Laurenz Hudetz (LSE): “The conceptual schemas account of interpretation”

Abstract: Philosophers of physics often discuss how particular theories could or should be interpreted. But what exactly is it to interpret a formalism in the first place? This is the question addressed in this talk. I propose a general framework for making talk of interpretations more rigorous. First, I clarify what I mean by a formalism. Second, I give an account of what it is to establish a link between a formalism and data. For this purpose, I draw on the theory of relational databases to explicate what data schemas and collections of data are. I introduce the notion of an interpretive link using ideas from mathematical logic. Third, I address the question how a formalism can be interpreted in a way that goes beyond a connection to data. The basic idea is that one extends a data schema to an ontological conceptual schema and links the formalism to this extended schema. I illustrate this account of interpretation using the harmonic oscillator as a simple running example. And I highlight how the account can be fruitfully applied to address issues in philosophy of physics such as the question whether the Newtonian theory of gravitation is fully equivalent to the geometrised Newton-Cartan theory.

Laurenz Hudetz is an Assistant Professor in LSE’s Department of Philosophy, Logic and Scientific Method. He specialises in philosophy of science, logic, and philosophy of physics.