Philosophical perspectives on infinity / Graham Oppy.

Format:

Book

Author/Creator:

Oppy, Graham, 1960-

Language:

English

Subjects (All):

Infinite.

Physical Description:

xvii, 316 pages ; 24 cm

Place of Publication:

Cambridge ; New York : Cambridge University Press, 2006.

Contents:

1 Beginnings and Puzzles 7

2 Mathematical Preliminaries 20

2.1 Set Theory 20

2.2 Numbers 23

2.3 Cantor's Paradise 24

2.4 Standard Analysis 31

2.5 Non-Standard Numbers 34

3 Some Cases Discussed 48

3.1 Al-Ghazali's Problem 49

3.2 Hilbert's Hotel 51

3.3 Craig's Library 53

3.4 Tristram Shandy 56

3.5 Counting from Infinity 59

3.6 Infinite Paralysis 63

3.7 Stick 66

3.8 Spaceship 69

3.9 Thomson's Lamp 71

3.10 Black's Marble Shifter 72

3.11 Pi Machine 74

3.12 Goldbach Machine 77

3.13 Ross Urn 79

3.14 Deafening Peals 81

3.15 Invisibility 83

3.16 Infinity Mob 85

3.17 String 86

3.18 Some Concluding Remarks 88

4 Space, Time, and Spacetime 90

4.1 Zeno's Paradoxes 91

4.2 Grunbaum's Metrical Puzzle 99

4.3 Skyrms's Measure Puzzle 106

4.4 Points, Regions, and Finite Lattices 110

4.5 First Kantian Antinomy 115

4.6 Infinity Machines in Relativistic Spacetimes 123

4.7 Singularities 128

5 Physical Infinities 133

5.1 Hotter than Infinite Temperatures 134

5.2 Extensive Magnitudes 136

5.3 Infinite Extensive Magnitudes? 138

5.4 Renormalisation 141

5.5 The Dark Night Sky 146

5.6 Some More General Considerations 150

5.7 Possibilities 153

5.8 Physical Possibilities 157

6 Probability and Decision Theory 160

6.1 Probabilities 160

6.2 Additivity Principles 165

6.3 Decision Theory 170

6.4 Approaching Infinite Decision Theory 175

6.5 Infinite Utility Streams 177

6.6 Infinite Decision Rules 181

6.7 Two Envelopes 185

6.8 St. Petersburg Game 194

6.9 Heaven and Hell 196

7 Mereology 201

7.1 Second Kantian Antinomy 202

7.2 Some Postulates 204

7.3 Forrest's Challenge 208

7.4 Taking Stock 213

7.5 Atoms and Indiscernible Particles 215

7.6 Vagueness and Infinite Divisibility 219

7.7 Continuity 224

7.8 Our Universe 226

8 Some Philosophical Considerations 231

8.1 Distinctions 232

8.2 Philosophies of Pure Mathematics 242

8.3 Knowing the Infinite 247

8.4 Putting Classical Mathematics First 250

8.5 Extrapolation from Finite Mathematics 253

8.6 Some Notes about Set Theory 256

8.7 Philosophies of Applied Mathematics 259

8.8 Skolem's Paradox 266

8.9 Infinitesimals 270

9 Infinite Regress and Sufficient Reason 275

9.1 Strong Principles of Sufficient Reason 275

9.2 Self-Explanation and Sufficient Reason 277

9.3 Necessitation and Sufficient Reason 278

9.4 Problems for Strong Principles of Sufficient Reason 280

9.5 Weaker Principles of Sufficient Reason 281

9.6 Infinite Regresses 285.

Notes:

Includes bibliographical references (pages 297-309) and index.

ISBN:

0521860679

OCLC:

61211277

Online:

Publisher description