Proofs and Refutations

The Logic of Mathematical Discovery

Author: Imre Lakatos

Publisher: Cambridge University Press

ISBN: 1316425339

Category: Science

Page: N.A

View: 1584

Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the process, raises important questions about the nature of mathematical discovery and methodology. Lakatos shows that mathematics grows through a process of improvement by attempts at proofs and critiques of these attempts, and his work continues to inspire mathematicians and philosophers aspiring to develop a philosophy of mathematics that accounts for both the static and the dynamic complexity of mathematical practice. With a specially commissioned Preface written by Paolo Mancosu, this book has been revived for a new generation of readers.
Release

Indiscrete Thoughts

Author: Gian-Carlo Rota

Publisher: Springer Science & Business Media

ISBN: 9780817647810

Category: Mathematics

Page: 280

View: 8483

Indiscrete Thoughts gives a glimpse into a world that has seldom been described - that of science and technology as seen through the eyes of a mathematician. The era covered by this book, 1950 to 1990, was surely one of the golden ages of science and of the American university. Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period. Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. This beautifully written book is destined to become an instant classic and the subject of debate for decades to come.
Release

The Philosophy of Mathematics Education

Author: Paul Ernest,Ole Skovsmose,Jean Paul van Bendegem,Maria Bicudo,Roger Miarka,Ladislav Kvasz,Regina Moeller

Publisher: Springer

ISBN: 3319405691

Category: Education

Page: 26

View: 2515

This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant modern movements in the philosophy of mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the philosophy of mathematics education in Brazil. This illustrates one orientation towards research inquiry in the philosophy of mathematics education. It is part of a broader practice of ‘philosophical archaeology’: the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in mathematics education. An extensive bibliography is also included.
Release

Criticism and the Growth of Knowledge: Volume 4

Proceedings of the International Colloquium in the Philosophy of Science, London, 1965

Author: Imre Lakatos (ed)

Publisher: Cambridge University Press

ISBN: 9780521096232

Category: Philosophy

Page: 282

View: 665

This volume arose out of a symposium on Thomas Kuhn's work, with Karl Popper in the chair.
Release

Lakatos

An Introduction

Author: Brendan Larvor

Publisher: Routledge

ISBN: 1134765134

Category: Philosophy

Page: 144

View: 5128

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.
Release

The Methodology of Scientific Research Programmes: Volume 1

Philosophical Papers

Author: Imre Lakatos,John Worrall,Gregory Currie

Publisher: Cambridge University Press

ISBN: 9780521280310

Category: Philosophy

Page: 260

View: 5204

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.
Release

Philosophy of Mathematics

Structure and Ontology

Author: Stewart Shapiro

Publisher: Oxford University Press

ISBN: 9780198025450

Category: Philosophy

Page: 296

View: 3607

Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians.
Release

What is a Law of Nature?

Author: D. M. Armstrong

Publisher: Cambridge University Press

ISBN: 1316558894

Category: Philosophy

Page: N.A

View: 2806

First published in 1985, D. M. Armstrong's original work on what laws of nature are has continued to be influential in the areas of metaphysics and philosophy of science. Presenting a definitive attack on the sceptical Humean view, that laws are no more than a regularity of coincidence between stances of properties, Armstrong establishes his own theory and defends it concisely and systematically against objections. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Marc Lange, illuminating its continuing importance and relevance to philosophical enquiry, this influential work is available for a new generation of readers.
Release

Ancient Self-Refutation

The Logic and History of the Self-Refutation Argument from Democritus to Augustine

Author: Luca Castagnoli

Publisher: Cambridge University Press

ISBN: 0521896312

Category: History

Page: 394

View: 1679

This book-length treatment provides a unified account of what is distinctive in the ancient approach to the self-refutation argument.
Release

The Cambridge Companion to Atheism

Author: Michael Martin

Publisher: Cambridge University Press

ISBN: 9781139827393

Category: Religion

Page: N.A

View: 7291

In this 2007 volume, eighteen of the world's leading scholars present original essays on various aspects of atheism: its history, both ancient and modern, defense and implications. The topic is examined in terms of its implications for a wide range of disciplines including philosophy, religion, feminism, postmodernism, sociology and psychology. In its defense, both classical and contemporary theistic arguments are criticized, and, the argument from evil, and impossibility arguments, along with a non religious basis for morality are defended. These essays give a broad understanding of atheism and a lucid introduction to this controversial topic.
Release

An Introduction to the Philosophy of Mathematics

Author: Mark Colyvan

Publisher: Cambridge University Press

ISBN: 0521826020

Category: Mathematics

Page: 188

View: 9784

This introduction to the philosophy of mathematics focuses on contemporary debates in an important and central area of philosophy. The reader is taken on a fascinating and entertaining journey through some intriguing mathematical and philosophical territory, including such topics as the realism/anti-realism debate in mathematics, mathematical explanation, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics and the applications of mathematics. Each chapter has a number of discussion questions and recommended further reading from both the contemporary literature and older sources. Very little mathematical background is assumed and all of the mathematics encountered is clearly introduced and explained using a wide variety of examples. The book is suitable for an undergraduate course in philosophy of mathematics and, more widely, for anyone interested in philosophy and mathematics.
Release

