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On representing the relationship between the mathematical and the empirical

French, S.R.D., Bueno, O. and Ladyman, J. (2002) On representing the relationship between the mathematical and the empirical. Philosophy of Science, 69 (3). pp. 452-473. ISSN 0031-8248

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Abstract

We examine, from the partial structures perspective, two forms of applicability of mathematics: at the “bottom” level, the applicability of theoretical structures to the “appearances”, and at the “top” level, the applicability of mathematical to physical theories. We argue that, to accommodate these two forms of applicability, the partial structures approach needs to be extended to include a notion of “partial homomorphism”. As a case study, we present London’s analysis of the superfluid behavior of liquid helium in terms of Bose-Einstein statistics. This involved both the introduction of group theory at the top level, and some modeling at the “phenomenological” level, and thus provides a nice example of the relationships we are interested in. We conclude with a discussion of the “autonomy” of London’s model.

Item Type: Article
Copyright, Publisher and Additional Information: © 2002 University of Chicago Press. Reproduced in accordance with the publisher's self-archiving policy.
Institution: The University of Leeds
Academic Units: The University of Leeds > Faculty of Arts (Leeds) > School of Humanities (Leeds) > School of Philosophy (Leeds) > Division of the History and Philosophy of Science (Leeds)
Depositing User: Leeds Philosophy Department
Date Deposited: 10 Oct 2007 11:07
Last Modified: 08 Feb 2013 17:04
Published Version: http://www.journals.uchicago.edu/PHILSCI/journal/i...
Status: Published
Publisher: University of Chicago Press
Refereed: Yes
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/3346

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