Cover......Page 1
About......Page 2
The shape of space, Second Edition......Page 6
Copyright - ISBN: 0521450144......Page 7
Contents......Page 10
Preface......Page 14
Introduction......Page 18
1 Pure theories of reduction: Leibniz and Kant......Page 28
2 Impure theories of reduction: outlines......Page 31
3 Mediated spatial relations......Page 35
4 Surrogates for mediation......Page 38
5 Representational relationism......Page 40
6 On understanding......Page 45
7 Leibniz and the detachment argument......Page 50
8 Seeing places and travelling paths......Page 53
9 Non-Euclidean holes......Page 55
10 The concrete and the causal......Page 57
1 Counterparts and enantiomorphs......Page 61
2 Kant's pre-critical argument......Page 63
3 Hands and bodies: relations among objects......Page 64
4 Hands and parts of space......Page 66
5 Knees and space: enantiomorphism and topology......Page 68
6 A deeper premise: objects are spatial......Page 71
7 Different actions of the creative cause......Page 75
8 Unmediated handedness......Page 78
9 Other responses......Page 79
1 Space and shape......Page 86
2 Non-Euclidean geometry and the problem of parallels......Page 88
3 Curves and surfaces......Page 91
4 Intrinsic curvatures and intrinsic geometry......Page 93
5 Bending, stretching and intrinsic shape......Page 97
6 Some curved two-spaces......Page 98
7 Perspective and projective geometry......Page 100
8 Transformations and invariants......Page 103
9 Subgeometries of perspective geometry......Page 106
1 The manifold, coordinates, smoothness, curves......Page 111
2 Vectors, 1-forms and tensors......Page 117
3 Projective and affine structures......Page 122
4 An analytical picture of affine structure......Page 124
5 Metrical structure......Page 126
1 Kant's idea: things look Euclidean......Page 129
2 Two Kantian arguments: the visual challenge......Page 131
3 Non-Euclidean perspective: the geometry of vision......Page 133
4 Reid's non-Euclidean geometry of visibles......Page 135
5 Delicacy of vision: non-Euclidean myopia......Page 138
6 Non-geometrical determinants of vision: learning to see......Page 139
7 Sight, touch and topology: finite spaces......Page 142
8 Some topological ideas: enclosures......Page 143
9 A warm-up exercise: the space of S_2......Page 146
10 Non-Euclidean experience: the spherical space S_3......Page 149
11 More non-Euclidean life: the toral spaces T_2 and T_3......Page 151
1 A general strategy......Page 156
2 Privileged language and problem language......Page 158
3 Privileged beliefs......Page 161
4 Kant and conventionalism......Page 164
5 Other early influences......Page 167
6 Later conventionalism......Page 169
7 Structure and ontology......Page 173
8 Summary......Page 175
1 Some general criticisms of conventionalism......Page 177
2 Simplicity: an alleged merit of conventions......Page 179
3 Coordinative definitions......Page 182
4 Worries about observables......Page 184
5 The special problem of topology......Page 189
6 The problem of universal forces......Page 193
7 Summing up......Page 194
1 The geometry of mapping S_2 onto the plane......Page 197
3 Breaking the rules: a change in the privileged language......Page 200
4 Local and global: a vague distinction......Page 204
5 A second try: the torus......Page 205
6 A new problem: convention and dimension......Page 209
1 A new picture of conventionalism......Page 212
2 The conventionalist theory of continuous and discrete spaces......Page 213
3 An outline of criticisms......Page 217
4 Dividing discrete and continuous spaces......Page 220
5 Discrete intervals and sets of grains......Page 221
6 Grunbaum and the simple objection......Page 223
7 Measurement and physical law......Page 224
8 Inscribing structures on spacetime......Page 229
1 Relativity as a philosopher's idea: motion as pure kinematics......Page 236
2 Absolute motion as a kinematical idea: Newton's mechanics......Page 239
3 A dynamical concept of motion: classical mechanics after Newton......Page 242
4 Newtonian spacetime: classical mechanics as geometrical explanation......Page 246
5 Kinematics in Special Relativity: the idea of variant properties......Page 250
6 Spacetime in SR: a geometric account of variant properties......Page 261
7 The relativity of motion in SR......Page 265
8 Simultaneity and convention in SR......Page 268
9 The Clock Paradox and relative motion......Page 271
10 Time dilation: the geometry of 'slowing' clocks......Page 274
11 The failure of kinematic relativity in flat spacetime......Page 280
12 What GR is all about......Page 285
13 Geometry and motion: models of GR......Page 289
Bibliography......Page 296
Index......Page 304