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Philosophy Of Mathematics

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The Philosophy of Mathematics Education

The Philosophy of Mathematics Education Book
Author : Paul Ernest,Ole Skovsmose,Jean Paul van Bendegem,Maria Bicudo,Roger Miarka,Ladislav Kvasz,Regina Moeller
Publisher : Springer
Release : 2016-08-04
ISBN : 9783319405681
Language : En, Es, Fr & De

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Book Description :

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.

Why Is There Philosophy of Mathematics At All

Why Is There Philosophy of Mathematics At All  Book
Author : Ian Hacking
Publisher : Cambridge University Press
Release : 2014-01-30
ISBN : 1107050170
Language : En, Es, Fr & De

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Book Description :

Hacking explores how mathematics became possible for the human race, and how it ensured our status as the dominant species.

An Introduction to the Philosophy of Mathematics

An Introduction to the Philosophy of Mathematics Book
Author : Mark Colyvan
Publisher : Cambridge University Press
Release : 2012-06-14
ISBN : 9780521533416
Language : En, Es, Fr & De

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Book Description :

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.

Wittgenstein s Philosophy of Mathematics

Wittgenstein s Philosophy of Mathematics Book
Author : Pasquale Frascolla
Publisher : Routledge
Release : 2006-12-05
ISBN : 113497437X
Language : En, Es, Fr & De

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Book Description :

Wittgenstein's role was vital in establishing mathematics as one of this century's principal areas of philosophic inquiry. In this book, the three phases of Wittgenstein's reflections on mathematics are viewed as a progressive whole, rather than as separate entities. Frascolla builds up a systematic construction of Wittgenstein's representation of the role of arithmetic in the theory of logical operations. He also presents a new interpretation of Wittgenstein's rule-following considerations - the `community view of internal relations'.

Philosophy of Mathematics

Philosophy of Mathematics Book
Author : Øystein Linnebo
Publisher : Princeton University Press
Release : 2017-05-30
ISBN : 1400885248
Language : En, Es, Fr & De

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Book Description :

A sophisticated, original introduction to the philosophy of mathematics from one of its leading contemporary scholars Mathematics is one of humanity's most successful yet puzzling endeavors. It is a model of precision and objectivity, but 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 yet accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Written by Øystein Linnebo, one of the world's leading scholars on the subject, the book introduces all of the classical approaches to the field, including logicism, formalism, intuitionism, empiricism, and structuralism. It also contains accessible introductions to some more specialized issues, such as mathematical intuition, potential infinity, the iterative conception of sets, and the search for new mathematical axioms. The groundbreaking work of German mathematician and philosopher Gottlob Frege, one of the founders of analytic philosophy, figures prominently throughout the book. Other important thinkers whose work is introduced and discussed include Immanuel Kant, John Stuart Mill, David Hilbert, Kurt Gödel, W. V. Quine, Paul Benacerraf, and Hartry H. Field. Sophisticated but clear and approachable, this is an essential introduction for all students and teachers of philosophy, as well as mathematicians and others who want to understand the foundations of mathematics.

Philosophies of Mathematics

Philosophies of Mathematics Book
Author : Alexander L. George,Daniel Velleman
Publisher : Wiley-Blackwell
Release : 2001-12-03
ISBN : 9780631195443
Language : En, Es, Fr & De

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Book Description :

This book provides an accessible, critical introduction to the three main approaches that dominated work in the philosophy of mathematics during the twentieth century: logicism, intuitionism and formalism.

A Concise History of Mathematics for Philosophers

A Concise History of Mathematics for Philosophers   Book
Author : John Stillwell
Publisher : Cambridge University Press
Release : 2019-06-06
ISBN : 1108456235
Language : En, Es, Fr & De

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Book Description :

This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a large extent, the story of philosophy of mathematics.

