Proofs and Refutations: The Logic of Mathematical Discovery 1st Edition

by Imre Lakatos (Editor), John Worrall (Editor), Elie Zahar (Editor)

18 customer reviews

ISBN-13: 978-0521290388

ISBN-10: 0521290384

Why is ISBN important?

Have one to sell? Sell on Amazon

Added to

Unable to add item to List. Please try again.

Share <Embed>

Condition: Used - Very Good

In Stock. Sold by threehegemons, Fulfilled by Amazon

Access codes and supplements are not guaranteed with used items.

27 Used from $9.49

FREE Shipping on orders over $25.

Select delivery location

Turn on 1-Click ordering

Only 1 left in stock - order soon.

Ships from and sold by U-Books.

This item does not ship to France. Please check other sellers who may ship internationally.

List Price: $59.99
Save: $10.00 (17%)

6 New from $53.91

Select delivery location

$49.99

Turn on 1-Click ordering

More Buying Choices

6 New from $53.91 27 Used from $9.49

33 used & new from $9.49

See All Buying Options

There is a newer edition of this item:

Proofs and Refutations: The Logic of Mathematical Discovery (Cambridge Philosophy Classics)

Proofs and Refutations: The Logic of Mathematical Discovery (Cambridge Philosophy Classics)
$22.68
(18)
In stock.

Free%20Two-Day%20Shipping%20for%20College%20Students%20with%20Amazon%20Student

Proofs and Refutations is essential reading for all those interested in the methodology, the philosophy and the history of mathematics. Much of the book takes the form of a discussion between a teacher and his students. They propose various solutions to some mathematical problems and investigate the strengths and weaknesses of these solutions. Their discussion (which mirrors certain real developments in the history of mathematics) raises some philosophical problems and some problems about the nature of mathematical discovery or creativity. Imre Lakatos is concerned throughout to combat the classical picture of mathematical development as a steady accumulation of established truths. He shows that mathematics grows instead through a richer, more dramatic process of the successive improvement of creative hypotheses by attempts to 'prove' them and by criticism of these attempts: the logic of proofs and refutations.

Frequently bought together

+

Total price: $64.62

These items are shipped from and sold by different sellers. Show details

Buy the selected items together

This item:Proofs and Refutations: The Logic of Mathematical Discovery by Imre Lakatos Paperback $49.99
Only 1 left in stock - order soon.
Ships from and sold by U-Books.
$5.27 shipping
How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) by G. Polya Paperback $14.63
In Stock.
Ships from and sold by Amazon.com.
FREE Shipping on orders over $25. Details

Customers who bought this item also bought

Page 1 of 1 Start overPage 1 of 1

This shopping feature will continue to load items. In order to navigate out of this carousel please use your heading shortcut key to navigate to the next or previous heading.

Tyler Cowen
Hardcover
$17.00
G. Polya

127

Paperback
$14.63
Paul Feyerabend

34

Paperback
$21.05
Judea Pearl

43

in Biostatistics
Hardcover
$21.75
John Stillwell

4

Hardcover
$18.26
Sabine Hossenfelder

54

in Group Theory
Hardcover
$19.32

Editorial Reviews

Review

'For anyone interested in mathematics who has not encountered the work of the late Imre Lakatos before, this book is a treasure; and those who know well the famous dialogue, first published in 1963-64 in the British Journal for the Philosophy of Science, that forms the greater part of this book, will be eager to read the supplementary material ... the book, as it stands, is rich and stimulating, and, unlike most writings on the philosophy of mathematics, succeeds in making excellent use of detailed observations about mathematics as it is actually practised.' Michael Dummett, Nature

'The whole book, as well as being a delightful read, is of immense value to anyone concerned with mathematical education at any level.' C. W. Kilmister, The Times Higher Education Supplement

'In this book the late Imre Lakatos explores 'the logic of discovery' and 'the logic of justification' as applied to mathematics ... The arguments presented are deep ... but the author's lucid literary style greatly facilitates their comprehension ... The book is destined to become a classic. It should be read by all those who would understand more about the nature of mathematics, of how it is created and how it might best be taught.' Education

Book Description

A novel introduction to the philosophy of mathematics, mostly in the form of a discussion between a group of students and their teacher. It combats the positivist picture and develops a much richer, more dramatic progression.

Product details

Paperback: 188 pages
Publisher: Cambridge University Press; 1st edition (January 1, 1976)
Language: English
ISBN-10: 0521290384
ISBN-13: 978-0521290388
Product Dimensions: 5.4 x 0.5 x 8.5 inches
Shipping Weight: 9.1 ounces (View shipping rates and policies)
Average Customer Review: 18 customer reviews
Amazon Best Sellers Rank: #1,241,191 in Books (See Top 100 in Books)
- #571 in Books > Science & Math > Mathematics > Pure Mathematics > Logic
- #6457 in Books > Science & Math > History & Philosophy
- #8952 in Books > Textbooks > Humanities > Philosophy

Would you like to tell us about a lower price?
If you are a seller for this product, would you like to suggest updates through seller support?

Be the first video

Your name here

Important information

Ingredients

Example Ingredients

Directions

Example Directions

Customer reviews

4.3 out of 5 stars

3 star (0%)

2 star (0%)

Write a customer review

See all 18 customer reviews

Read reviews that mention

Top customer reviews

There was a problem filtering reviews right now. Please try again later.

If you are looking for a book on practical mathematical foundations, this is the book for you.

