 Quantifiers ranging over the outer domain of a dual-domain semantics are called outer quantifiers, and those ranging over the inner domain inner quantifiers. If the inner particular quantifier is interpreted to mean “there exists” and the members of the outer domain are possibilia, then the outer particular quantifier may mean something like “there is possible a thing such that” or “for at least one possible thing.” We shall use the generalized product symbol ‘\(\Pi\)’ for the outer universal quantifier and the generalized sum symbol ‘\(\Sigma\)’ for its particular dual. This notation enables us to formalize, for example, the notoriously puzzling but obviously true statement ‘Some things don’t exist’ (Routley 1966) as: