The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and Its History (Logic and Computation in Philosophy)

William Tait is one of the most distinguished philosophers of mathematics of the last fifty years. This volume collects his most important published philosophical papers from the 1980's to the present. The articles cover a wide range of issues in the foundations and philosophy of mathematics, including some on historical figures ranging from Plato to G?del. Tait's main contributions were initially in proof theory and constructive mathematics, later moving on to more philosophical subjects including finitism and skepticism about mathematics. This collection, presented as a whole, reveals the underlying unity of Tait's work. The volume includes an introduction in which Tait reflects more generally on the evolution of his point of view, as well as an appendix and added endnotes in which he gives some interesting background to the original essays. This is an important collection of the work of one of the most eminent philosophers of mathematics in this generation.

William Tait is one of the most distinguished philosophers of mathematics of the last fifty years. This volume collects his most important published philosophical papers from the 1980's to the present. The articles cover a wide range of issues in the foundations and philosophy of mathematics, including some on historical figures ranging from Plato to Gödel.

Tait's main contributions were initially in proof theory and constructive mathematics, later moving on to more philosophical subjects including finitism and skepticism about mathematics. This collection, presented as a whole, reveals the underlying unity of Tait's work. The volume includes an introduction in which Tait reflects more generally on the evolution of his point of view, as well as an appendix and added endnotes in which he gives some interesting background to the original essays. This is an important collection of the work of one of the most eminent philosophers of mathematics in this generation.

Cover ......Page 1 Title ......Page 4 Preface ......Page 7 Contents ......Page 9 Introduction ......Page 11 1 Finitism ......Page 29 2 Remarks on Finitism ......Page 51 Appendix to Chapters 1 and 2 ......Page 62 3 Truth and Proof: The Platonism of Mathematics ......Page 69 4 Beyond the Axioms: The Question of Objectivity in Mathematics ......Page 97 5 The Law of Excluded Middle and the Axiom of Choice ......Page 113 6 Constructing Cardinals from Below ......Page 141 7 Plato's Second-Best Method ......Page 163 8 Noesis: Plato on Exact Science ......Page 186 9 Wittgenstein and the "Skeptical Paradoxes" ......Page 206 10 Frege versus Cantor and Dedekind: On the Concept of Number ......Page 220 11 Cantor's Grundlagen and the Paradoxes of Set Theory ......Page 260 12 GodePs Unpublished Papers on Foundations of Mathematics ......Page 284 References ......Page 322 Index ......Page 335 Back ......Page 341 "William Tait is one of the most distinguished philosophers of mathematics of the last fifty years. This volume collects his most important published philosophical papers from the 1980's to the present. The articles cover a wide range of issues in the foundations and philosophy of mathematics, including some on historical figures ranging from Plato to Godel." "Tait's main contributions were initially in proof theory and constructive mathematics, later moving on to more philosophical subjects including finitism and skepticism about mathematics. This collection, presented as a whole, reveals the underlying unity of Tait's work."--Jacket The crux to understanding Hilbert's conception of finitist mathematics (Hilbert, 1925, 1927) and (Hilbert and Bernays, 1934) is this question: In what sense can we prove general propositions, such as xy(x + y = y + x) about the natural numbers, without assuming the infinitude of numbers or some other infinite totality?