Wittgenstein s Philosophy of Mathematics

Wittgenstein   s Philosophy of Mathematics Book
Author : V.H. Klenk
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 9401013918
Language : En, Es, Fr & De

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Book Description :

Wittgenstein's remarks on mathematics have not received the recogni tion they deserve; they have for the most part been either ignored, or dismissed as unworthy of the author of the Tractatus and the I nvestiga tions. This is unfortunate, I believe, and not at all fair, for these remarks are not only enjoyable reading, as even the harshest critics have con ceded, but also a rich and genuine source of insight into the nature of mathematics. It is perhaps the fact that they are more suggestive than systematic which has put so many people off; there is nothing here of formal derivation and very little attempt even at sustained and organized argumentation. The remarks are fragmentary and often obscure, if one does not recognize the point at which they are directed. Nevertheless, there is much here that is good, and even a fairly system atic and coherent account of mathematics. What I have tried to do in the following pages is to reconstruct the system behind the often rather disconnected commentary, and to show that when the theory emerges, most of the harsh criticism which has been directed against these re marks is seen to be without foundation. This is meant to be a sym pathetic account of Wittgenstein's views on mathematics, and I hope that it will at least contribute to a further reading and reassessment of his contributions to the philosophy of mathematics.

Berkeley s Philosophy of Mathematics

Berkeley s Philosophy of Mathematics Book
Author : Douglas M. Jesseph
Publisher : University of Chicago Press
Release : 2010-12-15
ISBN : 0226398951
Language : En, Es, Fr & De

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Book Description :

In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work. Jesseph challenges the prevailing view that Berkeley's mathematical writings are peripheral to his philosophy and argues that mathematics is in fact central to his thought, developing out of his critique of abstraction. Jesseph's argument situates Berkeley's ideas within the larger historical and intellectual context of the Scientific Revolution. Jesseph begins with Berkeley's radical opposition to the received view of mathematics in the philosophy of the late seventeenth and early eighteenth centuries, when mathematics was considered a "science of abstractions." Since this view seriously conflicted with Berkeley's critique of abstract ideas, Jesseph contends that he was forced to come up with a nonabstract philosophy of mathematics. Jesseph examines Berkeley's unique treatments of geometry and arithmetic and his famous critique of the calculus in The Analyst. By putting Berkeley's mathematical writings in the perspective of his larger philosophical project and examining their impact on eighteenth-century British mathematics, Jesseph makes a major contribution to philosophy and to the history and philosophy of science.

Introduction to the Philosophy of Mathematics

Introduction to the Philosophy of Mathematics Book
Author : Hugh Lehman
Publisher : Unknown
Release : 1979
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Introduction to the Philosophy of Mathematics book written by Hugh Lehman, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Introducing Philosophy of Mathematics

Introducing Philosophy of Mathematics Book
Author : Michele Friend
Publisher : Routledge
Release : 2014-12-05
ISBN : 1317493796
Language : En, Es, Fr & De

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Book Description :

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.

A Mathematical Prelude to the Philosophy of Mathematics

A Mathematical Prelude to the Philosophy of Mathematics Book
Author : Stephen Pollard
Publisher : Springer
Release : 2016-09-03
ISBN : 9783319348339
Language : En, Es, Fr & De

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Book Description :

This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Gödel's theorems, interpretability, the hierarchy of sets, Frege arithmetic and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and real numbers and have some background in formal logic.

Thinking about Mathematics

Thinking about Mathematics Book
Author : Stewart Shapiro
Publisher : OUP Oxford
Release : 2000-07-13
ISBN : 0192893068
Language : En, Es, Fr & De

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Book Description :

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.

Philosophy of Mathematics

Philosophy of Mathematics Book
Author : James Robert Brown
Publisher : Psychology Press
Release : 2008
ISBN : 9780415960472
Language : En, Es, Fr & De

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Book Description :

"In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value?" "This clear and engaging book takes a unique approach, encompassing nonstandard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional topics such as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis."--BOOK JACKET.

