Synthese

pp 1–22 | Cite as

Mathematics is not the only language in the book of nature

S.I. : Abstraction and Idealization in Scientific Modelling

Abstract

How does mathematics apply to something non-mathematical? We distinguish between a general application problem and a special application problem. A critical examination of the answer that structural mapping accounts offer to the former problem leads us to identify a lacuna in these accounts: they have to presuppose that target systems are structured and yet leave this presupposition unexplained. We propose to fill this gap with an account that attributes structures to targets through structure generating descriptions. These descriptions are physical descriptions and so there is no such thing as a solely mathematical account of a target system.

Keywords

Application of mathematics Structure Mapping account Representation Isomorphism Physical descriptions 

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.History and Philosophy of Science ProgramUniversity of Notre DameNotre DameUSA
  2. 2.Centre for Philosophy of Natural and Social ScienceLondon School of Economics and Political Science (LSE)LondonUK
  3. 3.Department of Philosophy, Logic and Scientific MethodLondon School of Economics and Political Science (LSE)LondonUK

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