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This volume of essays tackles the main problem that arises when considering an epistemology for mathematics, the nature and sources of mathematical justification. Focusing both on particular and general issues, the essays from leading philosophers of mathematics raise important issues for our current understanding of mathematics. Is mathematical justification a priori or a posteriori ? What role, if any, does logic play in mathematical reasoning or inference? And how epistemologically important is the formalizability of proof? Michael Detlefsen has brought together an outstanding collection of essays, only two of which have previously appeared. It will be essential for philosophers and historians of mathematics interested in the nature of reasoning and justification.
Notes on contributors
Preface
Proof as a source of truth
Michael D.Resnik
Reflections on the concept of a priori truth and its corruption by Kant
William W.Tait
Logicism
Steven J.Wagner
Empirical inquiry and proof
Shelley Stillwell
On the concept of proof in elementary geometry
Pirmin Stekeler-Weithofer
Mathematical rigor in physics
Mark Steiner
Foundationalism and foundations of mathematics
Stewart Shapiro
Brouwerian intuitionism
Michael Detlefsen
Index