- The Oxford Handbook of Philosophical Methodology
- About the Contributors
- What is Philosophical Methodology?
- The Methodology of the History of Philosophy
- Methodology in Nineteenth-and Early Twentieth-Century Analytic Philosophy
- Nineteenth-Century and Early Twentieth-Century Post-Kantian Philosophy
- Logical Empiricism
- Ordinary Language Philosophy
- Wittgenstein’s Global Deflationism
- Philosophical Naturalism
- Method in Analytic Metaphysics
- The Pragmatic Method
- Reflective Equilibrium
- Analytic–Synthetic and A Priori–A Posteriori History
- Philosophical and Conceptual Analysis
- Philosophical Progress
- Conceivability and Possibility
- Philosophical Heuristics and Philosophical Methodology
- Disagreement in Philosophy: Its Epistemic Significance
- Faith and Reason
- Experimental Philosophy
- Transcendental Arguments
- Physics and Method
- Linguistic and Philosophical Methodology
- History of Ideas: A Defense
- The Methodology of Political Theory
- Philosophy and Psychology
- Logic and Philosophical Methodology
- Philosophy of Mathematics: Issues and Methods
- Methods in the Philosophy of Literature and Film
- Aesthetics and Philosophy of Art
- The Methodology of Legal Philosophy
- Critical Philosophy of Race
- Index of Names
Abstract and Keywords
This article examines a number of issues and problems that motivate at least much of the literature in the philosophy of mathematics. It first considers how the philosophy of mathematics is related to metaphysics, epistemology, and semantics. In particular, it reviews several views that account for the metaphysical nature of mathematical objects and how they compare to other sorts of objects, including realism in ontology and nominalism. It then discusses a common claim, attributed to Georg Kreisel that the important issues in the philosophy of mathematics do not concern the nature of mathematical objects, but rather the objectivity of mathematical discourse. It also explores irrealism in truth-value, the dilemma posed by Paul Benacerraf, epistemological issues in ontological realism, ontological irrealism, and the connection between naturalism and mathematics.
Stewart Shapiro is O'Donnell Professor of Philosophy at The Ohio State University and Professorial Fellow at the Arche Centre, University of St. Andrews.
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