Plural Propositional Quantification

Abstract

AbstractThe theory C5 motivated in previous chapters is shown not to entail the principle Atomicity, which the previous chapter noted to be required for taking talk of possible worlds at face value. Plural propositional quantifiers, which capture ways of quantifying plurally over propositions in the present higher-order framework, are introduced. The logic of these plural propositional quantifiers includes a principle of plural rigidity, as well as a plural comprehension principle. In the resulting logic, the principle of Atomicity becomes derivable. Plural propositional quantifiers therefore vindicate appeals to possible worlds. Having established Atomicity, the logic of metaphysical necessity is narrowed down further: a formula of propositional modal logic is true under every interpretation of the proposition letters just in case it is a theorem of S5.