An Aristotelian Realist Philosophy of Mathematics

An Aristotelian Realist Philosophy of Mathematics Book
Author : James Franklin
Publisher : Palgrave Macmillan
Release : 2014-04-08
ISBN : 9781137400727
Language : En, Es, Fr & De

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Book Description :

An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge.

Problems in the philosophy of mathematics

Problems in the philosophy of mathematics Book
Author : Imre Lakatos
Publisher : Elsevier
Release : 1967
ISBN : 0444534113
Language : En, Es, Fr & De

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Book Description :

Download Problems in the philosophy of mathematics book written by Imre Lakatos, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Philosophy of Mathematics

Philosophy of Mathematics Book
Author : Stewart Shapiro
Publisher : Oxford University Press on Demand
Release : 2000
ISBN : 9780195139303
Language : En, Es, Fr & De

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Book Description :

Moving beyond both realist and anti-realist accounts of mathematics, Shapiro articulates a "structuralist" approach, arguing that the subject matter of a mathematical theory is not a fixed domain of numbers that exist independent of each other, but rather is the natural structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle.

An Historical Introduction to the Philosophy of Mathematics A Reader

An Historical Introduction to the Philosophy of Mathematics  A Reader Book
Author : Russell Marcus,Mark McEvoy
Publisher : Bloomsbury Publishing
Release : 2016-02-11
ISBN : 1472525671
Language : En, Es, Fr & De

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Book Description :

As the first comprehensive collection of historical readings in the philosophy of mathematics, this much-needed introduction reveals the rich history of the subject. Focusing on the philosophy of mathematics before the 20th-century, An Historical Introduction to the Philosophy of Mathematics: A Readerbrings together an impressive collection of primary sources from ancient, medieval and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with modern thinkers. While a selection of recent texts offering insights the current state of the discipline, clearly illustrate the development of the subject. Presenting historical background essential to understanding contemporary trends, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates studying the philosophy of mathematics.

The Philosophy of Mathematical Practice

The Philosophy of Mathematical Practice Book
Author : Paolo Mancosu
Publisher : OUP Oxford
Release : 2011-12-01
ISBN : 9780199640102
Language : En, Es, Fr & De

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Book Description :

There is an urgent need in philosophy of mathematics for new approaches which pay closer attention to mathematical practice. This book will blaze the trail: it offers philosophical analyses of important characteristics of contemporary mathematics and of many aspects of mathematical activity which escape purely formal logical treatment.

The Oxford Handbook of Philosophy of Mathematics and Logic

The Oxford Handbook of Philosophy of Mathematics and Logic Book
Author : Stewart Shapiro
Publisher : OUP USA
Release : 2007-06-14
ISBN : 9780195325928
Language : En, Es, Fr & De

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Book Description :

Mathematics and logic have been central topics of concern since the dawn of philosophy. Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and a priority in any philosophical system. Philosophers have focused on mathematics as a case study for general philosophical issues and for its role in overall knowledge- gathering. Today, philosophy of mathematics and logic remain central disciplines in contemporary philosophy, as evidenced by the regular appearance of articles on these topics in the best mainstream philosophical journals; in fact, the last decade has seen an explosion of scholarly work in these areas. This volume covers these disciplines in a comprehensive and accessible manner, giving the reader an overview of the major problems, positions, and battle lines. The 26 contributed chapters are by established experts in the field, and their articles contain both exposition and criticism as well as substantial development of their own positions. The essays, which are substantially self-contained, serve both to introduce the reader to the subject and to engage in it at its frontiers. Certain major positions are represented by two chapters--one supportive and one critical. The Oxford Handbook of Philosophy of Math and Logic is a ground-breaking reference like no other in its field. It is a central resource to those wishing to learn about the philosophy of mathematics and the philosophy of logic, or some aspect thereof, and to those who actively engage in the discipline, from advanced undergraduates to professional philosophers, mathematicians, and historians.