- 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

# Philosophy of Mathematics and Its Logic:

# Philosophy of Mathematics and Its Logic:

Introduction

- Chapter:
- (p.3) 1 Philosophy of Mathematics and Its Logic:
- Source:
- The Oxford Handbook of Philosophy of Mathematics and Logic
- Author(s):
### Stewart Shapiro (Contributor Webpage)

- Publisher:
- Oxford University Press

This chapter provides a broad overview of the philosophy of mathematics and the philosophy of logic. It gives brief coverage to the various issues and positions, such as platonism or realism, varieties of nominalism, or anti-realism, logicism, intuitionism, empiricism, and structuralism.

*Keywords:*
mathematics, logic, platonism, realism, nominalism, anti-realism, logicism, intuitionism, empiricism, structuralism

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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