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Groups in Mind
David Hilbert and Nick Huggett
Philosophy of Science
Vol. 73, No. 5, Proceedings of the 2004 Biennial Meeting of The Philosophy of Science AssociationPart II: Symposia PapersEdited by Miriam Solomon (December 2006), pp. 765-777
Stable URL: http://www.jstor.org/stable/10.1086/518635
Page Count: 13
You can always find the topics here!Topics: Geometry, Euclidean space, Euclidean geometry, Mathematical objects, Geometric shapes, Trajectories, Kantianism, Conformal mapping, A priori knowledge, Psychology
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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.
Copyright 2006 by the Philosophy of Science Association. All rights reserved.