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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The book has been translated into more than 15 languages worldwide, including Chinese, Korean, Serbo-Croat and Turkish, and went into its second Chinese edition in None of the ‘creative’ periods and hardly any of the ‘critical’ periods of mathematical theories would be admitted into the formalist heaven, where mathematical theories dwell like the seraphim, purged of all the impurities of earthly uncertainty.
Proofs and Refutations: The Logic of Mathematical Discovery by Imre Lakatos
Jul 14, Jake rated it it was amazing. His proof still the standard proof in beginning analysis contained a ‘hidden lemma’.
Mar 12, Samuel Fout rated it it was amazing. Lakatos’ didactic text, the title essay which makes up the bulk of this book, is presented in the form of a discussion between a teacher and a number of students. 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.
Certainly the theorem statement can be improved and generalized, if the proof itself is improved and generalized. If you are going into mathematics at a University level, I would highly recommend this book. Jun 30, Kelly John Rose rated it it was amazing.
This book describes a lot of what I found missing while studying mathematics in the university, mainly the reasoning for the way proofs were, and the refutationx reasoning for the definitions and terms used. Naive conjectures and naive concepts are superseded by improved conjectures theorems and concepts proof-generated or theoretical concepts growing out of the method of proofs and refutations.
If you like books and love to build cool products, we may be looking for you. For example, the difference between a counterexample to a lemma a so-called ‘local counterexample’ and a counterexample to the specific conjecture under attack a ‘global counterexample’ to the Euler characteristic, in this case is discussed.
Refutwtions pretty readable for what it is – will revisit again someday.
rerutations Unfortunately, he choose Popper as his model. In best mathematical fashion each line builds on the previous, with all the fat trimmed away. I will admit that the book was a bit challenging for me, and I suspect I will revisit this book when I get a bit better at math, but for what it was I think it was quite readable and I enjoyed it.
Lakatoa discovery led to the definitional distinction between ‘point-wise convergence’ and ‘uniform convergence’. But I warn you, it’s a slow go itself. This is an excellent, though very difficult, read. So now we have got a theorem in which two mystical concepts, bounded variation and Riemann-integrability, occur.
Proofs and Refutations – Wikipedia
However, the dialogue possesses significant didactic and autotelic advantages. Nov 24, Arthur Ryman rated it it was amazing. Quotes from Proofs and Refuta With culture in the place of civilization there can be no question of the transcendent that applies to all men. And as theoretical ideas and concepts supersede naive ideas and concepts, theoretical language supersedes naive language.
Views Read Edit View history. This book is a wonderful blend of philosophy, history, pedagogy, and interesting mathematics.
According to Roger Kimball’s review of Refutationx, “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. The difference between man and animals is thus a matter of degree and not of kind.
Proofs and Refutations: The Logic of Mathematical Discovery
Just a moment while we sign you in to your Goodreads account. A number of mathematics teachers have implemented Lakatos’ method of proofs and refutations in the classroom, when teaching other mathematical topics. By far one of the best philosophical texts I’ve read.