Wim Veldman
Brouwer's new axioms: their meaning and use
Abstract: One may learn, from reading Brouwer's dissertation, that his call for an intuitionistic reform of mathematics was the outcome of his attempts to come to terms with the idea of the continuum. This reform may be said to consist of two parts. Firstly, the language of mathematics is made more precise: the logical constants are interpreted constructively, and indirect arguments receive a careful treatment. Secondly, some new axioms are proposed, as a result of philosophical reflection on the concept of the continuum. We want to consider the most important such axioms: the basic assumptions from which Brouwer derives, in the 1920's, the famous fact that every function from the compact interval [0, 1] to the set of the real numbers is uniformly continuous. These assumptions are: Brouwer's Continuity Principle, the Fan Theorem and the Bar Theorem. Some observations will be made on the plausibility and the fruitfulness of these assumptions.
About Wim Veldman
Wim Veldman has been a student of Johan J. de Iongh, who introduced him to Brouwer's intuitionistic mathematics and became his Ph. D. adviser.
He completed his dissertation, on intuitionistic descriptive set theory, in 1981. Since then, he has been a member of the
Department of Mathematics at the Radboud University Nijmegen, continuing his research in intuitionistic mathematics,
and teaching intuitionistic mathematics and various other subjects from the foundations of mathematics.
