Philosophy of Mathematics: An Anthology / Edition 1

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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.

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Editorial Reviews

From the Publisher
"For breadth of coverage, Jacquette's anthology of recent work in philosophy of mathematics has few if any rivals. Many of Jacquette's selections are important for understanding current debates, and he provides helpful introductory discussions. This collection will very likely become a standard resource for students and teachers of this field." Sanford Shieh, Wesleyan University
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Product Details

  • ISBN-13: 9780631218708
  • Publisher: Wiley
  • Publication date: 12/4/2001
  • Series: Blackwell Philosophy Anthologies Series
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 444
  • Product dimensions: 6.70 (w) x 9.70 (h) x 1.32 (d)

Meet the Author

Dale Jacquette is Professor of Philosophy at The Pennsylvania State University. He is the author of Philosophy of Mind (1994), Meinongian Logic: The Semantics of Existence and Nonexistence (1996), Wittgenstein's Thought in Transition (1998), Symbolic Logic (2001), David Hume's Critique of Infinity (2001) and On Boole: Logic as Algebra (2001) as well as numerous articles on logic, metaphysics, philosophy of mind, and Wittgenstein.

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Table of Contents

Introduction: Mathematics and Philosophy of Mathematics 1
Pt. I The Realm of Mathematics
1 What is Mathematics About? 19
2 Mathematical Explanation 30
3 Frege versus Cantor and Dedekind: On the Concept of Number 40
4 The Present Situation in the Philosophy of Mathematics 65
Pt. II Ontology of Mathematics and the Nature and Knowledge of Mathematical Truth
5 What Numbers Are 91
6 Mathematical Truth 99
7 Ontology and Mathematical Truth 110
8 An Anti-realist Account of Mathematical Truth 119
9 What Mathematical Knowledge Could Be 128
10 The Philosophical Basis of Our Knowledge of Number 147
Pt. III Models and Methods of Mathematical Proof
11 Mathematical Proof 173
12 What Does a Mathematical Proof Prove? 187
13 The Four-Color Problem 193
14 Knowledge of Proofs 209
15 The Phenomenology of Mathematical Proof 218
16 Mechanical Procedures and Mathematical Experience 226
Pt. IV Intuitionism
17 Intuitionism and Formalism 269
18 Mathematical Intuition 277
19 Brouwerian Intuitionism 289
20 A Problem of Intuitionism: The Apparent Possibility of Performing Infinitely Many Takes in a Finite Time 312
21 A Pragmatic Analysis of Mathematical Realism and Intuitionism 322
Pt. V Philosophical Foundations of Set Theory
22 Sets and Numbers 345
23 Sets, Aggregates, and Numbers 355
24 The Approaches to Set Theory 362
25 Where Do Sets Come From? 377
26 Conceptual Schemes in Set Theory 396
27 What is Required of a Foundation for Mathematics? 404
Index 417
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