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Author: Imre Lakatos Publisher: Cambridge University Press ISBN: 1107268109 Category : Science Languages : en Pages : 190
Book 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.
Author: Imre Lakatos Publisher: Cambridge University Press ISBN: 9780521290388 Category : Science Languages : en Pages : 188
Book 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.
Author: Arie Hinkis Publisher: Springer Science & Business Media ISBN: 3034802242 Category : Mathematics Languages : en Pages : 428
Book Description
This book offers an excursion through the developmental area of research mathematics. It presents some 40 papers, published between the 1870s and the 1970s, on proofs of the Cantor-Bernstein theorem and the related Bernstein division theorem. While the emphasis is placed on providing accurate proofs, similar to the originals, the discussion is broadened to include aspects that pertain to the methodology of the development of mathematics and to the philosophy of mathematics. Works of prominent mathematicians and logicians are reviewed, including Cantor, Dedekind, Schröder, Bernstein, Borel, Zermelo, Poincaré, Russell, Peano, the Königs, Hausdorff, Sierpinski, Tarski, Banach, Brouwer and several others mainly of the Polish and the Dutch schools. In its attempt to present a diachronic narrative of one mathematical topic, the book resembles Lakatos’ celebrated book Proofs and Refutations. Indeed, some of the observations made by Lakatos are corroborated herein. The analogy between the two books is clearly anything but superficial, as the present book also offers new theoretical insights into the methodology of the development of mathematics (proof-processing), with implications for the historiography of mathematics.
Author: Imre Lakatos Publisher: University of Chicago Press ISBN: 0226467031 Category : Science Languages : en Pages : 465
Book Description
The work that helped to determine Paul Feyerabend's fame and notoriety, Against Method, stemmed from Imre Lakatos's challenge: "In 1970 Imre cornered me at a party. 'Paul,' he said, 'you have such strange ideas. Why don't you write them down? I shall write a reply, we publish the whole thing and I promise you—we shall have a lot of fun.' " Although Lakatos died before he could write his reply, For and Against Method reconstructs his original counter-arguments from lectures and correspondence previously unpublished in English, allowing us to enjoy the "fun" two of this century's most eminent philosophers had, matching their wits and ideas on the subject of the scientific method. For and Against Method opens with an imaginary dialogue between Lakatos and Feyerabend, which Matteo Motterlini has constructed, based on their published works, to synthesize their positions and arguments. Part one presents the transcripts of the last lectures on method that Lakatos delivered. Part two, Feyerabend's response, consists of a previously published essay on anarchism, which began the attack on Lakatos's position that Feyerabend later continued in Against Method. The third and longest section consists of the correspondence Lakatos and Feyerabend exchanged on method and many other issues and ideas, as well as the events of their daily lives, between 1968 and Lakatos's death in 1974. The delight Lakatos and Feyerabend took in philosophical debate, and the relish with which they sparred, come to life again in For and Against Method, making it essential and lively reading for anyone interested in these two fascinating and controversial thinkers and their immense contributions to philosophy of science. "The writings in this volume are of considerable intellectual importance, and will be of great interest to anyone concerned with the development of the philosophical views of Lakatos and Feyerabend, or indeed with the development of philosophy of science in general during this crucial period."—Donald Gillies, British Journal for the Philosophy of Science (on the Italian edition) "A stimulating exchange of letters between two philosophical entertainers."—Tariq Ali, The Independent Imre Lakatos (1922-1974) was professor of logic at the London School of Economics. He was the author of Proofs and Refutations and the two-volume Philosophical Papers. Paul Feyerabend (1924-1994) was educated in Europe and held numerous teaching posts throughout his career. Among his books are Against Method; Science in a Free Society; Farewell to Reason; and Killing Time: The Autobiography of Paul Feyerabend, the last published by the University of Chicago Press.
Author: Imre Lakatos Publisher: Cambridge University Press ISBN: 1107113466 Category : Mathematics Languages : en Pages : 197
Book Description
This influential book discusses the nature of mathematical discovery, development, methodology and practice, forming Imre Lakatos's theory of 'proofs and refutations'.
Author: Karl Raimund Popper Publisher: Psychology Press ISBN: 9780415285940 Category : Knowledge, Theory of Languages : en Pages : 614
Book Description
Conjectures and Refutations is one of Karl Popper's most wide-ranging and popular works, notable not only for its acute insight into the way scientific knowledge grows, but also for applying those insights to politics and to history. It provides one of the clearest and most accessible statements of the fundamental idea that guided his work: not only our knowledge, but our aims and our standards, grow through an unending process of trial and error.
Author: R.S. Michalski Publisher: Springer Science & Business Media ISBN: 366212405X Category : Computers Languages : en Pages : 564
Book Description
The ability to learn is one of the most fundamental attributes of intelligent behavior. Consequently, progress in the theory and computer modeling of learn ing processes is of great significance to fields concerned with understanding in telligence. Such fields include cognitive science, artificial intelligence, infor mation science, pattern recognition, psychology, education, epistemology, philosophy, and related disciplines. The recent observance of the silver anniversary of artificial intelligence has been heralded by a surge of interest in machine learning-both in building models of human learning and in understanding how machines might be endowed with the ability to learn. This renewed interest has spawned many new research projects and resulted in an increase in related scientific activities. In the summer of 1980, the First Machine Learning Workshop was held at Carnegie-Mellon University in Pittsburgh. In the same year, three consecutive issues of the Inter national Journal of Policy Analysis and Information Systems were specially devoted to machine learning (No. 2, 3 and 4, 1980). In the spring of 1981, a special issue of the SIGART Newsletter No. 76 reviewed current research projects in the field. . This book contains tutorial overviews and research papers representative of contemporary trends in the area of machine learning as viewed from an artificial intelligence perspective. As the first available text on this subject, it is intended to fulfill several needs.
Author: Reuben Hersh Publisher: Springer Science & Business Media ISBN: 0387298312 Category : Mathematics Languages : en Pages : 346
Book Description
Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines
Author: Philip Ording Publisher: Princeton University Press ISBN: 0691218978 Category : Mathematics Languages : en Pages : 272
Book Description
An exploration of mathematical style through 99 different proofs of the same theorem This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo—whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp—Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau’s Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor. Readers will gain not only a bird’s-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape.
Author: Imre Lakatos
Author: Imre Lakatos
Author: Imre Lakatos
Author: Imre Lakatos
Author: Arie Hinkis
Author: Imre Lakatos
Author: Imre Lakatos
Author: Karl Raimund Popper
Author: R.S. Michalski
Author: Reuben Hersh
Author: Philip Ording