Formal frameworks for modal notions conceived as predicates
Philosophy strives for a better understanding of modal notions such as necessity, possibility, truth, knowledge. Modal logic, however, the formal tool privileged by philosophers to shape their theories about intensional notions, displays severe drawbacks: its use determines an incoherent treatment of different kinds of modalities and it is expressively weak as important general claims are not fully formalizable in it. In the project I develop an alternative approach to modal notions. Instead of treating them as operators applying to formulas, I will consider them as predicates applying to terms naming formulas. The overarching aim of the proposal is to provide philosophy with an expressive and coherent framework that could represent a valid alternative to modal logic. More precisely, I will develop three research objectives corresponding to three fundamental research gaps traceable in the current literature on modal predicates: the formulation of a natural account of the bearers of modal notions, a consistent and mathematically powerful treatment of the interaction of modal predicates, a predicate approach to de re modal ascriptions that will open the way for a new approach to modal metaphysics in the predicate setting. The project will develop a unified effort to bridge mathematical logic, philosophy of mathematics and metaphysics. It will result in the establishment of leading research profile setting the agenda for a network of researchers in the flourishing area of mathematical philosophy.