On representing the relationship between the mathematical and the empirical

Philosophy of Science 69 (3):497-518 (2002)
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.
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DOI 10.1086/342456
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Natural Kindness.Matthew H. Slater - 2015 - British Journal for the Philosophy of Science 66 (2):375-411.
Theories: Tools Versus Models.Mauricio Suárez & Nancy Cartwright - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (1):62-81.

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