The infinite / A.W. Moore.

Format:

Book

Author/Creator:

Moore, A. W., 1956- author.

Language:

English

Subjects (All):

Infinite.

Physical Description:

308 pages ; 23 cm

Edition:

Third Edition.

Place of Publication:

New York : Routledge, 2018.

Contents:

Part I The history p. 13

1 Early Greek thought p. 15

1.1 Anaximander and to apeiron p. 15

1.2 The Pythagoreans p. 17

1.3 The Eleatics p. 21

1.4 Plato p. 24

1.5 Early Greek mathematics p. 26

2 Aristotle p. 32

2.3 The solution: the potential infinite and the actual infinite p. 37

2.4 Application of the solution p. 38

2.5 A remaining difficulty p. 42

3 Medieval and Renaissance thought p. 44

3.1 The Greek legacy: reactions and developments p. 44

3.2 Aquinas p. 47

3.3 Later developments: the mathematically infinite p. 48

3.4 Nicholas of Cusa. The end of the Renaissance p. 53

4 The calculus p. 56

4.1 The fundamental principles of the calculus p. 56

4.2 A brief history of the calculus p. 61

4.3 Taking stock p. 68

5 The rationalists and the empiricists p. 73

5.1 The rationalists p. 73

5.2 The empiricists p. 77

6 Kant p. 82

6.1 The background: an outline of Kant's philosophy p. 82

6.2 The metaphysically infinite and the mathematically infinite p. 84

6.3 The infinitude of the world. The antinomies p. 85

6.4 The infinitude of reason p. 91

7 Post-Kantian metaphysics of the infinite p. 95

7.1 Hegel p. 95

7.2 Currents of thought in post-Hegelian metaphysics of the infinite I: the 'metaphysically big' p. 99

7.3 Currents of thought in post-Hegelian metaphysics of the infinite II: the 'metaphysically small' p. 101

7.4 Currents of thought in post-Hegelian metaphysics of the infinite III: the existentialists p. 103

7.5 Nietzsche p. 106

8 The mathematics of the infinite, and the impact of Cantor p. 109

8.1 Bolzano p. 111

8.2 Turn-of-the-century work on the foundation of mathematics p. 112

8.3 The main elements of Cantor's theory. Its early reception p. 116

8.4 The theory of ordinals. The Burali-Forti paradox p. 121

8.5 Cantor's attitude to the paradoxes p. 126

8.6 Later development: axiomatization p. 127

9.1 Intuitionism p. 131

9.2 Finitism p. 133

9.3 Wittgenstein p. 137

9.4 Recent work p. 141

Part II Infinity assessed p. 145

10 Transfinite mathematics p. 147

10.1 The iterative conception of a set. The paradox of the Set of all Sets p. 147

10.2 Ordinals as sets p. 150

10.3 Cardinals. Measuring infinite sets p. 151

10.4 The continuum hypothesis p. 154

10.5 Further thoughts on the infinite by addition and the infinite by division p. 155

11 The Löwenheim-Skolem theorem p. 159

11.1 An introduction to the Löwenheim-Skolem theorem. Reactions and counter-reactions p. 159

11.2 The solution to Skolem's paradox. Scepticism and relativism p. 163

11.3 Scepticism and relativism rebutted p. 165

11.4 Meaning and understanding. The Löwenheim-Skolem theorem finally defused p. 167

11.5 A lingering paradox p. 169

12 Gödel's theorem p. 172

12.1 Introduction: the Euclidean paradigm p. 172

12.2 A sketch of the proof of Gödel's theorem p. 174

12.3 Hilbert's programme p. 178

12.4 The human mind and computers p. 179

12.5 Self-consciousness p. 181

12.6 Meaning and understanding p. 181

13 Saying and showing p. 186

13.1 The saying/showing distinction in the Tractatus p. 187

13.2 The very idea of a saying/showing distinction p. 190

13.3 Wittgenstein's early views on the infinite p. 192

13.4 The infinite and the ineffable p. 196

14 Infinity assessed. The history reassessed p. 201

14.1 The infinite and the ineffable: early Greek thought, medieval and Renaissance thought, post-Kantian thought p. 202

14.2 Aristotle and Kant: an unsuccessful compromise? p. 203

14.3 The empiricists: an uncompromising success? p. 204

14.4 The Wittgensteinian critique. Aristotle and Kant vindicated? p. 205

14.5 The impossibility of an infinite co-incidence, and the law of the excluded middle p. 208

14.6 A problem for intuitionism p. 210

15 Human finitude p. 218

15.1 The nature of human finitude p. 218

15.2 Time p. 221

15.3 The infinite as an Idea of reason. The saying/showing distinction revisited p. 222

15.4 The poignancy of human finitude. Death p. 226

15.5 Being finite p. 230

Part III Infinity superseded p. 235

16 Infinity reassessed. The history reassessed anew p. 237

16.1 Spinoza versus Hegel p. 237

16.2 Negation p. 240

16.3 Transcendence p. 244

16.4 Spinoza versus Nietzsche p. 245

16.5 The infinite and the ineffable revisited p. 248

17 Learning how to be finite p. 251

17.1 The ethical significance of the Spinoza-Hegel-Nietzsche trialogue p. 251

17.2 The threat to our religion. The threat to our humanity p. 255

17.3 Learning how to live without the infinite p. 260

17.4 Reclaiming the infinite p. 263.

Notes:

Includes bibliographical references and index.

Other Format:

ebook version :

ISBN:

9781138504240

1138504246

9781138504257

1138504254

OCLC:

1043958084