Product Description
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. ... Read more

Customer Reviews (11)

Largely trivial
Lakatos' motives for writing this book seem to have been:
(a) "Under the present dominance of formalism, ... the history of mathematics, lacking the guidance of philosophy, has become blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, has become empty." (p. 2)
(b) "present mathematical and scientific education is a hotbed of authoritarianism and is the worst enemy of independent and critical thought" (pp. 142-143)
I passionately agree, but still found the actual book quite bland. It consists in a fairly amusing, semi-historical dialogue on Euler's formula V-E+F=2, intended to illustrate the very trivial thesis that creative mathematics is based on informal reasoning, heuristics, conjectures, counterexamples, etc., while also noting some general patterns of thought within this framework. Illustrations of similar patters in the history of the foundations of the calculus are also pointed out briefly; e.g., "the exception-barring method," is exemplified by Abel's reaction to his discovery of counterexamples such as sin(x)+sin(2x)/2+sin(3x)/3+... to Cauchy's theorem that the limit function of a convergent series of continuous functions is always continuous: "His response to these counterexamples is to start guessing: 'What is the safe domain of Cauchy's theorem?' ... All the known exceptions to this basic continuity principle were trigonometrical series so he proposed to withdraw analysis to within the safe boundaries of power series, thus leaving behind Fourier's cherished trigonometrical series as an uncontrollable jungle." (p. 133).

the heuristic of mathematical discovery
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.

nice reading for the general public
Very nice book if you are in high school or in college and would like to see how mathematics evolves. It makes a very pleasant reading although the mathematical ideas behind are not trivial.

It discusses polyhedra in 3 (or more) dimensions and Euler's formula that describes their numbers of vertices, edges, faces, e.t.c. The challenge is to determine what specific kinds of polyhedra satisfy the formula and conversely, how one could generalize the formula so as to describe more (if not all) polyhedra. Lots of historical references illustrate the fact that the discussion is not naive and that reflects the actual history of the subject.

One can realize through this book that math people are not Gods and do not produce theories out of nowhere, but they experiment with their objects like any other scientist, and then try to summarize in an elegant/rigorous way.

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). I tend to agree that "Proofs and Refutations" isn't a primer in mathematical proof-writing; it's certainly not a textbook for beginning mathematicians wanting to know how to practice their craft.

However, for those readers (including beginning mathematicians) who are interested in the broader picture, who are interested in the nature of mathematical proof, then Lakatos is essential reading. The examples chosen are vivid, and there is a rich sense of historical context. The dramatised setting (with Teacher and students Alpha, Beta, Gamma, etc) is handled skilfully. Now and then, a foolish-seeming comment from one of the students has a footnote tagged to it; more often than not, that student is standing in for Euler, Cauchy, Poincare or some other great mathematician from a past era, closely paraphrasing actual remarks made by them. That in some ways is the most important lesson I learned from this book; "obvious" now doesn't mean obvious then, even to the greatest intellects of the time.

Although "Proofs and Refuatations" is an easy book to begin reading, it is not an easy book per se. I have returned to it repeatedly over the last ten years, and I always learn something new. The text matures with the reader.

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 convex polyhedron, the number of vertices and faces together is exactly two more than the number of edges.

Displaying solid content with artful execution, this book interested me in both the math of the thing and the acompanying thought processes.

Content:This book has near-poetic density and elegance in arguing a non-linear approach to mathematical development and, for me, to just plain thinking.Our tendency (as born worshippers of linearity and causality) is to discover a brick for the building then immediately look for the next to stack on top.Lakatos contends that PERHAPS you have discovered a brick worthy of the building, now let's see what truly objective tests we will put to this brick and before giving it a final stamp of approval.It seems obvious to say "always question", but the exercise in this book will take you through the process and show you what you may take for granted in this simple concept.For example, do you observe HOW you question? See his discussion throughout on global vs. local counterexamples, just as a start.

Execution of the text:This is the beautiful part.Mr. Lakatos has written this book as theater: characters with definite identities, plot, drama. The narrative flows in the voices of students and a professor who proves to be a sound moderator, intervening at timely points, i.e. those where questions may be crystallized or thoughts prodded to that point.This is where learning takes place, in a heated, moderated debate over Euler's formula.What was most interesting to me about this method was that it lent itself easily to isolating a particular thread of discussion. I literally chose certain characters to research from beginning to end in order to follow the evolution or confirmation of their thinking.

You emerge with a good framework that makes this book excellent reference material for problem-solving.

One last, but important note.This book will have you praising the lowly footnote.I would buy it for that alone.You will read along with the discussion, then get off and examine a footnote, and then pick the dialogue back up not having lost a step.On the contrary, Mr. Lakatos deepens your context with on-point explanations and math history. ... Read more

Product Description
Imre Lakatos' philosophical and scientific papers are published here in two volumes. Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume II presents his work on the philosophy of mathematics (much of it unpublished), together with some critical essays on contemporary philosophers of science and some famous polemical writings on political and educational issues. Imre Lakatos had an influence out of all proportion to the length of his philosophical career. This collection exhibits and confirms the originality, range and the essential unity of his work. It demonstrates too the force and spirit he brought to every issue with which he engaged, from his most abstract mathematical work to his passionate 'Letter to the director of the LSE'. Lakatos' ideas are now the focus of widespread and increasing interest, and these volumes should make possible for the first time their study as a whole and their proper assessment. ... Read more

Customer Reviews (2)

