Epistemic Modality, Mind, and Mathematics

This book concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality relates to the computational theory of mind; metaphysical modality; the types of mathematical modality; to the epistemic status of undecidable propositions and abstraction principles in the philosophy of mathematics; to the modal profile of rational intuition; and to the types of intention, when the latter is interpreted as a modal mental state. Each essay is informed by epistemic logic, intensional semantics, hyperintensional semantics, modal and cylindric algebra or coalgebra, modal fixpoint logic, correspondence theory, or automata theory. The book's original contributions include theories of: (i) epistemic modal algebras and coalgebras; (ii) cognitivism about epistemic modality; (iii) epistemic two-dimensional truthmaker semantics, with applications to the epistemology of mathematics; (iv) the ground-theoretic ontology of consciousness; (v) fixed-points in vagueness and a novel approach to conditions of self-knowledge in the setting of the modal $\mu$-calculus; (vi) the modal foundations of mathematical platonism; (vii) a solution to the Julius Caesar problem based on metaphysical definitions availing of notions of ground and essence; (viii) a modal logic for rational intuition; and (ix) a novel epistemicist solution to Curry's paradox