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At the Heart of Analysis: Intuitionism and Philosophy

Charles McCarty
p. 81-94


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.

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For Dirk van Dalen
Victrix causa deis placuit sed vieta Catoni

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Charles McCarty, « At the Heart of Analysis: Intuitionism and Philosophy », Philosophia Scientiæ [En ligne], CS 6 | 2006, mis en ligne le 01 septembre 2009, consulté le 22 septembre 2017. URL : ; DOI : 10.4000/philosophiascientiae.411

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Charles McCarty

Indiana University, Bloomington (USA)

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