An Historical Introduction to the Philosophy of Mathematics: A Reader

by Marcus, Russell; McEvoy, Mark

• ISBN13: 9781472525673
• ISBN10: 1472525671
• Format: Paperback
• Copyright: 2016-02-11
• Publisher: Bloomsbury Academic

Summary

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.

Author Biography

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.

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. Gödel's Theorem
III.9. Gödel'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

Bibliography
Index