This book provides a survey of a number of the major issues in the philosophy of mathematics, such as ontological questions regarding the nature of mathematical objects, epistemic questions about the acquisition of mathematical knowledge, and the intriguing riddle of the applicability of mathematics to the physical world. Some of these issues go back to the nascent years of mathematics itself, others are just beginning to draw the attention of scholars. In addressing these questions, some of the papers in this volume wrestle with them directly, while others use the writings of philosophers such as Hume and Wittgenstein to approach their problems by way of interpretation and critique. The contributors include prominent philosophers of science and mathematics as well as promising younger scholars. The volume seeks to share the concerns of philosophers of mathematics with a wider audience and will be of interest to historians, mathematicians and philosophers alike.
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Preface.- Chapter 1. Introduction.- Chapter 2. Purity and Explanation: Essentially Linked?.- Chapter 3. Rules, Conventions, and Regularities.- Chapter 4. On Mathematical Explanation.- Chapter 5. Steiner’s Wittgenstein.- Chapter 6. Logic Discovered and Imposed.- Chapter 7. Mathematical Analogies and Applicability in Physics.- Chapter 8. Learning Cardinals and Ordinals.- Chapter 9. Buck Stopping and Identification of Numbers.- Chapter 10. Platonism and the Proto-Ontology of Mathematics.- Chapter 11. Potential infinity, Mathematical Explanation and
de re Reference to Mathematical Objects.- Chapter 12. Mathematics and Physical Discovery.- Chapter 13. Observer Dependent Naturalism.- Chapter 14. David Hume’s
Treatise View of Geometry.- Index.
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Carl Posy has published widely in the philosophy of mathematics and in the history of philosophy. He is the author of Mathematical Intuitionism (Cambridge 2020), and the editor of Kant’s Philosophy of Mathematics: Modern Essays (Kluwer, 1992). He co-edited (with Jack Copeland and Oron Shagrir) Computability: Turing, Gödel, Church and Beyond (MIT, 2013), and (with Ofra Rechter) Kant’s Philosophy of Mathematics, Volume I: The Critical Philosophy and Its Roots (Cambridge, 2020); and Kant’s Philosophy of Mathematics, Volume II: Reception and Influence (Cambridge, Forthcoming)
Yemima Ben-Menahem is a philosopher of science, specializing in the philosophy of physics. She is author of Conventionalism (Cambridge University Press, 2006) and Causation in Science (Princeton University Press, 2018. She edited Hilary Putnam (Cambridge University Press 2005) and coedited (with Meir Hemmo) Probability in Physics (Springer, 2012)
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