An Epistemic Augmentation to the Math-First Approach to Physical Theories

Abstract Echoing semanticists’ view on scientific theories, David Wallace has recently argued that physical theories are best understood if we conceive of them as mathematical structures. He supplements this idea by suggesting that they attach to the world by structural relations, e.g. isomorphism. This view, which he calls the math-first approach , contrasts with the language-first approach , according to which physical theories are collections of sentences latching onto the world by linguistic relations, e.g. truth. He then submits the structural realist stance is the appropriate metaphysics for this semantic framework. While agreeing that Wallace’s proposal is semantically and metaphysically tenable, I will argue that it is epistemically incomplete, since it leaves untouched the question “what are cognitive attitudes directed toward a physical theory?”. This issue becomes crucial especially when we notice that physical theories so construed cannot be the vehicle of propositional cognitive attitudes, e.g. belief and knowledge. Drawing on Elgin’s revisionary epistemology, I will suggest an augmentation to the math-first approach by certain non-propositional cognitive attitudes in such a way that both realist and anti-realist stances can be expressed within the resulting augmented math-first approach.