Learning to Represent: Mathematics-first accounts of representation and their relation to natural language

Abstract

I develop an account of how mathematized theories in physics represent physical systems, in response to the frequent claim that any such account must presuppose a non-mathematized, and usually linguistic, description of the system represented. The account I develop contains a circularity, in that representation is a mathematical relation between the models of a theory and the system as represented by some other model --- but I argue that this circularity is not vicious, in any case refers in linguistic accounts of meaning and representation, and is simply a consequence of the fact that we have no unmediated, representation-independent access to the world.

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