Popper redux, and then some
"Falsification and the Methodology of Scientific Research Programmes." "A series of theories is theoretically progressive ... if each new theory has some excess empirical content over its predecessor, that is, if it predicts some novel, hitherto unexpected fact. ... [It] is also empirically progressive ... if some of this excess empirical content is also corroborated, that is, if each new theory leads to the discovery of some new fact. Finally, let us call a problemshift progressive if it is both theoretically and empirically progressive, and degenerating if it is not." (pp. 33-34). "Justificationists valued 'confirming' instances of a theory; naive falsificationists stressed the 'refuting' instances; for the methodological falsificationist [i.e. Lakatos] it is the---rather rare---corroborating instances of the excess information which are the crucial ones ... We are no longer interested in the thousands of trivial verifying instances nor in the hundreds of readily available anomalies." (p. 36). One implication is that it may be perfectly rational to work on a theory even if it rests on false assumptions. "Indeed, some of the most important research programmes in the history of science were grafted on to older programmes with which they were blatantly inconsistent." (p. 56). In quantum mechanics, for example, "the decision to go ahead with temporarily inconsistent foundations was taken by Einstein in 1905, but even he wavered in 1913, when Bohr forged forward again" (p. 59). Similarly, "Cartesian push-mechanics" was "inconsistent with Newton's theory of gravitation," but "Newton worked both on his positive heuristic (successfully) and on a reductionist programme (unsuccessfully), and disapproved both of Cartesians who, like Huyghens, thought that it was not worth wasting time on an 'unintelligible' programme and of some of his rash disciples who, like Cotes, thought that the inconsistency presented no problem" (p. 59). Another consequence is that "The history of science has been and should be a history of competing research programmes ..., but it has not been and must not become a succession of periods of normal science: the sooner competition starts, the better for progress. 'Theoretical pluralism' is better than 'theoretical monism'" (p. 69).

I think Lakatos makes too much of the Popper/Kuhn dichotomy. Lakatos points out again and again that he "followed, and tried to improve, Popperian tradition" (p. 95), and has copious quotations and precise footnotes pointing to Popper. By contrast, Kuhn's theory is brusquely misrepresented without proper referencing; e.g. "there is no particular rational cause for the appearance of a Kuhnian 'crisis' ... 'Crisis' is a psychological concept; it is a contagious panic" (p. 90), for which there is no reference other than an inconspicuous "Kuhn [1970]" elsewhere on the page. This is all the more unfortunate since "Popper never abandoned his earlier (naive) falsification rules. He has demanded, until this day, that 'criteria of refutation have to be laid down beforehand: it must be agreed, which observable situations, if actually observed, mean that a theory is refuted'" (p. 94), which Lakatos has just demonstrated to be utter folly (e.g., pp. 17, 65ff.).

"Why did Copernicus's research programme supersede Ptolemy's?" Ptolemy's "research programme" was clearly degenerate. "Every single move in the geostatic programme ran counter to the Platonic heuristic" (p. 181), e.g. equants, and "it always lagged behind the facts" (p. 182). "Copernicus's programme was certainly theoretically progressive. It anticipated novel facts never observed before" (p. 183), such as the phases of Venus. But none of these anticipated novel facts were corroborated until the phases of Venus were observed in 1616. "It seems then that the Copernican Revolution only became a fully fledged scientific revolution in 1616, when it was almost immediately abandoned for the new dynamics-oriented physics" (p. 184). Hardly very satisfying, but we are saved by "Elie Zahar's modified methodology of scientific research programmes" (p. 185). "Zahar's modification lies primarily in his new conception of 'novel fact'. ... Zahar's claim is that several important facts concerning planetary motions are straightforward consequences of the original Copernican assumptions and that, although these facts were previously known, they lend much more support to Copernicus than to Ptolemy within whose system they were dealt with only in an ad hoc manner, by parameter adjustment. From the Copernican model ... the following facts can be predicted prior to any observation: (i) Planets have stations and retrogressions. ... (ii) The periods of the superior planets, as seen from the Earth are not constant. ... (iv) The elongation of the inferior planets is bounded" (pp. 185-186). Furthermore, "the determination of planetary distances represents excess content of Copernicus's theory over Ptolemy's" (p. 187). "But it turned out that apart from his initial successes, Copernicus could save all the Ptolemaic phenomena only in an ad hoc and, in its dynamical aspects, very unsatisfactory, way. So Kepler and Galileo took off from the Commentariolus rather than from De revolutionibus. They took off from the point where the steam ran out of the Copernican programme." (p. 188). Here Lakatos seems to forget that Copernicus determination of the planetary distances was necessary for Kepler's cherished polyhedral theory.

"History of science and its rational reconstructions." A philosophy of science (or a "logic of scientific discovery") "can be criticized by criticizing the rational reconstructions to which they lead" (p. 122). For example, "the internal history of inductivists consists of alleged discoveries of hard facts and of so-called inductive generalizations. The internal history of conventionalists consists of factual discoveries and of the erection of pigeon hole systems and their replacement by allegedly simpler ones. The internal history of falsificationists dramatizes bold conjectures ... and, above all, triumphant 'negative crucial experiments'. The methodology, finally, emphasizes long-extended theoretical and empirical rivalry of major research programmes [and] progressive and degenerating problemshifts." (p. 118). History is the ultimate test for any philosophy of science in that "history may be seen as a 'test' of its rational reconstructions" (p. 123)."If a historian's methodology provides a poor rational reconstruction, he may either misread history in such a way that it coincides with his rational reconstruction, or he will find that the history of science is highly irrational." (p. 127).

Lakatos apparently felt that the last article, on Newton, was "in need of substantial revision" (p. 193) and one can only agree. For one thing, Lakatos claims that "Newton turns the negation of his theory into its own foundation" (p. 210) just because the law of gravitation is derived from Kepler's laws with which it is strictly speaking inconsistent. This is hardly a very balanced statement, especially not from someone who accuses Kuhn of feeding "the New Left" (p. 136).

Methods of Scientific Research
Philosophy of Science is a crucial subset of philosophy, since it directly affects scientific research. We need to know what constitutes a properly constructed theory, and more to the point, which claims are not theoretical, or perhaps not even scientific. With that goal established, we need to know how to empirically verify the theory in question. Theories are developed within axiomatic systems, are based on assumptions, and present us with a compact thesis, or a set of theses. A theory is scientific if we can falsify it with empirical data. If a theory is not testable, then it is not a good theory, since we cannot accept or reject its propositions. An obvious point is to be raised here - when and under which conditions shall we reject a theory?

