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Philosophy of Mathematics:

Selected Readings
Front Cover
4 Reviews
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.
  

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Review: Philosophy of Mathematics: Selected Readings

User Review  - Mitchell - Goodreads

This was a collection of essays organized around a few of the major themes in early 20th century mathematical philosophy, such as formalism vs. intuitionism, the nature of mathematical truth, etc. The ... Read full review

Review: Philosophy of Mathematics: Selected Readings

User Review  - Alec - Goodreads

A must-have book, if you're a student of the philosophy of mathematics. This was THE anthology of important essays when it came out, and remained so for a lot of years. As an historical map of the phil-math terrain, this book is essential. Read full review

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Selected pages

Contents

II
3
III
41
IV
52
V
61
VI
66
VII
77
VIII
90
IX
97
XVII
295
XVIII
315
XIX
329
XX
355
XXI
377
XXII
394
XXIII
403
XXIV
421

X
130
XI
160
XII
183
XIII
202
XIV
207
XV
241
XVI
272
XXV
447
XXVI
470
XXVII
486
XXVIII
503
XXIX
530
XXX
571
Copyright

Other editions - View all

Philosophy of mathematics: selected readings
Philosophy of mathematics: selected readings
Paul Benacerraf,Hilary Putnam
Snippet view - 1964

Common terms and phrases

accept analysis analytic analytic propositions applies argument arithmetic assertion axiom of choice axiom of infinity axiom of replacement axiomatic set theory belongs calculus Cantor's cardinal concept F concept of set consistency consistency proof construction contains continuum hypothesis convention deduction defined definition derived elementary elements empirical entities example existence expressions fact false finite number finitist formal system formula Frege function geometry given Godel Hilbert idea impredicative impredicative definitions induction infinite integers interpretation intuition intuitionism intuitionist intuitionistic logic iterative conception language logical truth mathe mathematical truth matical meaning method natural numbers notion number theory ordinal numbers paradoxes philosophical philosophy of mathematics possible postulates predicate primitive principle problem proof propositions proved purely quantifiers question real numbers reason recursive reference relation rules Russell semantics sense sentence sequence set theory stage subsets symbols theorem things tion transfinite true words Zermelo set theory

References to this book

From other books

Mathematical Logic
Mathematical Logic
H.-D. Ebbinghaus,J. Flum,Wolfgang Thomas
Limited preview - 1994
The state of the art
The state of the art
Charles Francis Hockett
Snippet view - 1970
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From Google Scholar

Formal Methods and the Certification of Critical Systems
John Rushby
Connected Mathematics-Building Concrete Relationships with ...
Uriel Joseph Wilensky - 1993
Formalized Mathematics
John Harrison
Incompleteness: The Proof and Paradox of Kurt Gödel
Rebecca Goldstein
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References from web pages

JSTOR: Philosophy of mathematics: Selected Readings
Philosophy of mathematics, Selected readings, edited by Paul Benacerraf and Hilary Putnam, Prentice-Hall, Inc., Engle- wood Cliffs, New Jersey, 1964, pp. ...
links.jstor.org/ sici?sici=0022-4812(196903)34%3A1%3C107%3APOMSR%3E2.0.CO%3B2-V

Paul Benacerraf - Wikipedia, the free encyclopedia
(1983) Philosophy of Mathematics : Selected Readings 2nd edition, Cambridge University Press: New York. Benacerraf, Paul (1996) Recantation or Any old ...
en.wikipedia.org/ wiki/ Paul_Benacerraf

1899-1930: FROM HILBERT TO BROUWER (PHIL 296)
English translation in P. Benacerraf, H. Putnam, eds., Philosophy of Mathematics. Selected Readings Cambridge University Press, 1987. ...
orion.oac.uci.edu/ ~aldo/ hilbert-brouwer.html

Benacerraf Interview
Philosophy of Mathematics: Selected Readings. Benacerraf: I thank you and your colleagues for these questions. I’m afraid I shall not do them justice. ...
www.stanford.edu/ group/ dualist/ vol8/ pdfs/ benacerraf.pdf

Review: Paul Benacerraf, Hilary Putnam, Philosophy of mathematics ...
Paul Benacerraf, Hilary Putnam, Philosophy of mathematics: Selected Readings. Full-text: Access via JSTOR (no additional login). Go to this article in JSTOR ...
projecteuclid.org/ handle/ euclid.jsl/ 1183736632

Foundations Study Guide: Philosophy of Mathematics
There are several pieces by intuitionists— Brouwer, Heyting and Dummett— in the collection Philosophy of Mathematics, Selected Readings, edited by Paul ...
ios.org/ articles/ foundations_phil-of-mathematics.asp

Helsingin yliopisto - Humanistinen tiedekunta
Philosophy of Mathematics: Selected Readings, Cambridge: Cambridge University Press, 2nd edition, 272-294. (b) Benacerraf, Paul (1973). ...
www.helsinki.fi/ filosofia/ k2008/ Pietarinen.htm

The Notion of ‘Set’ in Cantor’s Transfinite Number Theory
The Philosophy of Mathematics: Selected Readings. 2nd ed. Eds. Paul Benacerraf & Hilary Putnam. Cambridge: Cambridge University Press, 1983a. 272-94. ...
www.sewanee.edu/ Philosophy/ Journal/ Current_Issue/ Compton.htm

<a href="http://www.cambridge.org">© Cambridge University Press</a ...
052129648X - Philosophy of Mathematics: Selected Readings, Second Edition. Edited by Paul Benacerraf and Hilary Putnam. Excerpt. More information ...
assets.cambridge.org/ 97805212/ 96489/ excerpt/ 9780521296489_excerpt.pdf

PART II PAPER 08: PHILOSOPHICAL LOGIC
Philosophy of Mathematics: selected readings (Oxford: Blackwell, 1964; 2nd edn. Cambridge University Press, 1983); and in Gödel's Collected Works, ...
www.phil.cam.ac.uk/ u_grads/ Tripos/ Phil_Logic/ Reading_List/ PHIRL_PartII_Paper08.pdf

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.

Bibliographic information

QR code for Philosophy of Mathematics
TitlePhilosophy of Mathematics: Selected Readings
AuthorPaul Benacerraf
EditorsPaul Benacerraf, Hilary Putnam
Photographs byHilary Putnam
ContributorPaul Benacerraf
Edition2, reprint, revised
PublisherCambridge University Press, 1983
ISBN052129648X, 9780521296489
Length600 pages
Subjects › 

Mathematics / History & Philosophy
Mathematics / Research
Philosophy / Methodology
Philosophy / Political
Science / Philosophy & Social Aspects
  
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