- Title Pages
- Preface
- THE OXFORD HANDBOOK OF PHILOSOPHY OF MATHEMATICS AND LOGIC
- 1 Philosophy of Mathematics and Its Logic:
- A Priority and Application:
- Later Empiricism and Logical Positivism*
- Wittgenstein on Philosophy of Logic and Mathematics
- THE LOGICISM OF FREGE, DEDEKIND, AND RUSSELL
- Logicism in the Twenty‐first Century
- Logicism Reconsidered
- Formalism
- Intuitionism and Philosophy
- Intuitionism in Mathematics
- Intuitionism Reconsidered
- Quine and the Web of Belief
- Three Forms of Naturalism
- Naturalism Reconsidered
- Nominalism
- Nominalism Reconsidered
- Structuralism
- Structuralism Reconsidered
- Predicativity
- Mathematics—Application and Applicability
- Logical Consequence, Proof Theory, and Model Theory
- Logical Consequence: A Constructivist View
- Relevance in Reasoning
- No Requirement of Relevance
- Higher‐order Logic
- Higher‐order Logic Reconsidered
- Index

# Intuitionism in Mathematics

# Intuitionism in Mathematics

- Chapter:
- (p.356) Intuitionism in Mathematics
- Source:
- The Oxford Handbook of Philosophy of Mathematics and Logic
- Author(s):
### D. C. McCarty (Contributor Webpage)

- Publisher:
- 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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- Title Pages
- Preface
- THE OXFORD HANDBOOK OF PHILOSOPHY OF MATHEMATICS AND LOGIC
- 1 Philosophy of Mathematics and Its Logic:
- A Priority and Application:
- Later Empiricism and Logical Positivism*
- Wittgenstein on Philosophy of Logic and Mathematics
- THE LOGICISM OF FREGE, DEDEKIND, AND RUSSELL
- Logicism in the Twenty‐first Century
- Logicism Reconsidered
- Formalism
- Intuitionism and Philosophy
- Intuitionism in Mathematics
- Intuitionism Reconsidered
- Quine and the Web of Belief
- Three Forms of Naturalism
- Naturalism Reconsidered
- Nominalism
- Nominalism Reconsidered
- Structuralism
- Structuralism Reconsidered
- Predicativity
- Mathematics—Application and Applicability
- Logical Consequence, Proof Theory, and Model Theory
- Logical Consequence: A Constructivist View
- Relevance in Reasoning
- No Requirement of Relevance
- Higher‐order Logic
- Higher‐order Logic Reconsidered
- Index