Methodological studies flourished in the XX century with the works of Karl Popper, Milton Friedman, Imre Lakatos, Harold Kuhn, Paul Feyerabend and other philosophers. The contribution of Imre Lakatos was significant. With his version of corroboration and refined fascificationism we were able to apply new standards towards the methods of rejection of scientific theories. A single rejection of the scientific theory is not likely to falsify it, unlike advocated previously. However, the main point is that while the absolute truth is always of importance, i.e. whether a given theory is considered "true" because we have not been able to negatively falsify that theory; it is more important that various theories can be compared to each other, even if they are all imperfect. To this end, we can specify a set of thresholds, and say that a research programme A is more empirically valid than a research programme B if it does withstand a larger number of empirical tests. Of course, as simple as it sounds, it is a useful method of evaluation of theories, and can be augmented as needed within a given science.

Philosophy of Science and methodology is of utmost importance to theorists, since more often than not, nonscientific methods of theory construction are used, and even worse, empirical data are inductively used to hypothesize about the causes for the pattern of these data. It's methodologically invalid and by construction, these theories are not falsifiable since they are derived from data. This is true especially within economic theory; labor economics and macroeconomics in particular.

The works of Lakatos are summarized and condensed in various descriptive volumes on the Philosophy of Science, however it is illuminating to read the original works of this ingenious philosopher, since by doing so you gain an additional layer of understanding.

I will not go as far as saying that it should have been a must reading for any scientist, since such proposition would be hardly realistic, but I will say that it is a treat for those who have already tasted methodology in a compact form, and would like to expand their knowledge. ... Read more

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Customer Reviews (6)

Opinionated and delightful
The tone throughout both Lakatos' lectures on scientific method and the correspondence is delightfully opinionated and full of contempt. Some examples will convey the flavour.

Lakatos on intellectuals. "I happened to say that the Philosophical Section of the British Academy is a bunch of idiots ... and the British Academy itself, of which [Kneale] is vice-president, is a bunch of phonies, and also that I shall consider it an honour if I can die without having been elected as their Fellow. It was only then that I discovered that poor Bill Kneale regards it as the acme of his career to have become vice-president of the British Academy and I kicked him where it hurt most. After this clash, it occurred to me that Lionel Robbins was an actual president of the British Academy so I thought I should do an experiment and I went to him and told him that the British Academy consists almost exclusively of common fools. Somewhat to my surprise he said that he had lately come to suspect as much." (pp. 288-289; cf. also p. 92)

Feyerabend on modern physicists. "The younger generation of physicists ... may be very bright ... but they are uncivilised savages, they lack in philosophical depth" (p. 385) "Good payment, good relations with the boss and colleagues ... are the chief aims of these human ants who excel in the solution of tiny problems but who cannot make sense of anything transcending their domain of competence." (p. 114)

One of many Popper jokes. "My main problem is now a crack which has developed on the wall of the downstairs loo. ... I am now trying to get a big blow up picture of Sir Karl and put it there in a Victorian gilded frame." (Lakatos, p. 270)

Lakatos on editors. "'Criticism and the Growth of Knowledge' was completely rewritten by a young woman at CUP ... I think that the woman who did it even mumbled something about making the style uniform ... [When] I found out that the book had been edited ... I ordered them to return the ms immediately and I solemnly burned the edited copy ... and told them to print the originals as I had sent it to them ... I also demanded her immediate dismissal" (p. 295-296)

For and Against Method - review
The book gives a good insight into Lakatos and Feyerabend views and ideas connected with the development and methodology of science, as well as illustrates the personalities of these two philosophers. The "Lakatos' Lectures on Scientific Method", mainly due to informal and illustrative language, is an easy to follow and understand piece of philisophic text.

Title is Misleading, but Entertaining Nonetheless.
This book looked very promising. After all, anyone whose read either Feyerabend or Lakatos knows that they had geared up to write, "For and Against Method" cut short by Lakatos's death. We've read "Against Method", just never the "For..". This book was to be our chance!

Why 'was'? Well, the correspondence that takes up most of this book is funny, personal, warm and caring. If you're looking for clarification of the thinkers, look elsewhere.Each letter will start "Dearest Imre/Paul, I just got your last article and am going to send you one of mine. Let's get together in Boston next week. By the way, I've something nasty to say about Popper/Kuhn/Searle. Take care, Imre/Paul." Not very insightful. To be sure, these letters ARE EXTREMELY ENTERTAINING and insightful into each thinker's personality. For instance, from reading this, it is easy to see that a large reason Feyarabend was a scientific 'anarchist' is because he loved to disagree with everyone and taking sides meant he had to agree with someone, thus spoil his devilish fun. In Lakatos, I see someone who wished he could be Feyerabend but could never shake that bugbear called common sense. As I said - insightful into each personality, not each philosophy.

There were, however, other parts of the book. The most educational was the opening dialogue (actually written by Matteo Matterlinski) where Feyerabend and Lakatos lay out their views and criticize the other's. Next, we have the Lakatos lectures which spend 7/8ths of the time reviewing other people's views and only then explaining his own (very badly, I may add). The two appendices were interesting. Lakatos and Feyerabend wrote on their views towards academic freedom. As one may expect, Lakatos is the more conservative here.

