Stating Structural Realism: Mathematics‐First Approaches to Physics and Metaphysics

Abstract

AbstractI respond to the frequent objection that structural realism fails to sharply state an alternative to the standard predicate‐logic, object / property / relation, way of doing metaphysics. The approach I propose is based on what I call a ‘math‐first’ approach to physical theories (close to the so‐called ‘semantic view of theories') where the content of a physical theory is to be understood primarily in terms of its mathematical structure and the representational relations it bears to physical systems, rather than as a collection of sentences that attempt to make true claims about those systems (a ‘language‐first’ approach). I argue that adopting the math‐first approach already amounts to a form of structural realism, and that the choice between epistemic and ontic versions of structural realism is then a choice between a language‐first and math‐first view of metaphysics; I then explore the status of objects (and properties and relations) in fundamental and non‐fundamental physics for both versions of math‐first structural realism.