Philosophy of Mathematics in the Twentieth Century: Selected Essays

Charles Parsons

Harvard University Press | 2014 | 365 páginas | rar - pdf |950 kb

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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

Contents
Preface
Introduction
Part I: Some Mathematicians as Philosophers
1. The Kantian Legacy in Twentieth-Century Foundations of Mathematics
2. Realism and the Debate on Impredicativity, 1917–1944 
Postscript to Essay 2
3. Paul Bernays’ Later Philosophy of Mathematics
4. Kurt Gödel
5. Gödel’s “Russell’s Mathematical Logic” ~
Postscript to Essay 5
6. Quine and Gödel on Analyticity
Postscript to Essay 6
7. Platonism and Mathematical Intuition in Kurt Gödel’s Thought
Postscript to Essay 7
Part II: Contemporaries
8. Quine’s Nominalism
9. Genetic Explanation in The Roots of Reference
10. Hao Wang as Philosopher and Interpreter of Gödel
11. Putnam on Existence and Ontology
12. William Tait’s Philosophy of Mathematics
Bibliography
Copyright Acknowledgments
Index