Still, I must give three stars as the correspondence was a treat to read. It will have you laughing, shaking your head and oddly enough, coming away with HUGE amounts of respect for both thinkers as their playful intellectual jabs at eachother and willingness to be on the recieving, as well as the giving, end, exemplify how all sciences should conduct themselves.

a glimpse of what could've been....
This book is an excellent introduction to the two great philosophers of the latter half of the twentieth century, Imre Lakatos and Paul Feyerabend. In the enlightening and lucid lectures, Imre Lakatos comes off as the established logician whose views on the philosophy of science is marvelously comprehensible and original, and serves as a springboard for the correspondence. What surprised me was the natural humor and gaiety in the letters, that they promised to annihilate one another in the joint efforts at a book, and yet they could not stop talking about the women in their lives. In a way, the book is also an autobiography, a profile of the two proud and brilliant men and serves as an inside peek at their relationship. Kudos to the editors of this book. I recommend reading this book in order to get your feet wet before tackling on Lakatos' other books and Feyerabend's Against Method.

an amusing and instructive book
The most valuable part of the book is the first one, a collection of conferences where Lakatos wittily explains the shortcomings and inconsistencies of Popper's methodology of science, and develops his own views on scientific progress and rationality. The style is vivid. Lakatos apparently cannot avoid disparaging Popper every minute, and actually depicts him as a slobbering fool. I think this is psychologically explainable as a consequence of Popper's not having recognized any of Lakatos's criticisms of his views on empirical science. Lakatos had the dream of renewing popperism by subjecting it to a "hegelian" refutation, i.e. one which simply shows a view as merely initial and which needs a self-movement towards something richer. But Popper saw things differently, and spurned his disciple's heretic proposals. Lakatos must have been hurt by this. [Note: Lakatos' general criticisms of Popper's philosophy might be correct; but there are some points of detail in which he is wrong: for instance, when he says that Popper's analysis of the relations between Kepler's and Newton's laws added nothing to Duhem's treatment of this issue].

The Lakatos-Feyerabend correspondence is interesting. These were surely very special guys. Feyerabend, strange as it may seem, stands out as the meeker of the two; for Lakatos is pure cunning. Their exchange of opinions and invectives over Feyerabend's "Against Method" are worth reading ("Against Method" is worth reading along with this book, as a matter of fact).

Feyerabend compares the trio Popper-Lakatos-Feyerabend with Kant-Hegel-Lenin. I guess Popper himself might have thought this comparison quite fair. ... Read more

Product Description
Two books have been particularly influential in contemporary philosophy of science: Karl R. Popper's Logic of Scientific Discovery, and Thomas S. Kuhn's Structure of Scientific Revolutions. Both agree upon the importance of revolutions in science, but differ about the role of criticism in science's revolutionary growth. This volume arose out of a symposium on Kuhn's work, with Popper in the chair, at an international colloquium held in London in 1965. The book begins with Kuhn's statement of his position followed by seven essays offering criticism and analysis, and finally by Kuhn's reply. The book will interest senior undergraduates and graduate students of the philosophy and history of science, as well as professional philosophers, philosophically inclined scientists, and some psychologists and sociologists. ... Read more

Customer Reviews (4)

Useful confrontations
Kuhn was never able to solve the paradox within his idea of sciences: if his "language of incommensurability implies that we cannot understand another's scheme or paradigm" (Dasenbrock, TRUTH AND CONSEQUENCES pp. 49), how can we then know that we can't understand this? Other people's sciences are so radically different from "our" science that we can never understand theirs or they ours and, yet, Kuhn can know that: he understands that; the rest of us don't.

Kuhn's appeal to fallacy pervades all of his work in The Structure of Scientific Revolutions, Reflections on my Critics, and The Essential Tension. Basically, Kuhn alleges that we cannot even begin to understand other people's paradigms; we understand only our paradigm. Yet Kuhn understood enough to "see" this. He can use the "historical study of scientific development" to argue that Popper is wrong, but he also wants the rest of us to see that we cannot understand the science paradigm of previous centuries: Kuhn can use history and its language to attack ideas that punch holes in his idea (or to tell us about Aristotle's concept of science); the rest of us cannot use history because, you see, we cannot understand other paradigms.

If Kuhn were right, then his theory would be nothing but a fad, a "paradigm" that will pass and be replaced by some other fad. In a sense this has happened, but only in the social sciences because Kuhn was "adopted" by a particular group of philosophers and literary critics who saw the usefulness of a theory that claimed that science, this spawn of the modernism, reason and humanism that Heidegger and more recent characters such as Foucault and Derrida have relentlessly attacked, was nothing but an opinion held by an old boys network. Now that such a philosophical fad has lost much of its appeal in France and the US, Kuhn's theory is seen for what it is: an opinion by a man who protected his opinion with fallacies. This opinion was interesting to many philosophers. These philosophers are either dead now, or interested in their next flavor-of-the-month.

This is a good book if you believe, as Popper did, that the clash of ideas and opinions was the best way to get results. Kuhn confesses early on that he does not agree with this position: he has found "the" truth regarding science. Why can't everybody just accept it? Popper is excellent, Kuhn is unintentionally funny, Feyerabend is way out there (no news).

For and against normal science
Kuhn's "Logic of Discovery or Psychology of Research?" is a beautiful criticism of Popper. I. Criteria of demarcation should be based on the nature of normal science rather than revolutionary science (bold hypotheses, etc.). For example, astrology cannot be dismissed as unfalsifiable; in fact, it repeatedly made categorically false predictions, which were recognised as such. The reason why astrology is not a science is that it cannot digest these anomalies through puzzle solving. IV. Instead, to understand the development of science we must understand the mind of the scientist. "Knowing what scientists value, we may hope to understand what problems they will undertake and what choices they will make in particular circumstances of conflict." (p. 21)

Everyone else hates Kuhn's "normal science." Popper thinks it is "dangerous"because it is dogmatic. Feyerabend thinks it is "boring", "pedestrian", "anti-humanitarian", etc. Toulmin thinks it is indistinguishable from revolutionary science. Watkins attacks it as a demarcation criteria since it would seem to include biblical scholarship as a science (where the puzzles of normal research would be to explain away apparent inconsistencies in the Bible); Feyerabend, similarly, because it would seem to include organised crime. The former type of criticisms are not addressed directly by Kuhn in his reply, except for his observation that history is on his side (thus, regardless of what philosophers may think about it, to reject normal science is to reject the vast bulk of all science throughout history). The latter examples are dismissed by Kuhn on the grounds that "no problems are thereby created" since his description concerned theories dealing with natural phenomena (p. 245).

