David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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International Studies in the Philosophy of Science 16 (2):111 – 124 (2002)
Wigner found unreasonable the "effectiveness of mathematics in the natural sciences". But if the mathematics we use to describe nature is simply a carefully coded expression of our experience then its effectiveness is quite reasonable. Its effectiveness is built into its design. We consider group theory, the logic of symmetry. We examine the premise that symmetry is identity; that group theory encodes our experience of identification. To decide whether group theory describes the world in such an elemental way we catalogue the detailed correspondence between elements of the physical world and elements of the formalism. Providing an unequivocal match between concept and mathematical statement completes the case. It makes effectiveness appear reasonable. The case that symmetry is identity is a strong one but it is not complete. The further validation required suggests that unexpected entities might be describable by the irreducible representations of group theory.
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References found in this work BETA
Mark Steiner (1998). The Applicability of Mathematics as a Philosophical Problem. Harvard University Press.
Elena Castellani (ed.) (1998). Interpreting Bodies. Princeton University Press.
M. L. G. Redhead (1975). Symmetry in Intertheory Relations. Synthese 32 (1-2):77 - 112.
Bas C. Van Fraassen & Michael Tooley (1995). Laws and Symmetry. British Journal for the Philosophy of Science 46 (2):280.
Giuliano Toraldo di Francia (1998). A World of Individual Objects. In Elena Castellani (ed.), Interpreting Bodies. Princeton University Press
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