Chapter

Intuitionism and Philosophy

Carl Posy*

in The Oxford Handbook of Philosophy of Mathematics and Logic

Published in print March 2005 | ISBN: 9780195148770
Published online July 2005 | e-ISBN: 9780199835560 | DOI: http://dx.doi.org/10.1093/0195148770.003.0009

Series: Oxford Handbooks in Philosophy

Intuitionism and Philosophy

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After sketching the essentials of L. E. J. Brouwer’s intuitionistic mathematics—separable mathematics, choice sequences, the uniform continuity theorem, and the intuitionistic continuum—this chapter outlines the main philosophical tenets that go hand in hand with Brouwer’s technical achievements. It presents his views about general and mathematical phenomenology and shows how these views ground his positive epistemological and ontological positions and his stinging criticisms of classical mathematics and logic. The chapter then turns to intuitionistic logic and its philosophical side. It first sets out the basic meta-logical technical results, then discusses the relevant philosophical views—those of Arend Heyting and Michael Dummett. It concludes by tracing intuitionism’s philosophical and technical roots in Aristotle and Kant.

Keywords: Brouwer; intuitionistic mathematics; choice sequences; continuity; continuum; phenomenology; intuitionistic logic; Heyting; Dummett; Aristotle; Kant

Chapter.  16407 words. 

Subjects: Philosophy of Mathematics and Logic

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