Download or read book Lakatos and the Historical Approach to Philosophy of Mathematics written by Donald Gillies and published by Cambridge University Press. This book was released on 2023-12-31 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Element begins by claiming that Imre Lakatos (1922–74) in his famous paper 'Proofs and Refutations' (1963–64) was the first to introduce the historical approach to philosophy of mathematics. Section 2 gives a detailed analysis of Lakatos' ideas on the philosophy of mathematics. Lakatos died at the age of only 51, and at the time of this death had plans to continue his work on philosophy of mathematics which were never carried out. However, Lakatos' historical approach to philosophy of mathematics was taken up by other researchers in the field, and Sections 3 and 4 of the Element give an account of how they developed this approach. Then Section 5 gives an overview of what has been achieved so far by the historical approach to philosophy of mathematics and considers what its prospects for the future might be.
Download or read book Lakatos Philosophy of Mathematics written by T. Koetsier and published by North Holland. This book was released on 1991 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hardbound. In this book, which is both a philosophical and historiographical study, the author investigates the fallibility and the rationality of mathematics by means of rational reconstructions of developments in mathematics. The initial chapters are devoted to a critical discussion of Lakatos' philosophy of mathematics. In the remaining chapters several episodes in the history of mathematics are discussed, such as the appearance of deduction in Greek mathematics and the transition from Eighteenth-Century to Nineteenth-Century analysis. The author aims at developing a notion of mathematical rationality that agrees with the historical facts. A modified version of Lakatos' methodology is proposed. The resulting constructions show that mathematical knowledge is fallible, but that its fallibility is remarkably weak.
Download or read book Appraising Lakatos written by György Kampis and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Imre Lakatos (1922-1974) was one of the protagonists in shaping the "new philosophy of science". More than 25 years after his untimely death, it is time for a critical re-evaluation of his ideas. His main theme of locating rationality within the scientific process appears even more compelling today, after many historical case studies have revealed the cultural and societal elements within scientific practices. Recently there has been, above all, an increasing interest in Lakatos' philosophy of mathematics, which emphasises heuristics and mathematical practice over logical justification. But suitable modifications of his approach are called for in order to make it applicable to modern axiomatised theories. Pioneering historical research in England and Hungary has unearthed hitherto unknown facts about Lakatos' personal life, his wartime activities and his involvement in the political developments of post-war Europe. From a communist activist committed to Györgyi Lukács' thinking, Lakatos developed into a staunch anti-Marxist who found his intellectual background in Popper's critical rationalism. The volume also publishes for the first time a part of his Debrecen Ph.D. thesis and it is concluded by a bibliography of his Hungarian writings.
Download or read book Proofs and Refutations written by Imre Lakatos and published by Cambridge University Press. This book was released on 1976 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.
Download or read book Essays in Memory of Imre Lakatos written by Robert S. Cohen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 758 pages. Available in PDF, EPUB and Kindle. Book excerpt: The death of Imre Lakatos on February 2, 1974 was a personal and philosophical loss to the worldwide circle of his friends, colleagues and students. This volume reflects the range of his interests in mathematics, logic, politics and especially in the history and methodology of the sciences. Indeed, Lakatos was a man in search of rationality in all of its forms. He thought he had found it in the historical development of scientific knowledge, yet he also saw rationality endangered everywhere. To honor Lakatos is to honor his sharp and aggressive criticism as well as his humane warmth and his quick wit. He was a person to love and to struggle with. PAUL K. FEYERABEND ROBERT S. COHEN MARX W. WARTOFSKY TABLE OF CONTENTS Preface VII JOHN WORRALL / Imre Lakatos (1922-1974): Philosopher of Mathematics and Philosopher of Science JOSEPH AGASSI / The Lakatosian Revolution 9 23 D. M. ARMSTRONG / Immediate Perception w. W. BAR TLEY, III/On Imre Lakatos 37 WILLIAM BERKSON / Lakatos One and Lakatos Two: An Appreciation 39 I. B. COHEN / William Whewell and the Concept of Scientific Revolution 55 L. JONATHAN COHEN / How Can One Testimony Corroborate Another? 65 R. S. COHEN / Constraints on Science 79 GENE D'AMOUR/ Research Programs, Rationality, and Ethics 87 YEHUDA ELKANA / Introduction: Culture, Cultural System and Science 99 PA UL K.
Download or read book Lakatos written by Brendan Larvor and published by Routledge. This book was released on 2013-01-11 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lakatos: An Introduction provides a thorough overview of both Lakatos's thought and his place in twentieth century philosophy. It is an essential and insightful read for students and anyone interested in the philosophy of science.
