William Tait. The provenance of pure reason. Essays on the philosophy of mathematics and on its history
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Philosophia Mathematica 17 (2):220-247 (2009)
William Tait's standing in the philosophy of mathematics hardly needs to be argued for; for this reason the appearance of this collection is especially welcome. As noted in his Preface, the essays in this book ‘span the years 1981–2002’. The years given are evidently those of publication. One essay was not previously published in its present form, but it is a reworking of papers published during that period. The Introduction, one appendix, and some notes are new. Many of the essays will be familiar to the readers of this journal; indeed two first appeared here.It should be no surprise to those who know Tait's work that this is a very rich collection, with contributions on a wide variety of issues, both systematic and historical. That poses a problem for a reviewer, because a serious discussion of even all the major issues would be beyond the scope of a review.Before the essays in this collection, Tait's publications were almost all in mathematical logic, especially proof theory. He was a leading actor in the work on the revised Hilbert program stimulated after the war by Georg Kreisel, Kurt Schütte, and Gaisi Takeuti. Tait thus has an experience in mathematical research that is rare among those whose careers have been institutionally in philosophy. In the 1970s Tait became disillusioned with the proof-theoretic program on which he had worked. However, he draws on that background in several of these essays, and he has continued to work on mathematical questions. In particular, the set-theoretic project reflected in essay 6 is as much mathematical as philosophical.It is not easy to characterize Tait's philosophical viewpoint briefly. Both the title of the book and some of its content mark him as a rationalist. His hero in the earlier history …
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References found in this work BETA
Donald A. Martin (2005). Gödel's Conceptual Realism. Bulletin of Symbolic Logic 11 (2):207-224.
Von Kurt Gödel (1958). Über eine bisher noch nicht benützte erweiterung Des finiten standpunktes. Dialectica 12 (3‐4):280-287.
Charles Parsons (1995). Platonism and Mathematical Intuition in Kurt Gödel's Thought. Bulletin of Symbolic Logic 1 (1):44-74.
Nelson Goodman & W. V. Quine (1947). Steps Toward a Constructive Nominalism. Journal of Symbolic Logic 12 (4):105-122.
W. W. Tait (2005). Gödel's Reformulation of Gentzen's First Consistency Proof for Arithmetic: The No-Counterexample Interpretation. Bulletin of Symbolic Logic 11 (2):225-238.
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