Much time is spent discussing Kuhn's alleged relativism, incommensurability, etc. Most contributors are too fanatically attached to the idea of science as super-knowledge to be able to argue constructively: anti-Kuhn criticism and rhetoric ranges from ridiculous and absurd (such as Popper's accusation that Kuhn is using logic (sic!)) to various forms of misrepresentation of Kuhn's theory and their (to these people) philosophically unacceptable implications. This debate is rather uninteresting not only because it lacks objectivity and reason but also because it is concerned only with whether science deserves its pedestal, and not with understanding actual science, which is what Kuhn emphasised initially and what one wishes the book would have been about.

Lakatos' paper where he introduces his methodology of research programmes is very interesting, but would be even better if its perspective was reversed from pro-Popper & anti-Kuhn to anti-Popper & pro-Kuhn. His model plainly has much in common with Kuhn's. Kuhn points to some parallels: "hard core, work in the protective belt, and degenerative phase are close parallels for my paradigms, normal science, and crisis" (p. 256); one may add also that heuristic in Lakatos' model roughly corresponds to the ability to support puzzle-based normal science. At the same time, Lakatos presents conclusive refutations not only of "naive falsificationism" but also of the Popperian outlook altogether, e.g. when he embraces science with inconsistent foundations.

If you want to understand Kuhn: buy it.
I've been a big Kuhn fan for years. I thought I understood his ideas, too, until I read this book. This gem is a debate among some of the most interesting philosophers of science in the twentieth century-- all trying to make sense of Kuhn, most concluding that his ideas are deeply flawed.

The criticism helped me advance my own interpretation of Kuhn, but it was Kuhn's reply to the criticism that brought the whole thing into technicolor 3D. I could hardly have learned more if I had the man in my living room.

-- James

Nice collection of Essays
This is a collection of "essays" about T.S. Kuhn's distiction between normal science and revolutionary science. Various philosophers, including Karl Popper, Imre Lakatos and Paul Feyerabend, criticize variousaspects of Kuhn's argument. Finally Kuhn presents a reply to his critics. ... Read more

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Customer Reviews (1)

lakatos' hegelian roots
excellent book for what concerns the relation Lakatos-Hegel. The autor analyzes Lakatos' philosophy as it was a Bildungsroman. Excellent for the fact that usually only the relation Lakatos- Popper is considered. Kadvany puts also attention on Goedel's resuts viewing them with Lakatos' eyes; also economy is considered (Lakatos suggested it..).
Unfortunatly Lakatos didn't read a lot of Hegel in his life but activly followed Lukacs' (Georgy Lukacs the ungarian philosopher) lectures in Budapest. So, why not analyse the bridge Lakatos- Lukacs- (second hand) Hegel? ... Read more

Product Description
Lakatos: An Introduction is the first comprehensive analysis on the intellectual life and theories of the distinguished thinker Imre Lakatos. This book clearly presents Lakatos's development of a philosophy of mathematics and empirical science, Lakatos's thought as an important hybrid of Popperian philosophy and Hegelian-Marxist thought, the relationship between Lakatos's views on science and mathematics and his more general philosophical beliefs. Brendan Larvor clearly locates Lakatos in the liberal-rationalist tradition and explains connections between the philosopher's life, philosophy, politics, and technical work in science and mathematics. ... Read more

Customer Reviews (2)

a difficult subject treated with wonderful lucidity and brevity
This book is a masterpiece of its kind.I am a philosopher but not at all a philospher of science or (even less) of mathematics, but this little guide makes it quite clear why Lakatos is so highly regarded a thinker who steers a course between the relativist tendencides of a Kuhn and the unworldly rigidity of the formalists and Popperians.I was particularly impressed with his precise understanding of the dialectical nature of Lakatos' thinking.Dialectic, both in Plato and in Hegel, is a subtle form of thinking and often misunderstood.Larvor explains it expertly and yet simply.He also shows an easy familiarity with recently French thinking on the same topics.I have rarely learned so much from so short a book!

Lucid and Accessible
I am a layman with interest in philosophical concepts and how they can be applied to my own field of study. I am presenting this review as of interest to other layman and not of direct interest to professions in this field.

The above being said, I found this book to be a lucid and accessible introduction to the ideas of Lakatos. I would recommend it to anyone else who is in my position of trying to understand the philosophical space without an exhaustive philosophical background..

Larvor presents Lakatos ideas in an historical manner. He relates them to the ideas of Kuhn and Popper that they advanced. He shows their origin in Lakatos' personal background in Hegel and Marx.The connections to these other thinkers is made clear with their ideas as they relate to Lakatos work thoroughly explained. This connection provides and understanding of not only Lakatos' work in their context but of the broader scope of their ideas in philosophy.

