- Series Information
- The Oxford Handbook of Philosophy of Mathematics and Logic
- 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
- Intuitionism and Philosophy
- Intuitionism in Mathematics
- Intuitionism Reconsidered
- Quine and the Web of Belief
- Three Forms of Naturalism
- Naturalism Reconsidered
- Nominalism Reconsidered
- Structuralism Reconsidered
- 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
Abstract and Keywords
This article plans to sketch the outlines of the Quinean point of departure, then to describe how Burgess and this article differ from this, and from each other, especially on logic and mathematics. Though this discussion touches on the work of only these three among the many recent “naturalists,” the moral of the story must be that “naturalism,” even restricted to its Quinean and post-Quinean incarnations, is a more complex position, with more subtle variants, than is sometimes supposed.
Penelope Maddy is Professor of Logic and Philosophy of Science at the University of California, Irvine. Her work includes “Believing the Axioms” (Journal of Symbolic Logic, 1988), Realism in Mathematics (Oxford University Press, 1990), and Naturalism in Mathematics (Oxford University Press, 1997).
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