An Historical Introduction to the Philosophy of Mathematics: A Reader

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 (AncientsPythagoras, Plato and Aristotle) and part 2 (ModernsDescartes, 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 Gdel. However, the book also surveys the contemporary school of experimental mathematics and the ideas of its proponentsDoron 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 *

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.

How to use this book Introduction: Terminology and Axioms Part I: Ancients and Medievals Introductory overview I.1. Pythagoreans I.2. Parmenides and Zenos 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. Gdels Theorem III.9. Gdels Platonism Part IV: Contemporary Views Introductory overview IV.1. The Problem IV.2. The Indispensability Argument IV.3. Benacerrafs 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 Bibliography Index