Slides here. Paused slides here.

This will be a talk in the NUS Logic Seminar on 21 February 2024.

Abstract: A popular view in the philosophy of set theory is that of potentialism: the position that the set-theoretic universe unfolds as more sets come into existence or become accessible to us. This often gets formalised using modal logic, but there is always a question of how to move to non-modal theories. In this latter regard, a difficult question for the potentialist is to explain how intensional entities (entities individuated by an application condition rather than an extension) behave, and in particular what logic governs them. This talk will discuss some work in progress on this issue. We’ll see how to motivate acceptance of different propositional logics for different flavours of potentialism, and discuss the prospects for proving results about the kinds of first-order theories validated.