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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William rated it it was amazing Jan 10, And Lakatos knows the history of eulers theorem, presents it as a classroom discussion making us realize that nothing is ever static in mathematics. Many of you, I’m guessing, have some math problems. Taking the development of Eulerian-polyhedra as a central case study, Lakatos adopts the view of critical rationalism: Published January 1st by Cambridge University Press. That is, the proof always takes precedence. This deserves a higher rating, but the math was beyond my meager understanding so I struggled a bit.
Feb 05, Julian rated it really liked it Shelves: Relatively short, it is also a very dense book, with hardly a wasted word.
Proofs and Refutations – Imre Lakatos
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. I’ve never gotten past Algebra II, and I still understood most of the book, though to be sure I missed out proofw the bits 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.
Books by Imre Lakatos. 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.
Just a moment while we sign you in to your Goodreads account. He makes you think about the nature of proof, kind of along the lines of the great Morris Kline–still an occasional presence during my graduate school days at New York University–and who’s wonderful book, “Mathematics and This is an excellent, though very difficult, read.
This short, but inspiring read refutationw not a particular theorem or proof in mathematics, but rather the lakaots of how mathematics is developed from an initial idea, hypothesis, monster-barring, expansion of the theorem, etc. 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. What Lakatos shows you is that math is not the rigid formalistic system you may conceive of, but something far more fluid, something prone to frequent revision, something that must always have its underpinnings challenged in order to reach mathematical truth.
Proofs and Refutations: The Logic of Mathematical Discovery
The difference between man and animals is thus a matter of degree and not of kind. 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. Jun 13, Douglas rated it it was amazing Shelves: A book about the meaning and philosophy of mathematical proofs. So now we have got a theorem in which two mystical concepts, bounded variation and Riemann-integrability, occur.
Whenever one of the characters says something flowery and absurd, there’s a little footnote to something almost identical said by Poincare or Dedekind or some other prominent mathematician. Lakatos also displays a fine wit, and an elegant writing style. But I warn you, it’s a slow go itself. 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’.
Most remarkable is the narrative drive behind the argument. 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”. Open Preview See a Problem?
Lakatos argues that proof I rated this book 4 stars but it would be more accurate to call it 4 stars out of 5 for a mathematics book or for a school book or for a required reading book. The book includes two appendices. Written in Socratic dialogue. Though I find his critique of rigor appealing pakatos comes at too high a price if I also have to accept the attendant irrationalism.
Proofs and Refutations – Wikipedia
According to Roger Kimball’s review of Stove, “Who was David Stove”, New Criterion, March”In [Popper’s] philosophy of science, we find the curious thought that falsifiability, not verifiability, is the distinguishing mark of scientific theories; this means that, for Popper, one theory is better than another if it is more dis-provable than the other.
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 risk of being retaken by the sea.
Many are apt to shy away from it due to its apparent levity and lack of rigor.
Apr 15, Nick Black marked it as to-read Recommended to Nick by: The idea that the definition creates the mathematical meaning is a another powerful one, and I think it would be interesting to do proofd activity where students could come up with initial definitions and then try to rewrite them to make them more broad or more narrow.
The additional essays included here another case-study of the proofs-and-refutations idea, and a comparison of The Deductivist versus the Heuristic Approach offer more insight into Lakatos’ philosophy and are welcome appendices. What’s important here, for the non-mathematically inclined, is to understand how we apply those same formalisms proos our day-to-day thought.
Instead of treating definitions as if they have been conjured up by divine insight to allow the mathematician to deduce theorems from the bottom up, the heuristic approach recognizes the very top down aspect of performing mathematics, by which definitions develop as a consequence of the refinement of proofs and their related concepts. This poverty of rewards is the explicit erfutations of Kline, whom I had read years before coming across Lakatos. This book describes a lot of what I ahd missing while studying mathematics in the university, mainly the reasoning for the way proofs were, and the overall reasoning for the definitions and terms used.
Strongly invoking Popper both in its title and subtitle echoing Popper’s Conjectures and Refutations and The Logic of Scientific DiscoveryLakatos applies much of the master’s thinking to the specific example of mathematics. Stove attempts to show how this has lead to what he calls irrationalism; by which he means the destruction of the intellect. Lakatos contrasts the formalist method of approaching mathematical history against his own, consciously “heuristic” approach.
It is this destruction, not irrefutability as Popper claims, that has lead to the ascendancy of bogus ideas such as Marxism, feminism and, lately, deconstructionism.