Semantics is the discipline whose job it is to describe the meanings of expressions; metasemantics aims to explain why it is that a given expression means what it does. In my thesis, Semantics, Metasemantics, and Ontology, I gave a critique of what Davidson once called the method of truth in metaphysics, according to which we can determine the metaphysical nature and structure of reality through semantic investigations. I argued that it is not semantics, but meta-semantics, that reveals the metaphysically necessary and sufficient truth conditions of our claims.
I first argued that the metaphysically primary truth bearers are not abstract propositions, but rather concrete representations. I then considered the relationship between truth and existence, defending alethic pluralism: in some domains of discourse reference plays a metasemantic role in explaining truth, which therefore consists in correspondence; in others, such as mathematics, denotation plays a merely instrumental semantic role, and truth is nothing more than coherence. Finally, I rejected Quine’s criterion of ontological commitment, arguing that Hume’s Principle, which is sufficient for the derivation of Peano Arithmetic, can be true even though numbers do not exist.