Review of Walter P. van Stigt: Brouwer's Intuitionism

This book is the second volume of the new series of Elsevier Science Publishers Studies in the History and Philosophy of Mathematics. The contents of the book completely corresponds to the title of the series: it is devoted to the philosophical aspects of Brouwer's work, mainly to his philosophy of mathematics. There exists a voluminous literature pertaining to intuitionistic mathematics and logic. As a result one can see that problems of intuitionistic arithmetic, intuitionistic proof theory etc. have been minutely investigated in many remarkable books. But the area of intuitionistic philosophy is still remaining as some terra incognita. Meanwhile, just in field of philosophical "subtleties" one should look for features in which intuitionism differs from other constructive trends in logic and mathematics (e.g. from "Russian constructivism" of A. Markov). After all, historically, intuitionism arose just as philosophical conception in foundations of mathematics. Therefore the van Stigt's book (which deals in a comprehensive and detailed manner with a complex of problems related to this subject) is very important. First of all it should be indicated that the author does not have a claim on the all-round analysis of the whole Intuitionism, but he has restricted himself solely to investigation of work of L.E.J. Brouwer. He aimed at analysing "the whole of Brouwer's systematic speculation on the origine and nature of mathematics, his definition of norms and principles in accordance with this philosophy and his attempts to put these principles into practice". (p. XIV) The book under review is divided into six chapters. The first chapter contains a complete and thoroughly compiled list of Brouwer's known writings. It includes data of published as well as unpublished works of Brouwer and occupies 18 pages. The next chapter is a biographical essay of Brouwer's work. Van Stigt describes a historical formation and development of Brouwer's ideas in the light of his original personality. The author does not much care about detailed description of the whole Brouwer's life: he concentrates only upon the focal points and the most important periods of Brouwer's work: (1) creating of the book "Life, Art and Mysticism" (1905) (van Stigt gives great consideration to this remarkable book and in that way he makes up some deficiency which