### 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 language | English (US) |
---|---|

Pages (from-to) | 497-518 |

Number of pages | 22 |

Journal | Philosophy of Science |

Volume | 69 |

Issue number | 3 |

DOIs | |

State | Published - Sep 2002 |

Externally published | Yes |

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### ASJC Scopus subject areas

- History
- History and Philosophy of Science
- Philosophy

### Cite this

*Philosophy of Science*,

*69*(3), 497-518. https://doi.org/10.1086/342452

**On Representing the Relationship between the Mathematical and the Empirical.** / Bueno, Otavio; French, Steven; Ladyman, James.

Research output: Contribution to journal › Article

*Philosophy of Science*, vol. 69, no. 3, pp. 497-518. https://doi.org/10.1086/342452

}

TY - JOUR

T1 - On Representing the Relationship between the Mathematical and the Empirical

AU - Bueno, Otavio

AU - French, Steven

AU - Ladyman, James

PY - 2002/9

Y1 - 2002/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0042879581&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042879581&partnerID=8YFLogxK

U2 - 10.1086/342452

DO - 10.1086/342452

M3 - Article

AN - SCOPUS:0042879581

VL - 69

SP - 497

EP - 518

JO - Philosophy of Science

JF - Philosophy of Science

SN - 0031-8248

IS - 3

ER -