Philosophy of Mathematics in the Twentieth Century: Selected Essays

In this illuminating collection, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the course of the past century. Parsons begins with a discussion of the Kantian legacy in the work of L. E. J. Brouwer, David Hilbert, and Paul Bernays, shedding light on how Bernays revised his philosophy after his collaboration with Hilbert. He considers Hermann Weyl’s idea of a “vicious circle” in the foundations of mathematics, a radical claim that elicited many challenges. Turning to Kurt Gödel, whose incompleteness theorem transformed debate on the foundations of mathematics and brought mathematical logic to maturity, Parsons discusses his essay on Bertrand Russell’s mathematical logic—Gödel’s first mature philosophical statement and an avowal of his Platonistic view. Philosophy of Mathematics in the Twentieth Century insightfully treats the contributions of figures the author knew personally: W. V. Quine, Hilary Putnam, Hao Wang, and William Tait. Quine’s early work on ontology is explored, as is his nominalistic view of predication and his use of the genetic method of explanation in the late work The Roots of Reference. Parsons attempts to tease out Putnam’s views on existence and ontology, especially in relation to logic and mathematics. Wang’s contributions to subjects ranging from the concept of set, minds, and machines to the interpretation of Gödel are examined, as are Tait’s axiomatic conception of mathematics, his minimalist realism, and his thoughts on historical figures.

About the Author :
Charles Parsons is Edgar Pierce Professor of Philosophy, Emeritus, at Harvard University.

Review :
Parsons is a much admired and highly respected philosopher of mathematics and logic, well-known for his thoughtful and careful reflections on both the great historical figures and on work of the previous century. He is also an astute commentator on the current literature, engaging the contemporary debates and offering illuminating insights about its content and direction. This volume offers a unique opportunity for those not fortunate enough to have attended classes of Parsons’s to form some idea of what such an experience would be like. This is a truly superb book. Parsons is quite possibly the most distinguished writer on philosophy of mathematics now working and certainly the most careful and probing. These essays examine a rather wide range of historical opinion on mathematical matters, both with an eye to demanding more careful interpretations and formulations from important writers such as Kant or Gödel while remaining sympathetic to their overall philosophical ambitions. Parsons’s treatments are unsurpassed.