Ether Lin

I 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.

In this paper I aim to defend one version at least of Hume’s dictum: roughly, the idea that possibility is determined by ontology through something like independent variation. My defence is broadly pragmatic, in the sense that adherence to something like Hume’s dictum delivers at least three benefits. The first benefit is that, through Hume’s dictum, a physical theory’s ontology delimits a range of possibilities, that I call kinematical possibilities, which serves as a sufficiently permissive notion of possibility to sustain something like an intensional semantics for its claims, and a sufficiently demanding notion of supervenience to sustain plausible claims of inter-theoretic reduction and theoretical equivalence. The second benefit is that Hume’s dictum allows us to work backwards from a range of kinematical possibilities to an ontology. This is especially useful when aiming to glean an interpretation of a physical theory, since often we are more confident that we have arrived at the right space of possibilities than that we have arrived at the right ontology. The third benefit is that Hume’s dictum —- at least the version I aim to defend here —- may be applied to physical theories more or less as we find them, and therefore we can practice something resembling ontology without having to force our theories into some Procrustean bed, such as a first-order language.