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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Philosopher of mathematics and science, known for his thesis of the fallibility of mathematics and its ‘methodology of proofs and refutations’ in its pre-axiomatic stages of development, and also for introducing the concept of the ‘research programme’ in his methodology of scientific research programmes.
From Wikipedia, the free encyclopedia. I would have to reread this some day. As an enthusiastic but relatively feeble intellect–at least by the standards of today’s ultra-competitive modern university wizards–I felt cheated.
So now we have got a theorem in which two mystical concepts, bounded variation and Riemann-integrability, occur.
Proofs and Refutations: The Logic of Mathematical Discovery
In fact, the definitions themselves have become more generally encompassing without this fact being consciously realized by the mathematicians working with the new rerutations. Jun 23, J.
And this is why, even though I recommend Lakatos’ book, ultimately I must back away from it. 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 very idea of mathematical truth and the changing notions of rigour and proof are all discussed with stunning clarity.
This way, the reader has a chance to experience the process. Lakatos refutatoons that proofs are either far too limited to be of any use, or else they invariable let in some “monsters”.
Lakatos himself did not finish the preparations to publish his essay in book form, but his editors have done a fine job. Both of these examples resonate with my personal mathematical journey. And it is presented in the form of an entertaining and even suspenseful narrative.
Proofs and Refutations – Imre Lakatos
At the end of the Introduction, Lakatos explains that his purpose is to defutations formalism in mathematicsand to show that informal mathematics grows by a logic of “proofs and refutations”. He gave me the reassurance to go on reading and seeking mathematical presentations which preserved the spirit of the amateur and the enthusiast.
What is the them of this book? This is an excellent, though very difficult, read. Jul 16, Gwern rated it really liked it.
Proofs and Refutations: The Logic of Mathematical Discovery by Imre Lakatos
I once thought I had found Lakatos to be putting the final nail into the lakatps of the certainty of overly rigorous mathematical proof; that slight were the blessings of such rigor compared to loss in clarity and direction in mathematics. I have proofw background in set theory or axiomatics, and so the material in this book initially appeared quite shocking to me.
Stove attempts to show how this has lead to what he calls irrationalism; by which he means the destruction of the intellect. 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. The mathematics is generally except in the appendices about analysis quite elementary and doesn’t require any prior knowledge, though it will feel pproofs familiar if you have some experience with mathematical proofs.
I really enjoyed wrestling with the idea that “proofs” can not be the perfect ideal that mathematics and mathematicians should strive for. 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.
Progress indeed replaces naive classification by refutatoons classification, that is, by theory-generated proof-generated, or if you like, explanation-generated classification. Apr 15, Nick Black marked it as to-read Recommended to Nick by: We see how new definitions emerge, like simply connected, from the nature of the naive, but incomplete, proofs of the conjecture.
Preview — Proofs oroofs Refutations by Imre Lakatos. The discovery led to the definitional distinction between ‘point-wise convergence’ and ‘uniform convergence’. Sep 30, Robb Seaton rated it it was amazing Shelves: Such a view fit in with my own frustration over rigorism which diverts the student from the rich meat of mathematical ideas towards the details of the implements by which it is to be served.
It combats the positivist picture and develops a much richer, more dramatic progression. Begins strong with a deconstruction of the Euler characteristic, but soon gets bogged down in philosophy, along with a troubling amount of relativism, although I’m not entirely clear about what Lakatos intends when he writes about truth, certainty, and progress.
It was a little dry at times but the dialogue was very interesting and posed some very interesting questions about the way people have approached solving problems throughout history.
This page was last edited on 28 Februaryat It really shows and demonstrates how you can take a really simple relation and build it up to create an extensive and interesting theory and lakaros field of mathematics one step at a time.
Most remarkable is the narrative drive behind the argument.
It is this destruction, not irrefutability as Popper claims, that has lead to the ascendancy rffutations bogus ideas such as Marxism, feminism and, lately, deconstructionism. I’ve never gotten past Algebra II, and I still understood most of the book, though to be sure I missed out on the bits of calculus here and there, and didn’t know enough about math to discern which dialogue participant stood for which philosopher.
The gist of it is that non-obvious mathematical concepts and definitions emerge through the process of refuting proposed proofs by exhibiting counter-examples. While their dispute is ultimately intellectual for the most part the personal tensions also realistically make themselves felt. See 1 question about Proofs and Refutations….