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Date : 2015-10-08
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Proofs and Refutations Cambridge Core ~ Imre Lakatoss Proofs and Refutations is an enduring classic which has never lost its relevance Taking the form of a dialogue between a teacher and some students the book considers various solutions to mathematical problems and in the process raises important questions about the nature of mathematical discovery and methodology
Proofs and Refutations The Logic of Mathematical ~ Imre Lakatoss Proofs and Refutations is an enduring classic which has never lost its relevance Taking the form of a dialogue between a teacher and some students the book considers various solutions to mathematical problems and in the process raises important questions about the nature of mathematical discovery and methodology
Proofs and Refutations Cambridge University Press ~ chapter 2 of Lakatos’s 1961 Cambridge thesis The original ‘Proofs and Refutations’ essay was a much amended and improved version of chapter 1 of that thesis A part of chapter 3 of this thesis becomes here appendix 1 which contains a further casestudy in the method of proofs and refutations
Proofs and Refutations The Logic of Mathematical Discovery ~ Proofs and Refutations The Logic of Mathematical Discovery 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
Proofs and Refutations Wikipedia ~ Proofs and Refutations is a 1976 book by philosopher Imre Lakatos expounding his view of the progress of mathematics The book is written as a series of Socratic dialogues involving a group of students who debate the proof of the Euler characteristic defined for the polyhedron A central theme is that definitions are not carved in stone but often have to be patched up in the light of later insights in particular failed proofs This gives mathematics a somewhat experimental flavour At the end
Citations of Proofs and Refutations The Logic of ~ The article shows by analysis of the Gettier programme that conceptual analysis shares the proofs and refutations form Lakatos identified in mathematics Upon discovery of a counterexample this structure aids the search for a replacement hypothesis The search is guided by heuristics The heuristics
Proofs and Refutations The Logic of Mathematical Discovery ~ Proofs and Refutations The Logic of Mathematical Discovery 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
Proofs and Refutations The Logic of Mathematical Discovery ~ There is a sizable contingent of mathematicians who clearly believe that the path to discovery need not or should not be reflected in the path to justification and exposition This disagreement of course has some consequences for the way mathematics is taught In some sense it echoes the mathematical culture wars of the past several years
Proofs and Refutations UCB Mathematics ~ PROOFS AND REFUTATIONS I The dialogue form should reflect the dialectic of the story it is meant to contain a sort of rationally reconstructed or distilled history The real history will chime in in the footnotes most of which are to be taken therefore as an organic part of the essay
Proofs and Refutations The Logic of Mathematical Discovery ~ Proofs and Refutations is not everyone’s cup of tea its discussioncumdialectic style is shall we say unusual As a Platonist I have serious objections to the dialectical position Lakatos appears to embrace already in his aforementioned introduction suggesting that the history of mathematics can be described entirely in terms of the opposing poles of dogmatism and skepticism in the author’s parlance
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