Philosophy of Mathematics: An Introduction / Edition 1

Philosophy of Mathematics: An Introduction / Edition 1

by David Bostock
     
 

ISBN-10: 1405189924

ISBN-13: 9781405189927

Pub. Date: 03/17/2009

Publisher: Wiley

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.  See more details below

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.

Product Details

ISBN-13:
9781405189927
Publisher:
Wiley
Publication date:
03/17/2009
Pages:
344
Product dimensions:
5.70(w) x 9.10(h) x 1.00(d)

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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