Philosophy of Mathematics: Selected Readings

Front Cover
Paul Benacerraf, Hilary Putnam
Cambridge University Press, 1983 - Mathematics - 600 pages
The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.
 

Contents

II
3
III
41
V
52
VII
61
VIII
66
IX
77
X
90
XII
97
XXII
295
XXIII
315
XXIV
329
XXV
355
XXVI
377
XXVII
394
XXVIII
403
XXIX
421

XIV
130
XV
160
XVI
183
XVII
202
XIX
207
XX
241
XXI
272
XXX
447
XXXI
470
XXXII
486
XXXIII
503
XXXIV
530
XXXV
571
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About the author (1983)

According to John Passmore, Hilary Putnam's work is a "history of recent philosophy in outline" (Recent Philosophers). He adds that writing "about "Putnam's philosophy' is like trying to capture the wind with a fishing-net." Born in Chicago and educated at the University of Pennsylvania and the University of California at Los Angeles, Putnam taught at Northwestern University, Princeton University, and the Massachusetts Institute of Technology before moving to Harvard University in 1965. In his early years at Harvard, he was an outspoken opponent of the war in Vietnam. Although he writes in the idiom of analytic philosophy, Putnam addresses major themes relating science to ethics and epistemology. If these themes are reminiscent of David Hume---as, for that matter, is much of analytic philosophy---his treatment of them is not. Putnam's work is far more profoundly shaped by recent work in logic, foundations of mathematics, and science than would have been possible for Hume; Putnam has contributed to each. He differs from Hume and stands more in the tradition of Willard Quine and American pragmatism in his treatment of the crucial distinctions between analytic and synthetic statements and between facts and values. Both distinctions, sharply made by Hume, are claimed by Putnam not to be absolute. He attempts to show, for example, that basic concepts of philosophy, science, and mathematics all are interrelated, so that mathematics bears more similarity to empirical reasoning than is customarily acknowledged.

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