Aspects of intuitionism

Abstract

Three aspects of intuitionism are discussed in this thesis. First there is an attempt to locate a source for the philosophical view of number that L.E.J. Brouwer has formulated in his "First Act of Intuitionism". A similarity is pointed out between Brouwer and Kant and a contrast is made between a Platonic and an intuitionistic view of arithmetic. Secondly there is a development of intuitionistic mathematics from the rational numbers to the intuitionistic form of the Heine-Borel theorem. Thirdly there is a discussion of features of intuitionistic logic centred on S. A. Kripke's semantic analysis of intuitionistic logic. These three aspects are dealt with in chapters I, II and III respectively. Appendix A is related to Theorem 6, section c, chapter II. (T6, (c), chapt. II).