Numbers and Necessity


Mellon/ACLS Dissertation Completion Fellowships




Humans seem to know about numbers and sets without laying eyes or fingers on them. We also seem to have modal knowledge about what is necessary or possible even though we don’t seem to experience anything necessary as necessary or anything possible as possible. So how might humans know mathematical and modal truths? This dissertation develops metaphysical accounts of both mathematical and modal reality which are sensitive to questions about how creatures like us might know about them. This work is part of an overarching project of justifying logic and mathematics within the view that modal and mathematical truths concern ideas in an infinite mind. Along the way, this dissertation develops a novel semantics for classical first-order logic, another for modal propositional logic, and another for quantified modal logic. The semantic approaches to modal logic do not use possible worlds, accessibility relations, or stand-ins for either one.