Brouwer’s Philosophy

Abstract

Philosophical remarks appear in many of Brouwer’s papers from various phases of his career. One can find them in his doctoral dissertation (1907) as well as in his late Cambridge lectures, delivered between 1947 and 1951. With respect to many significant themes, it is rather striking how little he changed his conceptions. Even more, some passages, like those presenting his account of language and linguistic communication, the relation between logic and mathematics, or abilities of the knowing subject are repeated in his later works almost word for word, as if they were quotations from his earlier papers. That is not to say that all Brouwer’s views remained unaltered. For instance, perhaps his most important concept, that of intuition, was substantially modified. Similarly, his mathematical notions evolved considerably. Nevertheless, the relative stability of Brouwer’s philosophical views justifies a reconstruction of his whole philosophy, without paying much attention to distinctions between periods or phases of the development of his philosophical thought. Thus, we shall attempt an overall and somehow ahistorical presentation of his philosophy, and only exceptionally, if a concept under consideration went through a process of substantial changes, shall we remark on its origin and evolution.⁴ To repeat, the objectives of our presentation of Brouwer’s philosophy are to find out whether his arguments are strong enough to justify the proposed revision of mathematics, whether it was an account of meaning that moved him to question classical mathematics, and whether his conception of mathematics allows for intersubjectivity.