Philosophies Of Mathematics

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Introducing Philosophy of Mathematics

Michele Friend
Introducing Philosophy of Mathematics Book PDF

Author : Michele Friend
Publisher : Routledge
Page : 240 pages
File Size : 50,9 Mb
Release : 2014-12-05
Category : Philosophy
ISBN : 9781317493785

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Introducing Philosophy of Mathematics by Michele Friend Pdf

What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.

Philosophy of Mathematics

Paul Benacerraf,Hilary Putnam
Philosophy of Mathematics Book PDF

Author : Paul Benacerraf,Hilary Putnam
Publisher : Cambridge University Press
Page : 604 pages
File Size : 46,7 Mb
Release : 1984-01-27
Category : Science
ISBN : 9781107268135

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Philosophy of Mathematics by Paul Benacerraf,Hilary Putnam Pdf

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

Philosophy of Mathematics

Øystein Linnebo
Philosophy of Mathematics Book PDF

Author : Øystein Linnebo
Publisher : Princeton University Press
Page : 214 pages
File Size : 41,9 Mb
Release : 2020-03-24
Category : Mathematics
ISBN : 9780691202297

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Philosophy of Mathematics by Øystein Linnebo Pdf

A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.

An Introduction to the Philosophy of Mathematics

Mark Colyvan
An Introduction to the Philosophy of Mathematics Book PDF

Author : Mark Colyvan
Publisher : Cambridge University Press
Page : 199 pages
File Size : 54,5 Mb
Release : 2012-06-14
Category : Mathematics
ISBN : 9780521826020

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An Introduction to the Philosophy of Mathematics by Mark Colyvan Pdf

A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.

Lectures on the Philosophy of Mathematics

Joel David Hamkins
Lectures on the Philosophy of Mathematics Book PDF

Author : Joel David Hamkins
Publisher : MIT Press
Page : 350 pages
File Size : 51,5 Mb
Release : 2021-03-09
Category : Mathematics
ISBN : 9780262542234

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Lectures on the Philosophy of Mathematics by Joel David Hamkins Pdf

An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Introduction to Mathematical Philosophy

Bertrand Russell
Introduction to Mathematical Philosophy Book PDF

Author : Bertrand Russell
Publisher : Courier Corporation
Page : 230 pages
File Size : 42,6 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 0486277240

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Introduction to Mathematical Philosophy by Bertrand Russell Pdf

In the words of Bertrand Russell, "Because language is misleading, as well as because it is diffuse and inexact when applied to logic (for which it was never intended), logical symbolism is absolutely necessary to any exact or thorough treatment of mathematical philosophy." That assertion underlies this book, a seminal work in the field for more than 70 years. In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy. In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.

The Philosophy of Mathematics Education

Paul Ernest,Ole Skovsmose,Jean Paul van Bendegem,Maria Bicudo,Roger Miarka,Ladislav Kvasz,Regina Moeller
The Philosophy of Mathematics Education Book PDF

Author : Paul Ernest,Ole Skovsmose,Jean Paul van Bendegem,Maria Bicudo,Roger Miarka,Ladislav Kvasz,Regina Moeller
Publisher : Springer
Page : 33 pages
File Size : 48,6 Mb
Release : 2016-07-15
Category : Education
ISBN : 9783319405698

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The Philosophy of Mathematics Education by Paul Ernest,Ole Skovsmose,Jean Paul van Bendegem,Maria Bicudo,Roger Miarka,Ladislav Kvasz,Regina Moeller Pdf

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.

What Is Mathematics, Really?

Reuben Hersh
What Is Mathematics Really Book PDF

Author : Reuben Hersh
Publisher : Oxford University Press
Page : 368 pages
File Size : 53,7 Mb
Release : 1997-08-21
Category : Mathematics
ISBN : 9780198027362

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What Is Mathematics, Really? by Reuben Hersh Pdf

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.

Thinking about Mathematics

Stewart Shapiro
Thinking about Mathematics Book PDF

Author : Stewart Shapiro
Publisher : OUP Oxford
Page : 323 pages
File Size : 40,8 Mb
Release : 2000-07-13
Category : Philosophy
ISBN : 9780192893062

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Thinking about Mathematics by Stewart Shapiro Pdf

Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.

Mathematics, Logic, and their Philosophies

Mojtaba Mojtahedi,Shahid Rahman,Mohammad Saleh Zarepour
Mathematics Logic and their Philosophies Book PDF

Author : Mojtaba Mojtahedi,Shahid Rahman,Mohammad Saleh Zarepour
Publisher : Springer Nature
Page : 493 pages
File Size : 43,6 Mb
Release : 2021-02-09
Category : Philosophy
ISBN : 9783030536541

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Mathematics, Logic, and their Philosophies by Mojtaba Mojtahedi,Shahid Rahman,Mohammad Saleh Zarepour Pdf

This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. The third category contains papers on Avicenna’s logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community.

