Tait William. The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and Its History

Oxford, UK: Oxford University Press, 2005. — 332 p. — ISBN10: 019514192X; ISBN13: 978-0195141924 — (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 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.Finitism
Remarks on FinitismAppendix to the previous ChaptersTruth and Proof: The Platonism of Mathematics
Beyond the Axioms: The Question of Objectivity in Mathematics
The Law of Excluded Middle and the Axiom of Choice
Constructing Cardinals from Below
Plato’s Second-Best Method
Noesis: Plato on Exact Science
Wittgenstein and the “Skeptical Paradoxes”
Frege versus Cantor and Dedekind: On the Concept of Number
Cantor’s Grundlagen and the Paradoxes of Set Theory
Godel’s Unpublished Papers on Foundations of Mathematics