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Philosophy of Mathematics: An Anthology (Blackwell Philosophy Anthologies) ISBN: 063121870X ISBN13: 9780631218708 Philosophy of Mathematics: An Anthology (Blackwell Philosophy Anthologies) By: Edited by Dale Jacquette Publisher: Blackwell Publishers Format: Paperback Our Price: 24.83 Discount: 8% RRP: 26.99

This distinctive anthology includes many of the most important recent contributions to the philosophy of mathematics. The featured papers are organized thematically, rather than chronologically, to provide the best overview of philosophical issues connected with mathematics and the development of mathematical knowledge. Coverage ranges from general topics in mathematical explanation and the concept of number, to specialized investigations of the ontology of mathematical entities and the nature of mathematical truth, models and methods of mathematical proof, intuitionistic mathematics, and philosophical foundations of set theory. This volume explores the central problems and exposes intriguing new directions in the philosophy of mathematics, making it an essential teaching resource, reference work, and research guide. The book complements Philosophy of Logic: An Anthology and A Companion to Philosophical Logic, also edited by Dale Jacquette (Blackwell 2001).


Contents:

Preface

 Acknowledgments

 Introduction: Mathematics and Philosophy of Mathematics: Dale Jacquette

 Part I: The Realm of Mathematics: 1

What is Mathematics About?: Michael Dummett

 2

Mathematical Explanation: Mark Steiner

 3

Frege versus Cantor and Dedekind: On the Concept of Number: William W

Tait

 4

The Present Situation in Philosophy of Mathematics: Henry Mehlberg

 Part II: Ontology of Mathematics and the Nature and Knowledge of Mathematical Truth: 5

What Numbers Are: N.P

White

 6

Mathematical Truth: Paul Benacerraf

 7

Ontology and Mathematical Truth: Michael Jubien

 8

An Anti-Realist Account of Mathematical Truth: Graham Priest

 9

What Mathematical Knowledge Could Be: Jerrold J

Katz

 10

The Philosophical Basis of our Knowledge of Number: William Demonpoulos

 Part III: Models and Methods of Mathematical Proof: 11

Mathematical Proof: G.H

Hardy

 12

What Does a Mathematical Proof Prove?: Imre Lakatos

 13

The Four-Color Problem: Kenneth Appel and Wolfgang Haken

 14

Knowledge of Proofs: Peter Pagin

 15

The Phenomenology of Mathematical Proof: Gian-Carlo Rota

 16

Mechanical Procedures and Mathematical Experience: Wilfried Sieg

 Part IV: Intuitionism: 17

Intuitionism and Formalism: L.E.J

Brouwer

 18

Mathematical Intuition: Charles Parsons

 19

Brouwerian Intuitionism: Michael Detlefsen

 20

A Problem for Intuitionism: The Apparent Possibility of Performing Infinitely Many Tasks in a Finite Time: A.W

Moore

 21

A Pragmatic Analysis of Mathematical Realism and Intuitionism: Michel J

Blais

 Part V: Philosophical Foundations of Set Theory: 22

Sets and Numbers: Penelope Maddy

 23

Sets, Aggregates, and Numbers: Palle Yourgrau

 24

The Approaches to Set Theory: John Lake

 25

Where Do Sets Come From? Harold T

Hodes

 26

Conceptual Schemes in Set Theory: Robert McNaughton

 27

What is Required of a Foundation for Mathematics? John Mayberry

 Index.


Brief Description:

Explores the central problems and the most intriguing new directions in the philosophy of mathematics. The papers are organized thematically, rather than chronologically, to give the best overview of philosophical issues connected with mathematics and the development of mathematical knowledge.

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