Proofs and Refutations

Proofs and Refutations
Author: Imre Lakatos
Publisher: Cambridge University Press
Total Pages: 190
Release: 1976
Genre: Mathematics
ISBN: 9780521290388

Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.

Lakatos' Philosophy of Mathematics

Lakatos' Philosophy of Mathematics
Author: T. Koetsier
Publisher: North Holland
Total Pages: 336
Release: 1991
Genre: Mathematics
ISBN:

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.

Mathematics, Science and Epistemology: Volume 2, Philosophical Papers

Mathematics, Science and Epistemology: Volume 2, Philosophical Papers
Author: Imre Lakatos
Publisher: Cambridge University Press
Total Pages: 302
Release: 1980-10-16
Genre: Mathematics
ISBN: 9780521280303

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his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement.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.

Imre Lakatos and the Guises of Reason

Imre Lakatos and the Guises of Reason
Author: John Kadvany
Publisher: Duke University Press
Total Pages: 400
Release: 2001-04-09
Genre: Biography & Autobiography
ISBN: 9780822326496

DIVAn exploration of the philosophy of science and mathematics of Hungarian emigre, Imre Lakatos, demonstrating its contemporary relevance./div

Essays in the memory of Imre Lakatos

Essays in the memory of Imre Lakatos
Author: Imre Lakatos
Publisher: Springer Science & Business Media
Total Pages: 788
Release: 1976-10-31
Genre: Science
ISBN: 9789027706553

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.

Social Constructivism as a Philosophy of Mathematics

Social Constructivism as a Philosophy of Mathematics
Author: Paul Ernest
Publisher: SUNY Press
Total Pages: 336
Release: 1998-01-01
Genre: Philosophy
ISBN: 9780791435878

Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.

Towards a Philosophy of Real Mathematics

Towards a Philosophy of Real Mathematics
Author: David Corfield
Publisher: Cambridge University Press
Total Pages: 300
Release: 2003-04-24
Genre: Philosophy
ISBN: 1139436392

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.

Explaining Cancer

Explaining Cancer
Author: Anya Plutynski
Publisher: Oxford University Press
Total Pages: 281
Release: 2018-07-18
Genre: Science
ISBN: 0199967466

In Explaining Cancer, Anya Plutynski addresses a variety of philosophical questions that arise in the context of cancer science and medicine. She begins with the following concerns: · How do scientists classify cancer? Do these classifications reflect nature's "joints"? · How do cancer scientists identify and classify early stage cancers? · What does it mean to say that cancer is a "genetic" disease? What role do genes play in "mechanisms for" cancer? · What are the most important environmental causes of cancer, and how do epidemiologists investigate these causes? · How exactly has our evolutionary history made us vulnerable to cancer? Explaining Cancer uses these questions as an entrée into a family of philosophical debates. It uses case studies of scientific practice to reframe philosophical debates about natural classification in science and medicine, the problem of drawing the line between disease and health, mechanistic reasoning in science, pragmatics and evidence, the roles of models and modeling in science, and the nature of scientific explanation.

What Is Mathematics, Really?

What Is Mathematics, Really?
Author: Reuben Hersh
Publisher: Oxford University Press
Total Pages: 368
Release: 1997-08-21
Genre: Mathematics
ISBN: 0198027362

Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.