Abstract

According to a widely-held view of spatial experience known as structuralism, perceptual representations of spatial features are merely structurally isomorphic to abstract Euclidean geometry; they do not themselves comprise substantive Euclidean concepts. Building off of a distinction between geometrical and merely metaphorical spaces developed by Tim Maudlin, I show that this structuralist view fails to explain the way in which we apply our Euclidean concepts to the spatial features we perceive. For, on the structuralist picture, the results of Euclidean geometry would be equally applicable in perception to any set of features isomorphic to Euclidean space. Colours are one such set of features: their variations along the dimensions of hue, saturation and brightness can be used to generate a (metaphorical) colour ‘space’ that maps onto the structure of Euclidean space. But we do not perceive colours, in spite of their being isomorphic to the features we reason about in Euclidean proof, as instances of Euclidean spatial relations – we do not see groups of objects as, say, square in virtue of their colour properties. It is only when we perceive the literal spatial features of objects – for example, when we see a chessboard as a square – that we take our geometrical concepts to be applicable. This shows that, unlike in the case of colour, the connection between our spatial experience and our geometrical reasoning is more than merely structural.