Why Is There Philosophy of Mathematics At All?

Ian Hacking
Why Is There Philosophy of Mathematics At All Book PDF

Author : Ian Hacking
Publisher : Cambridge University Press
Page : 212 pages
File Size : 54,7 Mb
Release : 2014-01-30
Category : Science
ISBN : 9781107729827

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Why Is There Philosophy of Mathematics At All? by Ian Hacking Pdf

This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.

Mathematics: A Concise History and Philosophy

W.S. Anglin
Mathematics A Concise History and Philosophy Book PDF

Author : W.S. Anglin
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461208754

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Mathematics: A Concise History and Philosophy by W.S. Anglin Pdf

This is a concise introductory textbook for a one-semester (40-class) course in the history and philosophy of mathematics. It is written for mathemat ics majors, philosophy students, history of science students, and (future) secondary school mathematics teachers. The only prerequisite is a solid command of precalculus mathematics. On the one hand, this book is designed to help mathematics majors ac quire a philosophical and cultural understanding of their subject by means of doing actual mathematical problems from different eras. On the other hand, it is designed to help philosophy, history, and education students come to a deeper understanding of the mathematical side of culture by means of writing short essays. The way I myself teach the material, stu dents are given a choice between mathematical assignments, and more his torical or philosophical assignments. (Some sample assignments and tests are found in an appendix to this book. ) This book differs from standard textbooks in several ways. First, it is shorter, and thus more accessible to students who have trouble coping with vast amounts of reading. Second, there are many detailed explanations of the important mathematical procedures actually used by famous mathe maticians, giving more mathematically talented students a greater oppor tunity to learn the history and philosophy by way of problem solving.

Pluralism in Mathematics: A New Position in Philosophy of Mathematics

Michèle Friend
Pluralism in Mathematics A New Position in Philosophy of Mathematics Book PDF

Author : Michèle Friend
Publisher : Springer Science & Business Media
Page : 297 pages
File Size : 43,9 Mb
Release : 2013-11-20
Category : Science
ISBN : 9789400770584

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Pluralism in Mathematics: A New Position in Philosophy of Mathematics by Michèle Friend Pdf

This book is about philosophy, mathematics and logic, giving a philosophical account of Pluralism which is a family of positions in the philosophy of mathematics. There are four parts to this book, beginning with a look at motivations for Pluralism by way of Realism, Maddy’s Naturalism, Shapiro’s Structuralism and Formalism. In the second part of this book the author covers: the philosophical presentation of Pluralism; using a formal theory of logic metaphorically; rigour and proof for the Pluralist; and mathematical fixtures. In the third part the author goes on to focus on the transcendental presentation of Pluralism, and in part four looks at applications of Pluralism, such as a Pluralist approach to proof in mathematics and how Pluralism works in regard to together-inconsistent philosophies of mathematics. The book finishes with suggestions for further Pluralist enquiry. In this work the author takes a deeply radical approach in developing a new position that will either convert readers, or act as a strong warning to treat the word ‘pluralism’ with care.

Mathematics and Mind

Alexander George
Mathematics and Mind Book PDF

Author : Alexander George
Publisher : Oxford University Press, USA
Page : 218 pages
File Size : 53,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780195079296

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Mathematics and Mind by Alexander George Pdf

The essays in this volume investigate the conceptual foundations of mathematics illuminating the powers of the mind. Contributors include Alexander George, Michael Dummett, George Boolos, W.W. Tait, Wilfried Sieg, Daniel Isaacson, Charles Parsons, and Michael Hallett.

The Philosophy of Mathematics Education Today

Paul Ernest
The Philosophy of Mathematics Education Today Book PDF

Author : Paul Ernest
Publisher : Springer
Page : 377 pages
File Size : 42,6 Mb
Release : 2018-06-09
Category : Education
ISBN : 9783319777603

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The Philosophy of Mathematics Education Today by Paul Ernest Pdf

This book offers an up-to-date overview of the research on philosophy of mathematics education, one of the most important and relevant areas of theory. The contributions analyse, question, challenge, and critique the claims of mathematics education practice, policy, theory and research, offering ways forward for new and better solutions. The book poses basic questions, including: What are our aims of teaching and learning mathematics? What is mathematics anyway? How is mathematics related to society in the 21st century? How do students learn mathematics? What have we learnt about mathematics teaching? Applied philosophy can help to answer these and other fundamental questions, and only through an in-depth analysis can the practice of the teaching and learning of mathematics be improved. The book addresses important themes, such as critical mathematics education, the traditional role of mathematics in schools during the current unprecedented political, social, and environmental crises, and the way in which the teaching and learning of mathematics can better serve social justice and make the world a better place for the future.