's theory of extension, a general geometrical foundation. To this purpose, I first deal with the reasons which induced Whitehead to develop his theory and the underlying method of extensive abstraction. I then introduce and explain essential parts of this theory up to the definition of a point, examine their coherency and develop them into a formal deductive system by taking into account Whitehead's intentions to a large extent. After that I prove the consistency and independence of the proposed axiomatic system. I conclude with an examination of the contribution of Whitehead's theory to the clarification of the nature of geometrical entities, e. g. points, and to the solution of the problem of applicability of geometry to reality