Abstract

One’s first impression is that Brouwer’s Continuity Theorem of intuitionistic analysis, that every total, real-valued function of a real variable is continuous, stands in straightforward contradiction to a simple theorem of conventional real analysis, that there are discontinuous, real-valued func­tions. Here we argue that, despite philosophical views to the contrary, first impressions are not misleading; the Brouwer Theorem, together with its proof, presents mathematicians and philosophers of mathematics with an antimony, one that can only be resolved by a close, foundational study of the structure of the intuitive continuum.