January 24, 2018

Format: PaperbackVerified Purchase

I have never written a review for a book on amazon before this point, but I felt this book really deserves 5 stars, and I wanted to address the criticisms of the book directly. I believe many of the criticisms are a result of a misunderstanding of this book's goals. Specifically, the comparison to Polya's books are somewhat unfounded, because I believe the books have different goals. The goal of Polya's books are to provide a general method for finding solutions to unsolved problems. The goal of this book, on the other hand, is to explain the purpose and meaning of a proof once we already have it.

This book answers the questions "How can we be sure a formal proof is correct?" and "How can we be sure it actually proves what we intuitively intended?", and it does so better than anything else I have ever read. As a result, this is a book more about mathematical philosophy than mathematical technique.

If you are someone who has trouble reading or writing proofs because you keep thinking of weird edge cases and have to verify that the proof handles all of them, or you have frequent existential crises about how written mathematical symbols (which are just symbols and syntax) can be shown to say anything about reality, this is the book for you.

3 people found this helpful

Comment

Excellent book showing that doing mathematics is a complicated process ...

June 11, 2017

Format: PaperbackVerified Purchase

Excellent book showing that doing mathematics is a complicated process they goes far beyond just discovering results of some realm.

One person found this helpful

Comment

Michael Demkowicz

the heuristic of mathematical discovery

March 8, 2006

Format: PaperbackVerified Purchase

In a footnote to chapter 2 (much of the content of "Proofs and Refutations" is in the footnotes) Lakatos writes: "Until the seventeenth century, Euclidians approved the Platonic method of analysis as the method of heuristic; later they replaced it by the stroke of luck and/or genius." That stroke of luck and/or genius is a slight of hand that hides much of the story of the unfolding of mathematical research.

In "Proofs and Refutations," Lakatos illustrates how a single mathematical theorem developed from a naive conjecture to its present (far more sophisticated) form through a gruelling process of criticism by counterexamples and subsequent improvements. Lakatos manages to seemlessly narrate over a century of mathematical work by adopting a quasi-Platonic dialogue form (inspired by Galileo's "Dialogues"?), which he thoroughly backs up with hard historical evidence in the voluminous footnotes. The story he tells explores the clumsy and halting heuristic processes by which mathematical knowledge is created: the very process so carfully hidden from view in most mathematics textbooks!

The participants of Lakatos' dialogue argue over questions like "when is something proved?", "what is a trivial vs. severe counterexample?", "must you state all your assumptions or can some be thought of as implicit?", "in the end, what has been proved?",etc.. The answers to these questions change as the theorem under consideration is successively seen in a new light. Throughout, Lakatos is at pains to point out that the different perspectives adopted by his characters are representative of viewpoints that were once taken by the heroes of mathematics.

9 people found this helpful

Comment

July 18, 2016

Format: Kindle EditionVerified Purchase

Classic

One person found this helpful

Comment

A Math Mind for Philosophy

July 30, 2014

Format: PaperbackVerified Purchase

This book is a classic, and I am so happy to finally have my own copy. Lakatos was one of those rare minds in philosophy who influenced generations of people in multiple disciplines.

2 people found this helpful

Comment

An excellent, intriguing read.

February 10, 2014

Format: PaperbackVerified Purchase

Not only is this a very interesting argument about the nature of mathematical proof, it is a highly entertaining read. A classic of late 20th century mathematical philosophy.

One person found this helpful

Comment

Fernando Luis Valli

June 25, 2016

Format: Kindle EditionVerified Purchase

Very good text that gives many refutations to traditional proofs in science.

One person found this helpful

Comment

Classic. Timeless.

February 4, 2013

Format: PaperbackVerified Purchase

An important read for anyone studying the philosophy of mathematics. Also interesting for mathematics educators. Classic. Timeless. Not too long.

3 people found this helpful

Comment

Most recent customer reviews

Amazon Customer

My Favorite Book on Mathematical Philosophy

This is a book that really gets into how mathematics is done, instead of just focusing on what mathematics "is" or "should be.Read more

Published on January 31, 2014

Simply drop it. Polya's Mathematics and plausible reasoning is the right book. I have been reading books to understand conjecture making. This one turned out to be useless.Read more

Published on February 3, 2013

Largely trivial

Lakatos' motives for writing this book seem to have been:
(a) "Under the present dominance of formalism, ...Read more

Published on February 8, 2008

a study in mathematical thought

I want to add a few words to the brief comment by the reader in Monroe (who gave this book one star).Read more

Published on October 2, 2001

Amazon Customer

Excellent Critical Reasoning Framework

As a lay reader of mathematics, I am prone to read for more for analogy and thought methods instead of, for example, the real implications of variations on Eulers Formula: for any...Read more

Published on September 26, 2001

Customers who viewed this item also viewed

Page 1 of 1 Start overPage 1 of 1

This shopping feature will continue to load items. In order to navigate out of this carousel please use your heading shortcut key to navigate to the next or previous heading.

G. Polya

127

Paperback
$14.63
Thomas S. Kuhn

441

Paperback
$8.52
Paul Feyerabend

34

Paperback
$21.05
Richard Hammack

72

Paperback
$14.95
Imre Lakatos

2

Paperback
$25.92
John Stillwell

4

Hardcover
$18.26

English United States

Conditions of Use
Privacy Notice
Interest-Based Ads
© 1996-2018, Amazon.com, Inc. or its affiliates