The Shape of Space Second Edition

This is a revised and updated edition of Graham Nerlich's classic book The Shape of Space. It develops a metaphysical account of space which treats it as a real and concrete entity. In particular, it shows that the shape of space plays a key explanatory role in space and spacetime theories. Arguing that geometrical explanation is very like causal explanation, Professor Nerlich prepares the ground for philosophical argument, and, using a number of novel examples, investigates how different spaces would affect perception differently. This leads naturally to conventionalism as a non-realist metaphysics of space, an account which Professor Nerlich criticises, rejecting its Kantian and positivistic roots along with Reichenbach's famous claim that even the topology of space is conventional. He concludes that there is, in fact, no problem of underdetermination for this aspect of spacetime theories, and offers an extensive discussion of the relativity of motion. 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 This is a revised and updated edition of Graham Nerlich's classic book (1976). It develops a metaphysical account of space that treats it as a real and concrete entity, showing that shape plays a key explanatory role in space and spacetime theories. Arguing that geometrical explanation is very like causal explanation, Professor Nerlich prepares the ground for philosophical argument and investigates how different spaces would affect perception differently. Along the way Professor Nerlich criticizes and rejects conventionalism as a non-realist metaphysics of space, concluding that there is, in fact, no problem of underdetermination for this aspect of spacetime theories, while offering an extensive discussion of the relativity of motion. In this revised and updated edition of his classic book, Graham Nerlich develops a metaphysical account of space as a concrete entity, showing it to play a key explanatory role in space and spacetime theories.