The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and Its HistoryWilliam 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. 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. |
Contents
Finitism | 21 |
Remarks on Finitism | 43 |
Appendix to Chapters 1 and 2 | 54 |
Truth and Proof The Platonism of Mathematics | 61 |
Beyond the Axioms The Question of Objectivity in Mathematics | 89 |
The Law of Excluded Middle and the Axiom of Choice | 105 |
Constructing Cardinals from Below | 133 |
Platos SecondBest Method | 155 |
Noesis Plato on Exact Science | 178 |
Wittgenstein and the Skeptical Paradoxes | 198 |
Frege versus Cantor and Dedekind On the Concept of Number | 212 |
Cantors Grundlagen and the Paradoxes of Set Theory | 252 |
Godels Unpublished Papers on Foundations of Mathematics | 276 |
| 314 | |
| 327 | |
Common terms and phrases
abstract Ackermann function analysis apply arbitrary argue argument arithmetic assertion Axiom of Choice axioms Cantor cardinal number chapter computable concerning consistency consistency proof constructive mathematics Dedekind defined definition discussion domain Dummett elements equations equipollent example existence explicitly expression extension fact finitist formula foundation Frege function geometry given Gödel Grundlagen Hilbert idea inaccessible cardinal induction interpretation intuition intuitionistic iteration kind knowledge language logic mathematical objects means natural numbers noted notion number classes number theory object of type obtained ordinals paradox particular passage Phaedo phenomena philosophy philosophy of mathematics Plato precisely primitive recursive primitive recursive arithmetic primitive recursive functions principle proof provability prove question real numbers reason reference second-best method second-order seems sense sensible objects sequence set theory Socrates speak structure subsets Tait theorem things transfinite numbers true truth understand variables well-ordered sets Wittgenstein writes