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Philosophy of Mathematics: An Introduction / Edition 1

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Overview

In this new introduction to the philosophy of mathematics, David Bostock guides the reader through the basic ideas on the nature of mathematics that have played a major part in the development of philosophy from antiquity to the present.
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Editorial Reviews

From the Publisher
“Given this caveat, Bostock’s new book is highly recommendable as a text for undergraduate seminars in the philosophy of mathematics and also for individual study. It covers all the essentials and more. It should appeal not only to students who have already developed a preference for the general approach and style of contemporary analytic philosophy, but also to a broader audience of students and to people with a non-professional interest in philosophy and mathematics.” (Erkenn, 2011)

"This is a concise as well as comprehensive presentation of core topics in the philosophy of mathematics, written in a clear and engaged manner, hence well readable." (Zentralblatt MATH, 2011)

"This book is an undergraduate introduction to the basic ideas on the nature of mathematics that have played a significant role in the development of philosophy from Antiquity to contemporary debates . . . throughout the book the emphasis is on the basic ideas as well as their current variations, leading up to recent debates between realists and nominalists." (Mathematical Reviews, 2011)

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Product Details

  • ISBN-13: 9781405189927
  • Publisher: Wiley
  • Publication date: 3/17/2009
  • Edition number: 1
  • Pages: 344
  • Product dimensions: 5.70 (w) x 9.10 (h) x 1.00 (d)

Meet the Author

David Bostock has been a Fellow and Tutor in Philosophy at Merton College, and Lecturer in Philosophy at the University of Oxford. His recent publications include Intermediate Logic (1997), Aristotle’s Ethics (2000), and Space, Time, Matter, and Form: Essays on Aristotle's Physics (2006).

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Table of Contents

Preface viii

1 Plato versus Aristotle 1

A Plato 1

1 The Socratic background 1

2 The theory of recollection 3

3 Platonism in mathematics 7

4 Retractions: the Divided Line in Republic VI (509d-511e) 9

B Aristotle 15

5 The overall position 15

6 Idealizations 17

7 Complications 20

8 Problems with infinity 23

C Prospects 28

2 From Aristotle to Kant 33

1 Mediaeval times 33

2 Descartes 35

3 Locke, Berkeley, Hume 38

4 A remark on conceptualism 43

5 Kant: the problem 44

6 Kant: the solution 51

3 Reactions to Kant 62

1 Mill on geometry 62

2 Mill versus Frege on arithmetic 69

3 Analytic truths 74

4 Concluding remarks 85

4 Mathematics and its Foundations 87

1 Geometry 87

2 Different kinds of number 90

3 The calculus 93

4 Return to foundations 97

5 Infinite numbers 103

6 Foundations again 111

5 Logicism 114

1 Frege 115

2 Russell 122

3 Borkowski/Bostock 136

4 Set theory 140

5 Logic 152

6 Definition 160

6 Formalism 167

1 Hilbert 168

2 Godel 175

3 Pure formalism 180

4 Structuralism 183

5 Some comments 191

7 Intuitionism 197

1 Brouwer 197

2 Intuitionist logic 201

3 The irrelevance of ontology 215

4 The attack on classical logic 218

8 Predicativism 224

1 Russell and the VCP 224

2 Russell's ramified theory and the axiom of reducibility 235

3 Predicative theories after Russell 244

4 Concluding remarks 253

9 Realism and Nominalism 261

A Realism 262

1 Godel 263

2 Neo-Fregeans 266

3 Quine and Putnam 275

B Nominalism 282

4 Reductive nominalism 282

5 Fictionalism 289

6 Concluding remarks 304

References 310

Index 325

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