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Accommodationism in Mathematics: Reference, Knowledge, and Realism book cover

1st Edition

Accommodationism in Mathematics Reference, Knowledge, and Realism

By Jeffrey W. Roland Copyright 2027
156 Pages 1 B/W Illustrations
by Routledge

Mathematics presents a fundamental puzzle: we possess extraordinary confidence in mathematical knowledge while struggling to explain how such knowledge is possible, especially in light of traditional realist conceptions of mathematics. This book solves this puzzle by resolving the tension between mathematical knowledge and mathematical realism through the development of an innovative... Read more

Introduction

1. Rethinking Causal-Historical Theories of Reference

1.1 Reference Fixing and Reference “Fixing”

1.2 Reference as an Epistemic Notion

2. Accommodationism in Science

3. Interlude: Causal Theories of Knowledge and Reliabilism

4. Stability in Mathematics

4.1 Mathematical Induction

4.2 Dovetailing Computations

4.3 Compactness Phenomena

4.4 Two Hierarchies and Post’s Theorem

5. Accommodationism in Mathematics

6. Answering the Benacerraf-Field Challenge

7. Defending Mathematical Realism

8. Preserving Apriority and Foundationalism

8.1 Apriority

8.2 Foundationalism

9. Concluding Thoughts

Biography

Jeffrey W. Roland is Associate Professor of Philosophy at Louisiana State University, USA. He specializes in the philosophy of mathematics, epistemology, and the philosophy of science with a special interest in the nature and scope of philosophical naturalism and the prospects for a realist philosophy of mathematics. His publications include articles in Philosophy and Phenomenological Research, The British Journal for the Philosophy of Science, The Australasian Journal of Philosophy, Erkenntnis, and Pacific Philosophical Quarterly.

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