CHALLENGE THE INFINITE SPEAKERS

Joel David Hamkins

Joel is the John Cardinal O'Hara Professor of Logic at the University of Notre Dame.

His long and distinguished career includes having been Professor of Logic at Oxford University and the Sir Peter Strawson Fellow at University College Oxford from 2018 to 2022,

Joel's main research interest lies in mathematical and philosophical logic, particularly set theory, with a focus on the mathematics and philosophy of the infinite.

His numerous publications include papers on set theoretic potentialism and potentialist maximality principles.

Title: What if your potentialism is implicitly actualist?

Abstract:

Many commonly considered forms of potentialism, I argue, are implicitly actualist in the sense that a corresponding actualist ontology and theory is interpretable within the potentialist framework using only the resources of the potentialist ontology and theory. And vice versa. For these forms of potentialism, therefore, there seems to be little at stake in the debate between potentialism and actualism—the two perspectives are bi-interpretable accounts of the same underlying semantic content. Meanwhile, more radical forms of potentialism, lacking convergence and amalgamation, do not admit such a bi-interpretation with actualism. In light of this, the central dichotomy in potentialism, to my way of thinking, is not concerned with any issue of height or width, but rather with convergent versus divergent possibility.