Cambridge Core – Philosophy of Science – Proofs and Refutations – edited by Imre Lakatos. PROOFS AND REFUTATIONS. ‘zip fastener’ in a deductive structure goes upwards from the bottom – the conclusion – to the top – the premisses, others say that. I. LAKATOS. 6 7. The Problem of Content Revisited. (a) The naivet6 of the naive conjecture. (b) Induction as the basis of the method of proofs and refutations.
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Proofs and Refutations – Wikipedia
Unfortunately, he choose Popper as his model. Mar 24, Conrad rated it it pakatos amazing Shelves: This page was last edited on 28 Februaryat It was a little dry at times lakatoos the dialogue was very interesting and posed some very interesting questions about the way people have approached solving problems throughout history.
What seems relatively straightforward is in fact a complex and convoluted problem, and as the various opinions regarding proper approaches are voiced the characters also grow richer.
As an enthusiastic but relatively feeble intellect–at least by the standards of today’s ultra-competitive modern university wizards–I felt cheated. We see how new definitions emerge, like simply connected, from the nature of the naive, but incomplete, proofs of the conjecture. At its lakattos, it can reveal without effort the dialectic manner in which lakats and disciplines develop. Shit, I think I might get a tattoo of that ferocious “urchin” on the book cover.
Nov 24, Arthur Ryman rated it it was amazing.
And Lakatos knows the history of eulers theorem, presents it as a classroom discussion making us realize that nothing is ever static in mathematics. Lakatos contrasts the formalist method of approaching mathematical history against his own, consciously “heuristic” approach. May 29, Nick rated it it was amazing Shelves: The mathematics is generally except in the appendices about analysis quite elementary and doesn’t require any prior knowledge, though it will feel more familiar if you have some experience with mathematical proofs.
If something is mathematically proven we know beyond any shadow of a doubt that it is true because it follows from elementary axioms. It does seem that the prevailing belief that we cannot really know anything–that there is uncertainty even in mathematical proof–has something to do with the loss of confidence in Western civilization itself; that the return to verifiability from falsifiability would herald a return to the old confidence in not only Western civilization but the idea of civilization itself.
I think I can describe it as “Plato’s The Republic meets Philosophy meets History of Mathematics” and that sentence can more or less describe the entirety of the book. By far one of the best philosophical texts I’ve read. What is the them of this rdfutations Today all we have is culture and that allows no judgment as to progress of mankind–except as an outworking of an all-encompassing statism.
Proofs and Refutations: The Logic of Mathematical Discovery
The idea that the definition creates the mathematical meaning is a another powerful one, and I think it would be interesting to do an activity where stude Although I appreciates Lakatos’ classroom discussion style as original I had a hard time keeping up with the development of the conversation and keeping the original question in mind. In this essay Stove makes a devastating critique of Popper and portrays Lakatos as his over-eager acolyte; a sort of Otis to Lex Luther, if you will.
The idea that the definition creates the mathematical meaning is a another powerful one, and I think it would be interesting to do an activity where students could come up with initial definitions and then try to rewrite them to make them more broad or more narrow.
Jul 09, Devi rated it it was amazing Shelves: Lists with This Book.
I am not a philosopher and so I make no pretense to speak authoritatively about this. Anc 16, Gwern rated it really liked it.
Proofs and Refutations: The Logic of Mathematical Discovery by Imre Lakatos
Out of this Lakatos has fashioned an extremely effective essay explaining much about mathematics and its methods. If you like books and love to build cool products, we may be looking for proods. I’ve never gotten past Algebra II, and I still understood most of the book, though to be sure I missed out on the proofz of calculus here and there, and didn’t know enough about math to discern which dialogue participant stood By far one of the best philosophical texts I’ve read.
Despite playing such a major role in philosophy’s formal genesis, the dialogue has often presented a challenge to contemporary philosophers. We develop mathematical definitions, examples, theorems, and proofs to meet human needs through heuristics.
This is an excellent, though very difficult, read. Return to Book Page. Theorems begin as mere conjectures, whose proofs are informal and whose terms are vaguely defined. Is the theorem wrong, then?