Historical Introduction to the Philosophy of Mathematics: A Reader

Inbunden, Engelska, 2016

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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.

Produktinformation

Utgivningsdatum2016-02-11
Mått169 x 244 x 49 mm
Vikt1 533 g
FormatInbunden
SpråkEngelska
Antal sidor848
FörlagBloomsbury Publishing PLC
ISBN9781472525345

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How to use this bookIntroduction: Terminology and AxiomsPart I: Ancients and MedievalsIntroductory overviewI.1. PythagoreansI.2. Parmenides and Zeno’s ParadoxesI.3. PlatoI.4. AristotlePart II: ModernsIntroductory overviewII.1. The RationalistsII.2. The EmpiricistsII.3. KantPart III: 19th and Early 20th CenturiesIntroductory overviewIII.1. MillIII.2. CantorIII.3. LogicismIII.4. FormalismIII.5. IntuitionismIII.6. ConventionalismIII.7. WittgensteinIII.8. Gödel’s TheoremIII.9. Gödel’s PlatonismPart IV: Contemporary ViewsIntroductory overviewIV.1. The ProblemIV.2. The Indispensability ArgumentIV.3. Benacerraf’s Number Puzzle and StructuralismIV.4. ModalismIV.5. Fictionalism.IV.6. ApriorismIV.7. Naturalism.IV.8. Plenitudinous PlatonismV.9. Challenges to Mathematical ApriorismBibliographyIndex

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 Gödel. 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.