The shape of space / Graham Nerlich.

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Space and spatial relations -- Pure theories of reduction: Leibniz and Kant -- Impure theories of reduction: outlines -- Mediated spatial relations -- Surrogates for mediation -- Representational relationism -- On understanding -- Leibniz and the detachment argument -- Seeing places and travelling paths -- Non-Euclidean holes -- The concrete and the causal -- Hands, knees and absolute space -- Counterparts and enantiomorphs -- Kant's pre-critical argument -- Hands and bodies: relations among objects -- Hands and parts of space -- Knees and space: enantiomorphism and topology -- A deeper premise: objects are spatial -- Different actions of the creative cause -- Unmediated handedness -- Other responses -- Euclidean and other shapes -- Space and shape -- Non-Euclidean geometry and the problem of parallels -- Curves and surfaces -- Intrinsic curvatures and intrinsic geometry -- Bending, stretching and intrinsic shape -- Some curved two-spaces -- Perspective and projective geometry -- Transformations and invariants -- Subgeometries of perspective geometry -- Geometrical structures in space and spacetime -- The manifold, coordinates, smoothness, curves -- Vectors, 1-forms and tensors -- Projective and affine structures -- An analytical picture of affine structure -- Metrical structure -- Shapes and the imagination -- Kant's idea: things look Euclidean -- Two Kantian arguments: the visual challenge -- Non-Euclidean perspective: the geometry of vision -- Reid's non-Euclidean geometry of visibles.

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.