David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Imre Lakatos (ed.)
Cambridge University Press (1976)
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.
|Keywords||Mathematics Philosophy Logic, Symbolic and mathematical|
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Roger Penrose (1990). Precis of the Emperor's New Mind. Behavioral and Brain Sciences 13 (4):643-705.
Robert Wilensky (1990). Computability, Consciousness, and Algorithms. Behavioral and Brain Sciences 13 (4):690-691.
Deborah Hodgkin & Alasdair I. Houston (1990). Selecting for the Con in Consciousness. Behavioral and Brain Sciences 13 (4):668-669.
Ken Binmore (1987). Modeling Rational Players: Part I. Economics and Philosophy 3 (02):179-.
Matti Tedre (2011). Computing as a Science: A Survey of Competing Viewpoints. [REVIEW] Minds and Machines 21 (3):361-387.
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