Mathematics is not the only language in the book of nature
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.
KeywordsApplication of mathematics Structure Mapping account Representation Isomorphism Physical descriptions
We would like to thank the participants in JN’s ‘Models and Representation’ spring 2016 research seminar at the University of Notre Dame, Otávio Bueno, Mark Colyvan, Susana Lucero, and two anonymous referees for helpful discussions and/or comments on earlier drafts. Thanks also to the audiences in Nikosia and Rostock for helpful feedback. Special thanks goes to Demetris Portides for inviting us to be part of this project.
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