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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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 refutatioons to the old confidence in not only Western civilization but the idea of civilization itself.
I’m excited about this one, riding in as it does on a ringing recommendation of Conrad’s although I’m a bit puzzled by his tagging of House of Leaves with “masterpieces”. Both of these This is a frequently cited work in the philosophy of mathematics.
Proofs and Refutations – Imre Lakatos
Anyways, the bad is so negligible, I would say that if you like philosophy and if you like math, AND if you want a new perspective — read wnd very readable book. It is common for people starting out in Mathematics, by the time they’ve mastered Euclidean Geometry or some other first rigorous branch, to believe in its complete infallibility.
Jul 15, Zain rated it really liked it Shelves: The book is profoundly deep, in a philosophical way, and it was not too difficult, which is probably why I enjoyed it so much.
Lkaatos to meet all your book preview and review needs. Many important logical ideas are explained in the book.
And the exact condition necessary proots Cauchy’s proof to be correct became the definition of uniform convergence. One particularly enlightening application of this ‘proof-first’ method comes via the proof of Cauchy that the limit of a sequence of continuous functions is continuous.
We assume, incorrectly that mathematics are solid continents of rules and facts, but what we observe are loosely connected archipelagos of calibrated and stable forms where those islands are in constant lroofs of being retaken by the sea.
An important look at the history and philosophy of maths a field not quite as esoteric as one might refutatiohs this book refutatiojs certainly recommended to all who are involved with mathematics, as well as all historians and philosophers of science. Jul 14, Jake rated it it was amazing. A book about the meaning and philosophy of mathematical proofs. May 29, Nick rated it it was amazing Shelves: Goodreads helps you keep track of books you want to read.
Retrieved from ” https: To quote Northrop Frye, we go see MacBeth to learn what it feels like for a man to gain a kingdom but lose his soul. It reminds me of Ernest Mach’s “Science of Mechanics”–the latter is not in the form of a dialogue. Jul 16, Gwern rated it really liked it. If y Probably one of the most important books I’ve read in my mathematics career. If something is mathematically proven we know beyond any shadow amd a doubt that it is true because it follows from elementary axioms.
His main argument takes the form of a dialogue between a number of students and a te It is common for people starting out in Mathematics, by the time they’ve mastered Euclidean Geometry or some other first rigorous branch, to believe in its complete infallibility.
Many of you, I’m guessing, have some math problems. To see what your friends thought of this book, please sign up. Oct 22, Andrew added it Shelves: A number of mathematics teachers have implemented Lakatos’ method of proofs and refutations in the classroom, when teaching other mathematical topics.
Proofs and Refutations: The Logic of Mathematical Discovery
If you are going into mathematics at a University level, I would highly recommend this book. For example, the difference between a counterexample to a lemma a so-called ‘local counterexample’ porofs a counterexample to the specific conjecture under attack a ‘global counterexample’ to the Euler characteristic, in this case is discussed.
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.
Definitely required reading for mathematicians and philosophers of mathematics. Lakatos himself did not finish the preparations to publish his essay in book form, but his editors have done a fine job. Arda rated it it was amazing Mar 31, Nov 24, Arthur Ryman rated it it was amazing.
Using just a few historical case studies, the book presents retutations powerful rebuttal of the formalist characterization of mathematics as an additive process in which absolute truth is gradually arrived at through infallible deductions.
E prima di tutto il confronto: Or perhaps they do for “We might be more interested in this proposition if we really understood just why the Riemann — Stieltjes integrable functions are so important. I think we need to revert to an older point of view, echoed as well in the writings of the late Mortimer Adler, who also had some points to pick along these lines with modern philosophy and who would have us hearken back to the concreteness of Aristotle.
Trivia About Proofs and Refuta I would recommend it to anyone with an interest in mathematics and philosophy. In the first, Lakatos gives examples of the heuristic process in mathematical discovery. Definitions stretch as the history of mathematics rolls on; quite often slowly, and imperceptibly, so that when old theorems are seen in the light of the new stretched definitions, suddenly the proof is seen to be false, or to assume a ‘hidden lemma’.
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Apr 02, Jonathan rated it it was amazing. Here is Lakatos talking about the formalists, “Formalism denies the status of mathematics to most of what has been commonly understood to be mathematics, and can say nothing about its growth.
Proofs and Refutations – Wikipedia
And it is presented in the form of an entertaining and even suspenseful narrative. Unfortunately, he choose Popper as his model.
Jun 30, Kelly John Rose refutatiions it it was amazing. With culture in the place of civilization there can be no question of the transcendent that applies to all men.
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. Ahd 24, Conrad rated it it was amazing Shelves: