From a Brouwerian Point of View
D. van Dalen · Philosophia Mathematica · 1998
In the paper below we will discuss a number of topics that are central in Brouwer’s intuitionism. A complete treatment is beyond the scope of the paper, the reader may find it a useful introduction to Brouwer’s papers. There are a number of loosely related notions and schools of construc-tivism in mathematics; in some cases there is only an attempt to capture certain constructive notions and procedures in the existing body of mathe-matics, in other, more fundamental, cases the object is to reconstruct math-ematics as a whole within the frame work of a constructivistic philosophy. It is almost a platitude to state that constructivism has always been around in mathematics, and indeed, a, say, eighteenth century mathemati-cian would have accepted the constructivist claim of his twentieth century colleague of the mild variety, i.e. the practical non-dogmatic practitioner, as self-evident and rather commonplace. The issue of constructivism in math-ematics only became urgent after the discovery of abstract, non-effective techniques and notions. The watershed is David Hilbert’s famous solution