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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No trivia or quizzes yet. I would recommend it to anyone with an interest in mathematics and philosophy. Theorems begin as mere conjectures, whose proofs are informal and whose terms are vaguely defined.
You didn’t do so hot in higher-level math, are more comfortable with the subjectivity of the written word, and view the process of mathematical discovery from a position of respect and distance.
I am not a philosopher and so I make no pretense to speak authoritatively about this. To create the most apt theorem A book about the meaning and philosophy of mathematical proofs. 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.
Lakatos contrasts the formalist method of approaching mathematical history against his own, consciously “heuristic” approach. That is, the proof always takes precedence.
Proofs and Refutations: The Logic of Mathematical Discovery
Mar 24, Conrad rated it it was amazing Shelves: Lists with This Book. Imre Lakatos has written a highly readable book that ought to be read and re-read, to remind current and future generations of mathematicians that mathematics is not a quest for knowledge with an actual end, but shared cultural, even psychological, human activity.
It takes a theory about the sides of a polyhedron by Euler and uses dialogue form to show how the methods of inquiry of a handful of different theoreticians fall apart when attempting to prove or disprove the proposition. 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.
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. Open Preview See a Problem? The book looks into those from the purely mathematical standpoint, and shows that they can be a lot easier to grasp and understand.
Portions of Proofs and Refutations were required reading for one of my classes for my master’s degree, but I liked it enough that I finished it after the course was completed.
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 the Loss of Certainty” reinvigorated my love for mathematics; because it showed mathematics didn’t have to be presented in the dry theorem-lemma-proof style that has had it in a strangle hold since the 20th century predominance of the rigorists called formalists by Lakatos.
One of the issues is, in fact, the definition of a polyhedron, as well as the difference between Eulerian and non-Eulerian polyhedra. Progress indeed replaces naive classification by theoretical classification, that is, by theory-generated proof-generated, or if you like, explanation-generated classification.
Though the book is written as a narrative, an actual method of investigation, that of “proofs and refutations”, is developed. Proofs and Refutations – Canada. Trying to meet all your book preview and review needs. Many important logical ideas are explained in the book.
So now we have got a theorem in which two mystical concepts, bounded variation and Riemann-integrability, occur.
Proofs and Refutations – Wikipedia
The difference between man and animals is thus a matter of degree and not of kind. Published January 1st by Cambridge University Press. With culture in the place of civilization there can be no question of the transcendent priofs applies to all men.
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.
The polyhedron-example that is used has, in fact, a long and storied past, and Lakatos uses this to keep the example from being simply an abstract one — the book allows one to see the nad progression of maths, and to hear the echoes of the voices of past mathematicians that grappled with the same question.
This deserves a higher rating, but the math was beyond my lakqtos understanding so I struggled regutations bit. Want to Read saving…. This way, the reader has a chance to experience the process. Feb 05, Julian rated it really liked it Shelves: The book lakahos structured as a philosophical dialogue. We also see how generally it is the refutations, the counterexamples, that help us in the development by forcing us to specify more conditions in the theorems, using more specific definitions and hint at further developments of the theorem.
An important look at the history and philosophy of maths a field not quite as esoteric as one might imagine this book is certainly recommended to all who are involved with mathematics, as well as all historians and philosophers of science. It was a little dry at times but the dialogue was very interesti I picked this up seeing it on a list of Robb Seaton’s favorite books”.
I would have to reread this some day. I really enjoyed wrestling with the idea that annd can not be the perfect ideal that mathematics and mathematicians should strive for. At some parts of the book, the amount of prerequisite mathematical knowledge is small, then suddenly takes a giant leap into undefined but commonly known in advanced mathematics literatureso it can be a little difficult.