This is the second of three sessions, on inferentialist semantics. Greg will be in Taiwan delivering the 2025 Wendy Huang Lectures, and these three sessions in the M&L seminar are his opportunity to give the lectures a preliminary outing.

I have three aims for this set of lectures. Two are central, and the third is incidental:

1. To give an account of what is so distinctive about logic, insofar as logical notions have a grip on whatever can be said or thought.
2. To clarify the connections between logic and semantics, the theory of meaning.
3. The product of these two aims is that I get to provide a philosophical prolegomena and a non-technical introduction to the more technical work I have done in my forthcoming manuscript Proof, Rules and Meaning.

Today, I aim to show how this inferentialist semantics applies to issues of predication, quantification and modality, and thereby provides some distinctive insight into ‘possible worlds’ models for quantified modal logics.