A New Solution to the Curry Paradox

In this dissertation, I accomplish four main tasks. First, I construct a canonical model for constant domain basic first-order logic (BQLCD), the logic obtained model-theoretically by dropping the requirement on the Kripke models for constant domain intuitionistic first-order logic that the accessibility relation is reflexive. Second, I prove completeness for BQLCDR, the extension of BQLCD obtained by only allowing reflexive worlds to serve as counterexamples to logical consequence. Third, I show that the naive theory of truth, the theory obtained by adding the Tarski biconditionals to the Peano axioms, is ω-consistent in BQLCDR by building a standard model. Fourth, I defend a normative analysis of logical consequence and use the normative analysis to argue that the propositional fragment of BQLCDR is the correct propositional logic.