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The Oxford Handbook of Philosophy of Mathematics and Logic$
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Stewart Shapiro

Print publication date: 2005

Print ISBN-13: 9780195148770

Published to Oxford Scholarship Online: July 2005

DOI: 10.1093/0195148770.001.0001

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Intuitionism in Mathematics

Intuitionism in Mathematics

(p.356) Intuitionism in Mathematics
The Oxford Handbook of Philosophy of Mathematics and Logic

D. C. McCarty (Contributor Webpage)

Oxford University Press

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

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