Quantification and Higher-Order Modal Logic

This dissertation advances debates in modal metaphysics, philosophy of language and formal semantics by refining the logical systems traditionally employed in the analysis of natural language. Since linguistic phenomena underlie such debates, innovation in our approaches to semantics offers a means of resolution. My extension of these approaches through higher-order and alternative logics challenges established philosophical theses, while also providing a broad framework for the evaluation and comparison of philosophical and linguistic theories.The first chapter extends an alternative semantics for quantification to the modal setting, establishing its cogency while clarifying the roles of identity in logic. The second chapter rebuts an argument by Timothy Williamson for necessitism in modal metaphysics by developing an admissible extension of his higher-order logic which, by his own methodology, undermines his claim. The third chapter (joint with Sean Walsh) develops a generalization of Montague’s intensional type theory to allow for varying domains of objects across possible worlds, creating a framework suitable for the comparison of semantic theories. The fourth chapter considers the iterative application of reflection principles to formal theories of truth, revealing that what appears to be a purely mathematical choice between proof-theoretic reflection principles in fact commits one to competing stances on the properties of truth as a predicate