Download or read book Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by . This book was released on 2020 with total page 985 pages. Available in PDF, EPUB and Kindle. Book excerpt: The philosophy of mathematics can be traced back in time to the dawn of mathematics itself. The axiomatization of Euclid in "The Elements" did not hinder innovations in mathematical practice to develop outside the realm of the deductive method. In fact the history of mathematics shows a rich tapestry of practice that include visual, algorithmic, experimental, probabilistic and computational approaches. However the philosophy of mathematics as argued by Imre Lakatos suggests that the innovations and impasses in mathematical practice have remained more or less unacknowledged in philosophy. For instance mathematical argumentation was primarily the domain of theologians and medieval and postmedieval scholastics for over 1700 years after Aristotle. Similarly the study of logic became the purview of mathematical philosophy criticized by Reuben Hersh as "Quinean ping-pong". In two prior Springer books 18 Unconventional Essays on the Nature of Mathematics (Hersh,2006) and Humanizing Mathematics and its Philosophy (Sriraman, 2017), it is sufficiently clear that the philosophy of mathematics is no longer centered around it origins in theology and logic, but influences and is influenced by other domains. Today the philosophy of mathematics can be informed by computer scientists, historians, logicians, linguists, educators, physicists, psychologists, neuroscientists, statisticians and last but not least mathematicians. At the dawn of the 21st century we still have a cadre of scholars influenced first-hand by the likes of Quine and Brouwer, as well as those who were influenced by Imre Lakatos' seminal work Proofs and Refutations (in the 1970s) that espouse the views of practicing mathematicians. Pluralism is the avant-garde term in vogue today suggesting a "post- modern" view of mathematics that would have been frowned upon a century ago. The purpose of this unique Handbook is to unfold the transformation of the philosophy of mathematics from its origins in the history of mathem atical practice. In order to do so, chapters will describe different mathematical practices in different time periods of history and contrast it with the development of philosophy. The contributions will include scholars from other disciplines who have contributed to the richness of perspectives that abound the study of philosophy today. The Handbook aims to synthesize what is known, and what has unfolded but also offer directions in which the study of philosophy of mathematics as evident in increasingly diverse mathematical practices is headed. Different sections of the Handbook will offer insights into the origins, debates, methodologies and newer perspectives that characterize the discipline today. This Handbook is curated by an editorial advisory board consisting of leading scholars from the disciplines of mathematics, history and philosophy. Editorial Advisory Board Andrew Aberdein Jody Azzouni William Byers Carlo Cellucci Chandler Davis Paul Ernest Michele Friend Reuben Hersh Yuri Manin Athanase Papadopoulos Ulf Persson Kim Plofker John Stillwell David Tall.
Download or read book Imre Lakatos and the Guises of Reason written by John Kadvany and published by Duke University Press. This book was released on 2001-04-09 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Hungarian émigré Imre Lakatos (1922–1974) earned a worldwide reputation through the influential philosophy of science debates involving Thomas Kuhn, Paul Feyerabend, and Sir Karl Popper. In Imre Lakatos and the Guises of Reason John Kadvany shows that embedded in Lakatos’s English-language work is a remarkable historical philosophy rooted in his Hungarian past. Below the surface of his life as an Anglo-American philosopher of science and mathematics, Lakatos covertly introduced novel transformations of Hegelian and Marxist ideas about historiography, skepticism, criticism, and rationality. Lakatos escaped Hungary following the failed 1956 Revolution. Before then, he had been an influential Communist intellectual and was imprisoned for years by the Stalinist regime. He also wrote a lost doctoral thesis in the philosophy of science and participated in what was criminal behavior in all but a legal sense. Kadvany argues that this intellectual and political past animates Lakatos’s English-language philosophy, and that, whether intended or not, Lakatos integrated a penetrating vision of Hegelian ideas with rigorous analysis of mathematical proofs and controversial histories of science. Including new applications of Lakatos’s ideas to the histories of mathematical logic and economics and providing lucid exegesis of many of Hegel’s basic ideas, Imre Lakatos and the Guises of Reason is an exciting reconstruction of ideas and episodes from the history of philosophy, science, mathematics, and modern political history.
Download or read book Mathematics Science and Epistemology Volume 2 Philosophical Papers written by Imre Lakatos and published by Cambridge University Press. This book was released on 1980-10-16 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 together with some critical essays on contemporary philosophers of science.
Download or read book History and Philosophy of Modern Mathematics written by William Aspray and published by U of Minnesota Press. This book was released on 1988 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective. The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.
Download or read book Problems in the Philosophy of Mathematics written by Imre Lakatos and published by Elsevier. This book was released on 1967 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Imre Lakatos and Theories of Scientific Change written by K. Gavroglu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: How happy it is to recall Imre Lakatos. Now, fifteen years after his death, his intelligence, wit, generosity are vivid. In the Preface to the book of Essays in Memory of Imre Lakatos (Boston Studies, 39, 1976), the editors wrote: ... Lakatos was a man in search of rationality in all of its forms. He thought he had found it in the historical development of scientific knowledge, yet he also saw rationality endangered everywhere. To honor Lakatos is to honor his sharp and aggressive criticism as well as his humane warmth and his quick wit. He was a person to love and to struggle with. The book before us carries old and new friends of that Lakatosian spirit further into the issues which he wanted to investigate. That the new friends include a dozen scientific, historical and philosophical scholars from Greece would have pleased Lakatos very much, and with an essay from China, he would have smiled all the more. But the key lies in the quality of these papers, and in the imaginative organization of the conference at Thessaloniki in summer 1986 which worked so well.
Download or read book The Methodology of Scientific Research Programmes Volume 1 written by Imre Lakatos and published by Cambridge University Press. This book was released on 1980-10-16 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection exhibits and confirms the originality, range and the essential unity of his work.
Download or read book Mathematics Science and Epistemology Volume 2 Philosophical Papers written by Imre Lakatos and published by Cambridge University Press. This book was released on 1978-05-18 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Towards a Philosophy of Real Mathematics written by David Corfield and published by Cambridge University Press. This book was released on 2003-04-24 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, to the use of analogy, the prospects for a Bayesian confirmation theory, the notion of a mathematical research programme and the ways in which new concepts are justified. His inspiring book challenges both philosophers and mathematicians to develop the broadest and richest philosophical resources for work in their disciplines and points clearly to the ways in which this can be done.
Download or read book The Space of Mathematics written by Javier Echeverria and published by Walter de Gruyter. This book was released on 2012-10-25 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by Springer Nature. This book was released on with total page 3221 pages. Available in PDF, EPUB and Kindle. Book excerpt:
