William W. Tait

Home Address: 5522 S. Everett Ave., Chicago, IL 60637, (773) 241-7288, williamtait@mac.com

Books:

• Early Analytic Philosophy: Frege, Russell, Wittgenstein (in honor of Leonard Linsky) (Editor). Lasalle: Open Court (1996)
• The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and Its History. Oxford: Oxford University Press (2005)

Recent Papers (PDF format)

• Philosophy/ History
  • Frege versus Cantor and Dedekind: on the concept of number. Frege, Russell, Wittgenstein: Essays in Early Analytic Philosophy (in honor of Leonard Linsky) (ed. W.W. Tait). Lasalle: Open Court Press (1996): 213-248. Reprinted in Frege: Importance and Legacy (ed. M. Schirn). Berlin: Walter de Gruyter (1996): 70-113. (43 pages)
  • Cantor's Grundlagen and the paradoxes of set theory. Between Logic and Intuition: Essays in Honor of Charles Parsons (ed. G. Sher and R. Tieszen). Cambridge: CUP (2000): 269-290. (27 pages)
  • Beyond the axioms: the question of objectivity in mathematics. Philosophia Mathematica 9 (2001): 21-36 (19 pages)
  • Noesis: Plato on exact science.  Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics to Honor Howard Stein on His 70th Birthday (ed. David Malament). Chicago and La Salle: Open Court (2002). (22 pages)
  • Remarks on finitism. Reflections on the Foundations of Mathematics: Essays in honor of Solomon Feferman (ed. Wilfried Sieg and Richard Sommer and Carolyn Talcott). Urbana: Association for Symbolic Logic, Lecture Notes in Logic, Volume 15 (2002): 407-16. (11 pages)
  • Gödel's unpublished papers on foundations of mathematics. Philosophia Mathematica 9 (2001): 87-126 (48 pages)
  • The myth of the mind. Topoi  21, Nos. 1-2 (2002):65-74. (20 pages)
  • Gödel's correspondence on proof theory and constructive mathematics. Philosophia Mathematica 14, No. 1 (2006): 76-111. (41 pages)
  • Gödel's interpretation of intuitionism. Philosophia Mathematica 14, No. 2 (2006): 208-228. (41 pages)
  • The Five Questions . Philosophy of Mathematics: Five Questions (ed. V.F. Hendricks and H Leitgeb). Automatic Press/VIP (2008): 249-263 (8 pages)
  • Gödel on Intuition and on Hilbert's Finitism . Kurt Gödel: Essays for His Centenial (ed. Solomon Feferman and Charles Parsons and Stephen Simpson). Cambridge : Association for Symbolic Logic, Lecture Notes in Logic, Volume 33 (2010): 88-108.
  (26 pages)
  • Primitive recursive arithmetic and its role in the foundations of arithmetic: historical and philosophical reflections: In honor of Per Martin-Löf on the occasion of his retirement . Epistemology Versus Ontology: Essays in the Philosophy of Mathematics in Honor of Per Martin-Löf (ed. P. Dybjer, S. Lindström, E. Palmgren and G. Sundholm). Springer (2012): 161-180.
  (261 pages)
  • In defense of the Ideal . To appear in the proceedings of the Exploring the Fronteers of Incompleteness workshop.
  (31 pages).
• Logic
  • Variable-free formalization of the Curry-Howard Theory of Types. Twenty-Five Years of Constructive Type Theory (ed. G. Sambin and J. Smith). Oxford: OUP (1998): 265-274. (15 pages)
  • The completeness of Heyting first-order logic. The Journal of Symbolic Logic 68, Number 3 (2003): 751-763 (11 pages)
  • Proof-theoretic semantics for classical mathematics. Synthese 148, N0. 3 (2006) 603-622. (23 pages)
  • Constructing cardinals from below. Chapter 6 of The Provenence of Pure Reason. (26 pages)
  • Gödel's reformulation of Gentzen's first consistency proof for arithmetic: the no-counterexample interpretation . The Bulletin of Symbolic Logic 11, Number 2 (2005): 225-238. Reprinted in Kurt Gödel: Essays for His Centenial (ed. Solomon Feferman and Charles Parsons and Stephen Simpson). Cambridge : Association for Symbolic Logic, Lecture Notes in Logic, Volume 33 (2010): 74-87. (15 pages)
  • The substitution method revisited . Proofs, Categories and Computations: Essays in Honor of Grigori Mints. (ed. Solomon Feferman and Wilfried Sieg). College Publications (2010): 231-241. (11 pages)
  • Gentzen's original consistency proof and the Bar Theorem . Gentzen's Centenary: The Quest for Consistency. (ed. Reinhard Kahle and Michael Rathjen). Springer. (To appear) (20 pages)

Syllabi and Lecture Notes (PDF format)

• Lectures on Proof Theory .