The Evolution of Reason

Logic as a Branch of Biology

Author: William S. Cooper

Publisher: Cambridge University Press

ISBN: 9780521540254

Category: Philosophy

Page: 226

View: 6502

This book, first published in 2001, outlines a theory of rationality in which logical law emerges as an intrinsic aspect of evolutionary biology.
Release

Principia Mathematica

Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: N.A

View: 8142

Release

Conjectures and Refutations

The Growth of Scientific Knowledge

Author: Karl Popper

Publisher: Routledge

ISBN: 1135971374

Category: Philosophy

Page: 608

View: 1611

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.
Release

Making and Breaking Mathematical Sense

Histories and Philosophies of Mathematical Practice

Author: Roi Wagner

Publisher: Princeton University Press

ISBN: 1400883784

Category: Mathematics

Page: 256

View: 9103

In line with the emerging field of philosophy of mathematical practice, this book pushes the philosophy of mathematics away from questions about the reality and truth of mathematical entities and statements and toward a focus on what mathematicians actually do—and how that evolves and changes over time. How do new mathematical entities come to be? What internal, natural, cognitive, and social constraints shape mathematical cultures? How do mathematical signs form and reform their meanings? How can we model the cognitive processes at play in mathematical evolution? And how does mathematics tie together ideas, reality, and applications? Roi Wagner uniquely combines philosophical, historical, and cognitive studies to paint a fully rounded image of mathematics not as an absolute ideal but as a human endeavor that takes shape in specific social and institutional contexts. The book builds on ancient, medieval, and modern case studies to confront philosophical reconstructions and cutting-edge cognitive theories. It focuses on the contingent semiotic and interpretive dimensions of mathematical practice, rather than on mathematics' claim to universal or fundamental truths, in order to explore not only what mathematics is, but also what it could be. Along the way, Wagner challenges conventional views that mathematical signs represent fixed, ideal entities; that mathematical cognition is a rigid transfer of inferences between formal domains; and that mathematics’ exceptional consensus is due to the subject’s underlying reality. The result is a revisionist account of mathematical philosophy that will interest mathematicians, philosophers, and historians of science alike.
Release

Zeno of Elea

Author: H. D. P. Lee

Publisher: Cambridge University Press

ISBN: 1107480272

Category: Philosophy

Page: 132

View: 7297

Originally published in 1936, this book presents the ancient Greek text of the paraphrases and quotations of Zeno's philosophical arguments, together with a facing-page English translation and editorial commentary. Detailed notes are incorporated throughout and a bibliography is also included. This book will be of value to anyone with an interest in Zeno and ancient philosophy.
Release

The Cambridge Companion to Wittgenstein

Author: Hans D. Sluga,David G. Stern

Publisher: Cambridge University Press

ISBN: 9780521465915

Category: Philosophy

Page: 509

View: 5392

The essays in this volume address central themes in Wittgenstein's writings on the philosophy of mind, language, logic, and mathematics.
Release

The Darkening Age

The Christian Destruction of the Classical World

Author: Catherine Nixey

Publisher: Houghton Mifflin Harcourt

ISBN: 0544800931

Category: History

Page: 384

View: 1295

A bold new history of the rise of Christianity, showing how its radical followers ravaged vast swathes of classical culture, plunging the world into an era of dogma and intellectual darkness “Searingly passionate…Nixey writes up a storm. Each sentence is rich, textured, evocative, felt…[A] ballista-bolt of a book.” —New York Times Book Review In Harran, the locals refused to convert. They were dismembered, their limbs hung along the town’s main street. In Alexandria, zealots pulled the elderly philosopher-mathematician Hypatia from her chariot and flayed her to death with shards of broken pottery. Not long before, their fellow Christians had invaded the city’s greatest temple and razed it—smashing its world-famous statues and destroying all that was left of Alexandria’s Great Library. Today, we refer to Christianity’s conquest of the West as a “triumph.” But this victory entailed an orgy of destruction in which Jesus’s followers attacked and suppressed classical culture, helping to pitch Western civilization into a thousand-year-long decline. Just one percent of Latin literature would survive the purge; countless antiquities, artworks, and ancient traditions were lost forever. As Catherine Nixey reveals, evidence of early Christians’ campaign of terror has been hiding in plain sight: in the palimpsests and shattered statues proudly displayed in churches and museums the world over. In The Darkening Age, Nixey resurrects this lost history, offering a wrenching account of the rise of Christianity and its terrible cost.
Release