| Preface | p. xiii |
| Introduction | p. 1 |
| Space and spatial relations | p. 11 |
| Pure theories of reduction: Leibniz and Kant | p. 11 |
| Impure theories of reduction: outlines | p. 14 |
| Mediated spatial relations | p. 18 |
| Surrogates for mediation | p. 21 |
| Representational relationism | p. 23 |
| On understanding | p. 28 |
| Leibniz and the detachment argument | p. 33 |
| Seeing places and travelling paths | p. 36 |
| Non-Euclidean holes | p. 38 |
| The concrete and the causal | p. 40 |
| Hands, knees and absolute space | p. 44 |
| Counterparts and enantiomorphs | p. 44 |
| Kant's pre-critical argument | p. 46 |
| Hands and bodies: relations among objects | p. 47 |
| Hands and parts of space | p. 49 |
| Knees and space: enantiomorphism and topology | p. 51 |
| A deeper premise: objects are spatial | p. 54 |
| Different actions of the creative cause | p. 58 |
| Unmediated handedness | p. 61 |
| Other responses | p. 62 |
| Euclidean and other shapes | p. 69 |
| Space and shape | p. 69 |
| Non-Euclidean geometry and the problem of parallels | p. 71 |
| Curves and surfaces | p. 74 |
| Intrinsic curvatures and intrinsic geometry | p. 76 |
| Bending, stretching and intrinsic shape | p. 80 |
| Some curved two-spaces | p. 81 |
| Perspective and projective geometry | p. 83 |
| Transformations and invariants | p. 86 |
| Subgeometries of perspective geometry | p. 89 |
| Geometrical structures in space and spacetime | p. 94 |
| The manifold, coordinates, smoothness, curves | p. 94 |
| Vectors, 1-forms and tensors | p. 100 |
| Projective and affine structures | p. 105 |
| An analytical picture of affine structure | p. 107 |
| Metrical structure | p. 109 |
| Shapes and the imagination | p. 112 |
| Kant's idea: things look Euclidean | p. 112 |
| Two Kantian arguments: the visual challenge | p. 114 |
| Non-Euclidean perspective: the geometry of vision | p. 116 |
| Reid's non-Euclidean geometry of visibles | p. 118 |
| Delicacy of vision: non-Euclidean myopia | p. 121 |
| Non-geometrical determinants of vision: learning to see | p. 122 |
| Sight, touch and topology: finite spaces | p. 125 |
| Some topological ideas: enclosures | p. 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 conventionalism | p. 139 |
| A general strategy | p. 139 |
| Privileged language and problem language | p. 141 |
| Privileged beliefs | p. 144 |
| Kant and conventionalism | p. 147 |
| Other early influences | p. 150 |
| Later conventionalism | p. 152 |
| Structure and ontology | p. 156 |
| Summary | p. 158 |
| Against conventionalism | p. 160 |
| Some general criticisms of conventionalism | p. 160 |
| Simplicity: an alleged merit of conventions | p. 162 |
| Coordinative definitions | p. 165 |
| Worries about observables | p. 167 |
| The special problem of topology | p. 172 |
| The problem of universal forces | p. 176 |
| Summing up | p. 177 |
| Reichenbach's treatment of topology | p. 180 |
| The geometry of mapping S[subscript 2] onto the plane | p. 180 |
| Reichenbach's convention: avoid causal anomalies | p. 183 |
| Breaking the rules: a change in the privileged language | p. 183 |
| Local and global: a vague distinction | p. 187 |
| A second try: the torus | p. 188 |
| A new problem: convention and dimension | p. 192 |
| Measuring space: fact or convention? | p. 195 |
| A new picture of conventionalism | p. 195 |
| The conventionalist theory of continuous and discrete spaces | p. 196 |
| An outline of criticisms | p. 200 |
| Dividing discrete and continuous spaces | p. 203 |
| Discrete intervals and sets of grains | p. 204 |
| Grunbaum and the simple objection | p. 206 |
| Measurement and physical law | p. 207 |
| Inscribing structures on spacetime | p. 212 |
| The relativity of motion | p. 219 |
| Relativity as a philosopher's idea: motion as pure kinematics | p. 219 |
| Absolute motion as a kinematical idea: Newton's mechanics | p. 222 |
| A dynamical concept of motion: classical mechanics after Newton | p. 225 |
| Newtonian spacetime: classical mechanics as geometrical explanation | p. 229 |
| Kinematics in Special Relativity: the idea of variant properties | p. 233 |
| Spacetime in SR: a geometric account of variant properties | p. 244 |
| The relativity of motion in SR | p. 248 |
| Simultaneity and convention in SR | p. 251 |
| The Clock Paradox and relative motion | p. 254 |
| Time dilation: the geometry of 'slowing' clocks | p. 257 |
| The failure of kinematic relativity in flat spacetime | p. 263 |
| What GR is all about | p. 268 |
| Geometry and motion: models of GR | p. 272 |
| Bibliography | p. 279 |
| Index | p. 287 |
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