I would recommend this book to anyone who like me would like to understand the ides brought forth in philosophical investigations but lacks a formal background. It is an excellent book for self-instruction. It provides a clear grounding that makes the reading of the books by these major thinkers much more worthwhile. I had read Lakatos, Kuhn and Popper before I read this book. This book greatly helped me by giving greater clarity to the ideas that I had found there and by making subtle but important issues that I had not understood sufficiently much clearer. ... Read more

Product Description
Imre Lakatos' philosophical and scientific papers are published here in two volumes. Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume 2 presents his work on the philosophy of mathematics (much of it unpublished), together with some critical essays on contemporary philosophers of science and some famous polemical writings on political and educational issues. ... Read more

Customer Reviews (2)

Several excellent papers
Foundations of mathematics. The Hilbert--Russell meta-mathematical programmes were meant to establish the infallibility of mathematics by the Euclidean method: "derive all mathematics from trivial logical principles" (p. 12). Although "From the seventeenth to the twentieth century Euclideanism has been on a great retreat" (p. 10), having failed again and again in numerous branches of knowledge, Russell and others had no doubt that mathematics would be different: "Too often it is said that there is no absolute truth ... Of such scepticism mathematics is a perpetual reproof; for its edifice of truths stands unshakeable ... to all the weapons of doubting cynicism" (p. 14). "We all know how the brief Euclidean 'honeymoon' gave place to 'intellectual sorrow', how the intended logico-trivialization of mathematics degenerated into a sophisticated system, including 'axioms' like that of reducibility, infinity, choice, and also ramified type theory---of on the most complicated conceptual labyrinths a human mind ever invented. ... There even emerged the completely un-Euclidean need for a consistency proof to ensure that the 'trivially true axioms' should not contradict one another. All this and what followed must strike any student of the seventeenth century as a déjà vu: proof had to give way to explanation, ... Euclidean theory to empiricist theory. We also encounter the same refusal to accept the dramatic change", e.g. "Like Newton hoping to explain the Law of Gravitation by principles of Cartesian push-mechanics, Russell hoped for the trivialization of the reducibility axiom" (p. 14). But eventually Russell admitted defeat: "When pure mathematics is organized as a deductive system ... it becomes obvious that, if we are to believe in the truth of pure mathematics, it cannot be solely because we believe in the truth of the set of premisses. Some of the premisses are much less obvious than some of their consequences, and are believed chiefly because of their consequences. ... The only way in which work on mathematical logic throws light on the truth or falsehood of mathematics is by disproving the supposed antinomies. This shows that mathematics may be true. To show that mathematics is true would require other methods and other considerations." (p. 17). Thus logic "is an empiricist theory" like any other, albeit one that is hard to test. "The only way of criticizing this peculiar empiricist theory is, on the face of it, to test it for concistency. This leads us to the Hilbertian circle of ideas." (pp. 19-20). "Gödel's second theorem was a decisive blow to this hope for a Euclidean meta-mathematics. ... consistency proofs have to contain enough sophistication to render the consistency of the theory in which it is carried out dubitable ... For instance, Goldbach's conjecture---that every number is the sum of two primes---might be formally proved to-morrow, but we shall never know that it is true. For it would only be true if meta-mathematics, meta-meta-mathematics ... ad infinitum are consistent. This we shall never know. Gödel's first theorem showed a second way in which a formal theory could misfire: if it has a model at all, it has more models than intended. ... If the Goldbach conjecture is true in its intended interpretation, but false in an unintended one, there will be no formal proof leading to it in any formalization. Gödel's discovery of omega-inconsistent systems was still worse. ... A formalized arithmetic might be consistent, i.e. have models, but none of the models might be the intended one; every model, if containing all the numbers, might contain some other 'class-alien' elements which might provide counterexamples to propositions which are true in the narrower domain of the intended interpretation. In a consistent, but omega-inconsistent system we might prove the negation of the Goldbach conjecture even if the Goldbach conjecture is true." (pp. 20-21). Contemporary logic should not pretend to be the foundations of mathematics. "We read in one of the most competent books written on the subject that the 'ultimate test whether a method is admissible in meta-mathematics must of course be whether it is intuitively convincing.' But why then not stop earlier, why not say that 'the ultimate test whether a method is admissible in arithmetic must of course be whether it is intuitively convincing,' and omit meta-mathematics altogether...?" Or, for that matter, "why on earth have 'ultimate' tests" at all? "Why foundations, if they are admittedly subjective? Why not honestly admit mathematical fallibility, and try to defend the dignity of fallible knowledge from cynical scepticism, rather than delude ourselves that we shall be able to mend invisibly the latest tear in the fabric of our 'ultimate' intuitions?" (p. 23).

"The method of analysis--synthesis." A famous "heuristic" in Euclidean geometry was to prove a theorem by assuming it to be true, deriving something known (analysis), and then reversing the steps to obtain a proof (synthesis). This approach was explicated by Pappus, whence it may be called the "Pappusian Circuit" (p. 76). "A main feature of the story of modern scientific method is the critical elaboration of the ancient Pappusian Circuit into the Cartesian Circuit, followed---in spite of some partial successes and several intriguing rescue-operations---by its breakdown" (p. 77). "Both Descartes and Newton were very explicit about the necessity of starting the analysis from facts, from which one proceeded to 'mediate causes' and from there to first principles. They despised those who tried to arrive at first principles with no care for facts, by 'rash anticipation' instead of by laborious analysis" (p. 77), e.g., "Hooke only guessed the inverse square law, but he, Newton, deduced it from Kepler's empirical laws" (p. 80). This is also the meaning of Newton's "Hypothesis non fingo." "Hypotheses have to be embedded in a Cartesian Circuit and thereby cease to be hypotheses" (p. 77). "Descartes's main interest was to find a method of discovery of infallible knowledge, an infallibilist heuristic. The paragon of infalliable knowledge was of course Euclidean Geometry. And the only extant method was of discovery in Euclidean Geometry was the Pappusian Circuit. This was Descartes's natural starting point." (p. 83). "Now my differences with Hintikka's and Remes's rational reconstruction of Greek analysis--synthesis become clear. They base their reconstruction on the assumption that Pappusian analysis was a heuristic pattern in already axiomatized Euclidean Geometry ... In my view the most exciting analyses of Greek Geometry were pre-Euclidean and their role was to generate Euclid's axiomatic system." (p. 100).

Criticism of falsificationism. Popper "has refused to notice two [historical] facts: (1) 'Crucial experiments' are frequently listed first as harmless anomalies, rather than refutations ...; and (2) All important theories are born 'refuted'." (p. 201). Further discussion on this is limited to Lakatos' effortless refutations of two minor falsificationists (Agassi and Grünbaum).

