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The Shape of Space - Graham Nerlich

Hardcover

Published: 30th September 1994
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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.

'A fresh - and much needed - realistic perspective to the philosophy of space.' Philosophia

Prefacep. xiii
Introductionp. 1
Space and spatial relationsp. 11
Pure theories of reduction: Leibniz and Kantp. 11
Impure theories of reduction: outlinesp. 14
Mediated spatial relationsp. 18
Surrogates for mediationp. 21
Representational relationismp. 23
On understandingp. 28
Leibniz and the detachment argumentp. 33
Seeing places and travelling pathsp. 36
Non-Euclidean holesp. 38
The concrete and the causalp. 40
Hands, knees and absolute spacep. 44
Counterparts and enantiomorphsp. 44
Kant's pre-critical argumentp. 46
Hands and bodies: relations among objectsp. 47
Hands and parts of spacep. 49
Knees and space: enantiomorphism and topologyp. 51
A deeper premise: objects are spatialp. 54
Different actions of the creative causep. 58
Unmediated handednessp. 61
Other responsesp. 62
Euclidean and other shapesp. 69
Space and shapep. 69
Non-Euclidean geometry and the problem of parallelsp. 71
Curves and surfacesp. 74
Intrinsic curvatures and intrinsic geometryp. 76
Bending, stretching and intrinsic shapep. 80
Some curved two-spacesp. 81
Perspective and projective geometryp. 83
Transformations and invariantsp. 86
Subgeometries of perspective geometryp. 89
Geometrical structures in space and spacetimep. 94
The manifold, coordinates, smoothness, curvesp. 94
Vectors, 1-forms and tensorsp. 100
Projective and affine structuresp. 105
An analytical picture of affine structurep. 107
Metrical structurep. 109
Shapes and the imaginationp. 112
Kant's idea: things look Euclideanp. 112
Two Kantian arguments: the visual challengep. 114
Non-Euclidean perspective: the geometry of visionp. 116
Reid's non-Euclidean geometry of visiblesp. 118
Delicacy of vision: non-Euclidean myopiap. 121
Non-geometrical determinants of vision: learning to seep. 122
Sight, touch and topology: finite spacesp. 125
Some topological ideas: enclosuresp. 126
A warm-up exercise: the space of S[subscript 2]p. 129
Non-Euclidean experience: the spherical space S[subscript 3]p. 132
More non-Euclidean life: the toral spaces T[subscript 2] and T[subscript 3]p. 134
The aims of conventionalismp. 139
A general strategyp. 139
Privileged language and problem languagep. 141
Privileged beliefsp. 144
Kant and conventionalismp. 147
Other early influencesp. 150
Later conventionalismp. 152
Structure and ontologyp. 156
Summaryp. 158
Against conventionalismp. 160
Some general criticisms of conventionalismp. 160
Simplicity: an alleged merit of conventionsp. 162
Coordinative definitionsp. 165
Worries about observablesp. 167
The special problem of topologyp. 172
The problem of universal forcesp. 176
Summing upp. 177
Reichenbach's treatment of topologyp. 180
The geometry of mapping S[subscript 2] onto the planep. 180
Reichenbach's convention: avoid causal anomaliesp. 183
Breaking the rules: a change in the privileged languagep. 183
Local and global: a vague distinctionp. 187
A second try: the torusp. 188
A new problem: convention and dimensionp. 192
Measuring space: fact or convention?p. 195
A new picture of conventionalismp. 195
The conventionalist theory of continuous and discrete spacesp. 196
An outline of criticismsp. 200
Dividing discrete and continuous spacesp. 203
Discrete intervals and sets of grainsp. 204
Grunbaum and the simple objectionp. 206
Measurement and physical lawp. 207
Inscribing structures on spacetimep. 212
The relativity of motionp. 219
Relativity as a philosopher's idea: motion as pure kinematicsp. 219
Absolute motion as a kinematical idea: Newton's mechanicsp. 222
A dynamical concept of motion: classical mechanics after Newtonp. 225
Newtonian spacetime: classical mechanics as geometrical explanationp. 229
Kinematics in Special Relativity: the idea of variant propertiesp. 233
Spacetime in SR: a geometric account of variant propertiesp. 244
The relativity of motion in SRp. 248
Simultaneity and convention in SRp. 251
The Clock Paradox and relative motionp. 254
Time dilation: the geometry of 'slowing' clocksp. 257
The failure of kinematic relativity in flat spacetimep. 263
What GR is all aboutp. 268
Geometry and motion: models of GRp. 272
Bibliographyp. 279
Indexp. 287
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521450140
ISBN-10: 0521450144
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 308
Published: 30th September 1994
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 2.1
Weight (kg): 0.62
Edition Number: 2
Edition Type: Revised