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Groups in Mind

Published online by Cambridge University Press:  01 January 2022

David Hilbert  and
Nick Huggett
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Abstract

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.

Type
The Dimensions of Spacetime
Information
Philosophy of Science , Volume 73 , Issue 5: Proceedings of the 2004 Biennial Meeting of The Philosophy of Science Association. Part II: Symposia Papers. Edited by Miriam Solomon , December 2006 , pp. 765 - 777
Copyright
Copyright © The Philosophy of Science Association

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References

Ben-Menahem, Yemima (2001), “Convention: Poincaré and Some of His Critics,” British Journal for the Philosophy of Science 52:471–513.CrossRefGoogle Scholar
Carlton, Eloise H., and Shepard, Roger N. (1990), “Psychologically Simple Motions as Geodesic Paths: I. Asymmetric Objects,” Journal of Mathematical Psychology 34:127–188.CrossRefGoogle Scholar
Farrell, J. E., and Shepard, Roger N. (1981), “Shape, Orientation, and Apparent Rotational Motion,” Journal of Experimental Psychology: Human Perception and Performance 7:477–486.Google ScholarPubMed
Friedman, Michael (1996), “Poincaré’s Conventionalism and the Logical Positivists,” in Greffe, Jean-Louis, Heinzmann, Gerhard, and Lorenz, Kuno (eds.), Henri Poincaré: Science et Philosophie: Congrés International, Nancy, France, 1994. Berlin: Akademie Verlag; Paris: Albert Blanchard, 333–344.Google Scholar
Miller, Geoffrey F., and Shepard, Roger N. (1993), “An Objective Criterion for Apparent Motion Based on Phase Discrimination,” Journal of Experimental Psychology: Human Perception and Performance 19 (1): 48–62..Google ScholarPubMed
Poincaré, Henri (1952), Science and Hypothesis. New York: Dover.Google Scholar
Reichenbach, Hans (1958), The Philosophy of Space and Time. New York: Dover.Google Scholar
Shepard, Roger N. (1984), “Ecological Constraints on Internal Representation: Resonant Kinematics of Perceiving, Imagining, Thinking and Dreaming,” Psychological Review 91:417–447.CrossRefGoogle ScholarPubMed
Shepard, Roger N. (2001), “Perceptual-Cognitive Universals as Reflections of the World,” Behavioral and Brain Sciences 24:581–601.CrossRefGoogle Scholar
Shepard, Roger N., and Judd, Sherryl A. (1976), “Perceptual Illusion of Rotation of Three-Dimensional Objects,” Science 191 (4230): 952–954..CrossRefGoogle ScholarPubMed
Shepard, Roger N., and Metzler, J. (1971), “Mental Rotation of Three-Dimensional Objects,” Science 171:701–703.CrossRefGoogle ScholarPubMed
Sklar, Lawrence (1974), Space, Time, and Spacetime. Berkeley: University of California.Google Scholar