"Cauchy and the Continuum." Conventional histories claim that Cauchy made several "mistakes" in his Cours d'Analyse, e.g. his proof that the limit function of a convergent series of continuous functions is always continuous. This seems strange, however, because there were already published counterexamples and "today, if one gave Cauchy's false proof to a bright undergraduate, it would not take him long to put it right; and indeed, Seidel [who eventually corrected the proof] did not find the problem at all difficult! What inhibited a whole generation of the best minds from solving an easy problem?" (pp. 46-47). Actually, there is no "mistake", since the alleged counterexamples do not converge in Cauchy's sense, as he himself explained: "His example is the series sin(x)+sin(2x)/2+sin(3x)/3+... He shows that in the neighbourhood of zero where the limit function is discontinuous, 'the value of the remainder for xs very near to zero, for instance for x=1/n where n is a very large number, can differ considerably from zero,'" so that the series does not converge at the "moving point x=1/n" where n goes to infinity (p. 57).

Comprehensive
The author introduces the main lines of discussions in epistemeolgy and philosophy of mathematics in a very understandable but comphrehensive way. It is a brilliant reference book for the subject which also contains so-farunpublished articles of the author. ... Read more

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Criticism and the History of Science deals with Thomas Kuhn's, ImreLakatos's and Paul Feyerabend's criticism of Karl Popper's falsificationistconception of science. It argues that this criticism is based on two importantmethodological problems: the problem that observations and tests statementsare fallible and impregnated with theory, and the problem of how to testcomplex theoretical systems. In order to solve these problems it shows howproblematic test statements can be criticised and whole theoretical systemsfalsified. In this way the falsificationist conception of science is developedand defended in a way making a deeper understanding of science and its historypossible. ... Read more

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Chapters: Imre Lakatos. Source: Wikipedia. Pages: 90. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Imre Lakatos (November 9, 1922 February 2, 1974) was a 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. Lakatos was born Imre (Avrum) Lipsitz to a Jewish family in Debrecen, Hungary in 1922. He received a degree in mathematics, physics, and philosophy from the University of Debrecen in 1944. He avoided Nazi persecution of Jews by changing his name to Imre Molnár. His mother and grandmother died in Auschwitz. He became an active communist during the Second World War. He changed his last name once again to Lakatos (Locksmith) in honor of Géza Lakatos. After the war, from 1947 he worked as a senior official in the Hungarian ministry of education. He also continued his education with a PhD at Debrecen University awarded in 1948, and also attended György Lukács's weekly Wednesday afternoon private seminars. He also studied at the Moscow State University under the supervision of Sofya Yanovskaya in 1949. When he returned, however, he found himself on the losing side of internal arguments within the Hungarian communist party and was imprisoned on charges of revisionism from 1950 to 1953. More of Lakatos' activities in Hungary after World War II have recently become known. After his release, Lakatos returned to academic life, doing mathematical research and translating George Pólya's How to Solve It into Hungarian. Still nominally a communist, his political views had shifted markedly and he was involved with at least one dissident student group i...More: http://booksllc.net/?id=38455 ... Read more

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This digital document, covering the life and work of Imre Lakatos, is an entry from Contemporary Authors, a reference volume published by Thomson Gale. The length of the entry is 329 words. The page length listed above is based on a typical 300-word page. Although the exact content of each entry from this volume can vary, typical entries include the following information:

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Kapitel: Karl Popper, Paul Feyerabend, Ernst Gombrich, Hans Albert, Imre Lakatos, Thomas Szasz, Erich Weede, William Warren Bartley, Hans-Joachim Niemann, David Deutsch, Peter Brian Medawar, Heinz Reinders, Gerard Radnitzky, David Miller, Alan Musgrave, Jürgen Friedrichs, Joseph Agassi, Jeremy Shearmur. Aus Wikipedia. Nicht dargestellt. Auszug: Sir Karl Raimund Popper, CH, FRS, FBA (28 July 1902 - 17 September 1994) was an Austrian and British philosopher and a professor at the London School of Economics. He is widely regarded as one of the greatest philosophers of science of the 20th century; he also wrote extensively on social and political philosophy. Popper is known for his attempt to repudiate the classical observationalist / inductivist account of scientific method by advancing empirical falsification instead, for his opposition to the classical justificationist account of knowledge which he replaced with critical rationalism, "the first non justificational philosophy of criticism in the history of philosophy", and for his vigorous defense of liberal democracy and the principles of social criticism that he came to believe made a flourishing "open society" possible. Karl Popper was born in Vienna (then in Austria-Hungary) in 1902, to upper middle-class parents of assimilated Jewish origins, both of whom had converted to Christianity. Karl's father Dr Simon Siegmund Carl Popper was a lawyer from Bohemia, and mother Jenny Schiff was of Silesian and Hungarian descent. After establishing themselves in Vienna, the Poppers had made a rapid social climb in Viennese society: Simon Siegmund Carl became a legal partner of Vienna's liberal mayor Raimond Grübl and, after his death in 1898, took over the firm (Karl received his middle name from the mayor). Popper received a Lutheran upbringing and was educated at the University of Vienna. His father was a doctor of law at the Vienna University and a bibliophile who had 12,000-14,000 vol...http://booksllc.net/?l=de ... Read more

