- Series Information
- The Oxford Handbook of Philosophy of Mathematics and Logic
- Preface
- Notes on the Contributors
- Philosophy of Mathematics and Its Logic: Introduction
- A Priority and Application: Philosophy of Mathematics in the Modern Period
- 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 From a Constructivist View
- Relevance in Reasoning
- No Requirement of Relevance
- Higher‐order Logic
- Higher‐order Logic Reconsidered
- Index
Abstract and Keywords
Undoubtedly, the most enlightening published work dedicated to giving knowledgeable readers an overview of the topic of nominalism in contemporary philosophy of mathematics is A Subject with No Object by John Burgess and Gideon Rosen. This article begins with a brief description of that work, in order to provide readers with a solidly researched account of nominalism with which the article's own account of nominalism can be usefully compared. The first part, then, briefly presents the Burgess–Rosen account. A contrasting account is given in the longer second part.
Keywords: nominalism, contemporary philosophy, philosophy of mathematics, John Burgess, Gideon Rosen
Charles Chihara is Emeritus Professor of Philosophy at the University of California, Berkeley. He is the author of Ontology and the Vicious Circle Principle (1973), Constructibility and Mathematical Existence (Oxford University Press, 1990), The Worlds of Possibility: Model Realism and the Semantics of Modal Logic (Oxford University Press, 1998), and A Structural Account of Mathematics (Oxford University Press, 2004).
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- Series Information
- The Oxford Handbook of Philosophy of Mathematics and Logic
- Preface
- Notes on the Contributors
- Philosophy of Mathematics and Its Logic: Introduction
- A Priority and Application: Philosophy of Mathematics in the Modern Period
- 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 From a Constructivist View
- Relevance in Reasoning
- No Requirement of Relevance
- Higher‐order Logic
- Higher‐order Logic Reconsidered
- Index
