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On Representing the Relationship between the Mathematical and the Empirical

Published online by Cambridge University Press:  01 January 2022

Otávio Bueno ,
Steven French  and
James Ladyman
Otávio Bueno
Affiliation:
Department of Philosophy, University of South Carolina
Steven French
Affiliation:
Division of History and Philosophy of Science, University of Leeds
James Ladyman*
Affiliation:
Department of Philosophy, University of Bristol
*
Send reprint requests to Otávio Bueno, Department of Philosophy, University of South Carolina, Columbia, SC 29208, USA; obueno@sc.edu, or to Steven French, School of Philosophy, University of Leeds, Leeds LS2 9JT, UK; s.r.d.french@leeds.ac.uk, or to James Ladyman, Department of Philosophy, University of Bristol, Bristol BS8 1TB, UK; James.Ladyman@bristol.ac.uk.
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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.

Type
Research Article
Information
Philosophy of Science , Volume 69 , Issue 3 , September 2002 , pp. 497 - 518
Copyright
Copyright © The Philosophy of Science Association

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