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Chapters: Imre Lakatos, Miloš Forman, George Gamow, Nadia Comăneci, Georgi Markov, Vladimir Tismăneanu, Ion Negoiţescu, Eastern Bloc Emigration and Defection, Martina Navratilova, Ferenc Puskás, List of Soviet and Eastern Bloc Defectors, Viktor Korchnoi, Andrzej Panufnik, Sergei Fedorov, Rudolf Nureyev, Sándor Kocsis, Ion Mihai Pacepa, Igor Gouzenko, Ioan P. Culianu, Ján Kadár, Miodrag Belodedici, Abdurakhman Avtorkhanov, József Mindszenty, Svetlana Alliluyeva, Ryszard Kukliński, Zoltán Czibor, Józef Światło, Anatoly Kuznetsov, Cornel Chiriac, Jan Šejna, Vladas Česiūnas, Josef Škvorecký, Petr Beckmann, Viktoria Mullova, Ágnes Keleti, Grigol Robakidze, Stanislav Lunev, Natalia Makarova, Nikolai Khokhlov, Bohdan Stashynsky, Naim Süleymanoğlu, Victor Kravchenko, Alexander Godunov, Romuald Spasowski, Alena Vrzáňová, Jörg Berger, Vitali Vitaliev, Lutz Eigendorf, Aeroflot Flight 6833, Republikflucht, Lot Polish Airlines Flight 165 Hijacking, Vakhtang Jordania, G. M. Dimitrov, Falko Götz, Władysław Kozakiewicz, Vladimir Artemov, Nora Kovach, Ota Šik, Jenő Kalmár, Yuri Bregel, Ludmila Belousova, Oleg Protopopov, Tamás Buday, Norbert Nachtweih, Vladimir Rojansky, Matei Pavel Haiducu, Valentin Poénaru, Otar Iosseliani, Géza Füster, Conrad Schumann, Ante Žanetić, Kalinikos Kreanga, Konstantin Volkov, Jan Čep, Leho Laurine, Mircea Florian, Bela Berger, Ján Vilček, Ivan Diviš, Aeroflot Flight 244, Paul Barbă Neagră, Sulamith Messerer, Jürgen Pahl, Evdokia Petrova, Ivo Štakula, Miroslav Sláma, Romanas Arlauskas, András Törő, Alexander Elder, Wolfgang Leonhard, Jonas Pleškys. Source: Wikipedia. Pages: 478. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Vladimir Tismneanu (Romanian pronunciation: ; born July 4, 1951) is a Romanian and American political scientist, political analyst, sociologist, and professor...http://booksllc.net/?id=4096055 ... Read more

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This digital document is an article from New Criterion, published by Foundation for Cultural Review on May 1, 2000. The length of the article is 2807 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: Imre Lakatos and Paul Feyerabend.(Review) (book review)
Author: James Franklin
Publication: New Criterion (Magazine/Journal)
Date: May 1, 2000
Publisher: Foundation for Cultural Review
Volume: 18Issue: 9Page: 74

Article Type: Book Review

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Chapters: Michael Polanyi, Imre Lakatos, György Lukács, Ágnes Heller, Edmund Bordeaux Szekely, Matthias Bel, Peter Glassen, Zeno Vendler, Ervin László, Béla Hamvas, Péter Pázmány, János Apáczai Csere, Thomas Molnar, Richard Hönigswald, Menyhért Palágyi, Anthony de Jasay, János Kis, Georg Kühlewind, György Márkus, György Bence, Oskar Ewald, Géza Fodor. Source: Wikipedia. Pages: 113. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: György Lukács (Hungarian pronunciation: ; April 13, 1885 June 4, 1971) was a Hungarian Marxist philosopher and literary critic. He is a founder of the tradition of Western Marxism. He contributed the ideas of reification and class consciousness to Marxist philosophy and theory, and his literary criticism was influential in thinking about realism and about the novel as a literary genre. He served briefly as Hungary's Minister of Culture following the 1956 Hungarian Revolution. Lukács's full name, in German, was Georg Bernhard Lukács von Szegedin, and in Hungarian was Szegedi Lukács György Bernát; he published under the names Georg or György Lukács. (Lukács is pronounced by most English speakers, the original pronunciation being IPA: .) He was born Löwinger György Bernát to a wealthy Jewish family in Budapest. His father was József Löwinger (later Szegedi Lukács József; 1855, Szeged 1928), an investment banker, his mother was Adele Wertheimer (Wertheimer Adél; 1860, Budapest 1917). Lukács studied at the universities of Budapest and Berlin, receiving his Ph.D. in 1906. While attending grammar school and university in Budapest, Lukács's membership of various socialist circles brought him into contact with the anarcho-syndicalist Ervin Szabó, who in turn introduced him to the works of Georges Sorel. Lukács's outlook during this period was modernist and anti-positivist. ...More: http://booksllc.net/?id=310872 ... Read more

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Chapters: Karl Marx, Albert Einstein, Friedrich Nietzsche, Imre Lakatos, Anne Frank, John Demjanjuk, Nicholas Romanov, Prince of Russia, Gregor Von Rezzori, Mehran Karimi Nasseri, Margot Frank, Edith Frank-Holländer, Gustav Metzger, Marie Vassiltchikov, Robert Jovicic, Ruth Maier, Boris Dekanidze, Rosika Schwimmer, Virginia and Naomi Leong, Antal Nagy, Peter Qasim. Source: Wikipedia. Pages: 190. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: Albert Einstein (pronounced ; German: ; 14 March 187918 April 1955) was a theoretical physicist, philosopher and author who is widely regarded as one of the most influential and best known scientists and intellectuals of all time. He is often regarded as the father of modern physics. He received the 1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect." His many contributions to physics include the special and general theories of relativity, the founding of relativistic cosmology, the first post-Newtonian expansion, explaining the perihelion advance of Mercury, prediction of the deflection of light by gravity and gravitational lensing, the first fluctuation dissipation theorem which explained the Brownian movement of molecules, the photon theory and wave-particle duality, the quantum theory of atomic motion in solids, the zero-point energy concept, the semiclassical version of the Schrödinger equation, and the quantum theory of a monatomic gas which predicted BoseEinstein condensation. Einstein published more than 300 scientific and over 150 non-scientific works. Einstein additionally wrote and commentated prolifically on numerous philosophical and political subjects. Einstein at the age of 4. His father showed him a pocket compass, and Einstein realized that there m...More: http://booksllc.net/?id=736 ... Read more