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Philosophy of Mathematics Selected Readings

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ISBN-10: 052129648X

ISBN-13: 9780521296489

Edition: 2nd (Revised)

Authors: Hilary Putnam, Hilary Benacerraf, Paul Benacerraf

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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…    
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Book details

List price: $52.99
Edition: 2nd
Publisher: Cambridge University Press
Publication date: 1/27/1984
Binding: Paperback
Pages: 612
Size: 6.02" wide x 9.13" long x 1.54" tall
Weight: 1.936
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…    

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