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Philosophy of Mathematics Selected Readings

ISBN-10: 052129648X

ISBN-13: 9780521296489

Edition: 2nd (Revised)

Authors: Hilary Putnam, Hilary Benacerraf, Paul Benacerraf

List price: $88.00
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Description:

The twentieth century has witnessed an unprecedented `crisis in the foundations of mathematics, featuring a world-famous paradox (Russells Paradox), a challenge to `classical mathematics from a world-famous mathematician (the `mathematical intuitionism of Brouwer), a new foundational school (Hilberts Formalism), and the profound incompleteness results of Kurt Gdel. 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 Gdel 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.
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Book details

List price: $88.00
Edition: 2nd
Publisher: Cambridge University Press
Publication date: 1/27/1984
Binding: Paperback
Pages: 612
Size: 6.25" wide x 9.00" long x 1.25" tall
Weight: 1.694
Language: English

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.

Preface to the second edition
Introduction
The Foundations of Mathematics
The logicist foundations of mathematics
The intuitionist foundations of mathematics
The formalist foundations of mathematics
Disputation
Intuitionism and formalism
Consciousness, philosophy, and mathematics
The philosophical basis of intuitionistic logic
The concept of number
Selections from Introduction to Mathematical Philosophy
On the infinite
Remarks on the definition and nature of mathematics
Hilbert's programme
The Existence of Mathematical Objects
Empiricism, semantics, and ontology
On Platonism in mathematics
What numbers could not be
Mathematics without foundations
Mathematical Truth
The a priori Alfred
Truth by convention
On the nature of mathematical truth
On the nature of mathematical reasoning
Mathematical truth
Models and reality
The Concept of Set
Russell's mathematical logic
What in Cantor's continuum problem?
The iterative concept of set
The concept of set
Bibliography