On Representing the Relationship between the Mathematical and the Empirical

Otávio Bueno, Steven French, James Ladyman

Research output: Contribution to journalArticle

46 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)497-518
Number of pages22
JournalPhilosophy of Science
Volume69
Issue number3
DOIs
StatePublished - Sep 1 2002

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ASJC Scopus subject areas

  • History
  • Philosophy
  • History and Philosophy of Science

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