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1 Burnside - Bldg. 2 Mathematics- Foundations and Logic

This title in other editions

Proofs and Refutations: The Logic of Mathematical Discovery

by

Proofs and Refutations: The Logic of Mathematical Discovery Cover

 

Synopses & Reviews

Publisher Comments:

Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.

Synopsis:

Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.

Synopsis:

A novel introduction to the philosophy of mathematics, mostly in the form of a discussion between a group of students and their teacher. It combats the positivist picture and develops a much richer, more dramatic progression.

Synopsis:

Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.

Description:

Bibliography: p. 155-165.

Table of Contents

Editors' preface; Acknowledgments; Author's introduction; 1. A problem and a conjecture; 2. A proof; 3. Criticism of the proof by counterexamples which are local but not global; 4. Criticism of the conjecture by global counterexamples; 5. Criticism of the proof-analysis by counterexamples which are global but not local: the problem of rigour; 6. Return to criticism of the proof by counterexamples which are local but not global: the problem of content; 7. The problem of content revisited; 8. Concept-formation; 9. How criticism may turn mathematical truth into logical truth; Appendices; Bibliography; Index of names; Index of subjects.

Product Details

ISBN:
9780521290388
Editor:
Worrall, J.
Author:
Lakatos, E.
Author:
Worrall, John
Author:
Lakatos, Imre
Author:
Zahar, Elie
Author:
Zahar, E.
Author:
Worrall, J.
Publisher:
Cambridge University Press
Location:
New York
Subject:
General
Subject:
Philosophy
Subject:
Mathematics
Subject:
Logic
Subject:
Logic, symbolic and mathematical
Subject:
Proof theory
Subject:
General Philosophy
Subject:
Proof theory Proof theory
Subject:
Mathematics -- Philosophy.
Subject:
Mathematics-Logic and Philosophy
Subject:
Philosophy & Aspects
Copyright:
Edition Description:
Trade paper
Series Volume:
369
Publication Date:
19760131
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Yes
Pages:
188
Dimensions:
8.44x5.68x.45 in. .57 lbs.

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Related Subjects

Humanities » Philosophy » General
Reference » Science Reference » General
Reference » Science Reference » Philosophy of Science
Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » History
Science and Mathematics » Mathematics » Logic and Philosophy

Proofs and Refutations: The Logic of Mathematical Discovery Used Trade Paper
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Product details 188 pages Cambridge University Press - English 9780521290388 Reviews:
"Synopsis" by , Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.
"Synopsis" by , A novel introduction to the philosophy of mathematics, mostly in the form of a discussion between a group of students and their teacher. It combats the positivist picture and develops a much richer, more dramatic progression.
"Synopsis" by , Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.
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