Proofs and Refutations The Logic of Mathematical Discovery

ISBN-10: 0521290384

ISBN-13: 9780521290388

Edition: 1976

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Description: 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.

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Book details

List price: $59.99
Copyright year: 1976
Publisher: Cambridge University Press
Publication date: 1/1/1976
Binding: Paperback
Pages: 188
Size: 5.50" wide x 8.50" long x 0.75" tall
Weight: 0.550
Language: English

John L. Worrall is Professor of Criminology and Program Head at the University of Texas at Dallas (UTD). A Seattle native, he received a B.A., double majoring in psychology and law and justice, from Central Washington University in 1994. Both his M.A. (criminal justice) and Ph.D. (political science) were received from Washington State University, where he graduated in 1999. From 1999-2006, he was a member of the criminal justice faculty at California State University, San Bernardino. He joined UTD in Fall 2006, was promoted to full professor in 2008, and in 2010 was selected to direct the criminology program. Dr. Worrall has published articles and book chapters on a wide range of topics ranging from legal issues in policing to crime measurement, having recently been ranked one of the most prolific sole and lead authors in the discipline. Courses he regularly teaches (and has authored texts for) include introductory criminal justice, criminal procedure, and crime control policy. As Program Head at UTD, Dr. Worrall directs undergraduate, M.S., and Ph.D. programs in criminology, including an online MS program, which he developed. He is active in the Academy of Criminal Justice Sciences, the American Society of Criminology, and a number of regional associations. Finally, he continues to serve as editor of the journal Police Quarterly, a position he has held since 2008.

EditorsG++ preface
Acknowledgments
AuthorG++s introduction
A problem and a conjecture
A proof
Criticism of the proof by counterexamples which are local but not global
Criticism of the conjecture by global counterexamples
Criticism of the proof-analysis by counterexamples which are global but not local: the problem of rigour
Return to criticism of the proof by counterexamples which are local but not global: the problem of content
The problem of content revisited
Concept-formation
How criticism may turn mathematical truth into logical truth
Appendices
Bibliography
Index of names
Index of subjects
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