An Historical Introduction to the Philosophy of Mathematics: A Reader

An Historical Introduction to the Philosophy of Mathematics: A Reader

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A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject.

An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient 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 key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject.

Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.
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Product details

  • Hardback | 848 pages
  • 169 x 244 x 44.45mm | 1,630g
  • Bloomsbury Academic
  • London, United Kingdom
  • English
  • 1472525345
  • 9781472525345

Table of contents

How to use this book
Introduction: Terminology and Axioms

Part I: Ancients and Medievals
Introductory overview
I.1. Pythagoreans
I.2. Parmenides and Zeno's Paradoxes
I.3. Plato
I.4. Aristotle

Part II: Moderns
Introductory overview
II.1. The Rationalists
II.2. The Empiricists
II.3. Kant

Part III: 19th and Early 20th Centuries
Introductory overview
III.1. Mill
III.2. Cantor
III.3. Logicism
III.4. Formalism
III.5. Intuitionism
III.6. Conventionalism
III.7. Wittgenstein
III.8. Goedel's Theorem
III.9. Goedel's Platonism

Part IV: Contemporary Views
Introductory overview
IV.1. The Problem
IV.2. The Indispensability Argument
IV.3. Benacerraf's Number Puzzle and Structuralism
IV.4. Modalism
IV.5. Fictionalism.
IV.6. Apriorism
IV.7. Naturalism.
IV.8. Plenitudinous Platonism
V.9. Challenges to Mathematical Apriorism

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Review quote

This is a reader-friendly, broad collection of original works on the philosophy of mathematics, ranging from Pythagoras to other contemporary authors. The subjects are organized chronologically, rather than thematically. Each chapter starts with a valuable introductory overview; this puts the original works of the chapter into context, suggests aspects of information to explore, and offers recommendations for further reading. Part 1 ("Ancients"-Pythagoras, Plato and Aristotle) and part 2 ("Moderns"-Descartes, Leibniz, Locke, Kant, etc.) are primarily meant for undergraduate and beginning graduate students. The later parts of the work will be of interest to advanced graduate students and researchers. These include part 3 ("Nineteenth and Early Twentieth Centuries") and part 4 ("Contemporary Views"), which comprise more than two-thirds of the volume. Particularly refreshing is the fact that the book explores classic authors like Cantor and Goedel. However, the book also surveys the contemporary school of "experimental mathematics" and the ideas of its proponents-Doron Zeilberger (Rutgers Univ.) and Jonathan Borwein (The Univ. of Newcastle, Australia). This branch of mathematics did not exist as recently as 25 years ago. As a result, it is a milestone for experimental mathematics to be discussed in this volume. * CHOICE * [This book] brings together an impressive collection of primary sources from ancient and modern philosophy of mathematics ... It is aimed primarily at undergraduates and early graduate students, however it can serve as an invaluable sourcebook for working researchers as well. * Zentralblatt MATH * This rich historical collection is an invaluable resource. The greats are represented from Pythagorus to Putnam. Classic issues and even current ones, such as fictionalism and naturalism, are included. Plato famously insisted that no one gets into his academy who is ignorant of geometry. Today we should insist that no one gets out of the academy who is ignorant of the philosophy of mathematics. This book will greatly help in that regard. -- James Robert Brown, Professor of Philosophy, University of Toronto, Canada and author of 'Philosophy of Mathematics: A Contemporary Introduction to the World of Proofs and Pictures' A highly-accessible introduction to the philosophy of mathematics. This well-curated reader includes engaging introductory essays for each chapter that will help students tackle some challenging material. It is a welcome addition to the pedagogical literature. -- Lisa Warenski * Dr. Lisa Warenski, The City College of New York, USA * This is a unique anthology of texts in the philosophy of mathematics, thematically grouped, with informative introductory overviews. * Mathematical Reviews *
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About Russell Marcus

Russell Marcus is Assistant Professor in the Department of Philosophy at Hamilton College, New York, USA.

Mark McEvoy is Associate Professor of Philosophy at Hofstra University, USA.
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