The Logic of Quantificationalism, Part 1: Foundations

Quantificationalism is the view that some true propositions are false at or relative to some domains of quantification, in much the same sense in which propositions can be true or false at times or possible worlds. This paper seeks to give solid formal foundations to quantificationalism, comparable to what modal and tense logics are to the notions of contingent and temporary truth. It has the twofold purpose of understanding what sort of problems arise when we try and make precise sense of Quantificationalism, and of solving these problems by outlining a comprehensive higher-order logical framework in which Quantificationalism can be precisely formulated and shown to be consistent.