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Groups in Mind

Both Henri Poincaré and (more recently) Roger Shepard have argued that the geometry and topology of physical space are internalized by the mind in the form, not (or not only) of a Euclidean manifold, but in terms of the group of rigid Euclidean transformations. Since this issue can have bearing on various metaphysical and epistemological questions, we explore the different reasons they offer for holding this view. In this context, we show how most commentators misunderstand Poincaré’s ‘heated sphere/plate’ model and introduce Shepard’s ideas to the philosophy of science community.