Philosophy of Mathematics: An Anthology / Edition 1

Philosophy of Mathematics: An Anthology / Edition 1

by Dale Jacquette
     
 

ISBN-10: 063121870X

ISBN-13: 9780631218708

Pub. Date: 12/04/2001

Publisher: Wiley

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

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Overview

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).

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Product Details

ISBN-13:
9780631218708
Publisher:
Wiley
Publication date:
12/04/2001
Series:
Blackwell Philosophy Anthologies Series
Edition description:
New Edition
Pages:
444
Product dimensions:
6.70(w) x 9.70(h) x 1.32(d)

Table of Contents

Preface
Acknowledgments
Introduction: Mathematics and Philosophy of Mathematics1
Pt. IThe Realm of Mathematics
1What is Mathematics About?19
2Mathematical Explanation30
3Frege versus Cantor and Dedekind: On the Concept of Number40
4The Present Situation in the Philosophy of Mathematics65
Pt. IIOntology of Mathematics and the Nature and Knowledge of Mathematical Truth
5What Numbers Are91
6Mathematical Truth99
7Ontology and Mathematical Truth110
8An Anti-realist Account of Mathematical Truth119
9What Mathematical Knowledge Could Be128
10The Philosophical Basis of Our Knowledge of Number147
Pt. IIIModels and Methods of Mathematical Proof
11Mathematical Proof173
12What Does a Mathematical Proof Prove?187
13The Four-Color Problem193
14Knowledge of Proofs209
15The Phenomenology of Mathematical Proof218
16Mechanical Procedures and Mathematical Experience226
Pt. IVIntuitionism
17Intuitionism and Formalism269
18Mathematical Intuition277
19Brouwerian Intuitionism289
20A Problem of Intuitionism: The Apparent Possibility of Performing Infinitely Many Takes in a Finite Time312
21A Pragmatic Analysis of Mathematical Realism and Intuitionism322
Pt. VPhilosophical Foundations of Set Theory
22Sets and Numbers345
23Sets, Aggregates, and Numbers355
24The Approaches to Set Theory362
25Where Do Sets Come From?377
26Conceptual Schemes in Set Theory396
27What is Required of a Foundation for Mathematics?404
Index417

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