In so many possible worlds

Ordinary modal logic deals with the notion of a proposition being true in at least one possible world. This makes it natural to consider the notion of a proposition being true in n possible worlds for any nonnegative integer n. Such a notion would stand to Tarski’s numerical quantifiers as ordinary possibility stands to the existential quantifier. In this paper I present several logics for numerical possibility. First I give the syntax and semantics for a minimal such logic (sections 1 and 2); then I prove its completeness (sections 3 and 4); and finally I show how to extend this result to other logics (section 5).