Intuitionism in Mathematics

D. C. McCarty

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:

Series: Oxford Handbooks in Philosophy

Intuitionism in Mathematics

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This chapter presents and illustrates fundamental principles of the intuitionistic mathematics devised by L.E.J. Brouwer and then describes in largely nontechnical terms metamathematical results that shed light on the logical character of that mathematics. The fundamental principles, such as Uniformity and Brouwer’s Theorem, are drawn from the intuitionistic studies of logic and topology. The metamathematical results include Gödel’s negative and modal translations and Kleene’s realizability interpretation. The chapter closes with an assessment of anti-realism as a philosophy of intuitionism.

Keywords: intuitionism; mathematics; Brouwer; uniformity; Gödel; Kleene; realizability; anti-realism

Chapter.  13466 words. 

Subjects: Philosophy of Mathematics and Logic

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