In sensu diviso. De re ascriptions and necessary existence
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The paper investigates some ontological implications of an approach to modal notions that properly extends intensional logic by treating modal ascriptions as predicate-like. More specifically, we first introduce a semantics that can naturally deal with de re necessity and possibility ascriptions and that enables one to quantify directly in the object-language over properties and relations. We then show how, in this expressive framework, hidden metaphysical assumptions of standard modal logic become explicit. We focus on the problem of the modal status of collections of objects satisfying a certain relation by necessity (or possibly): although there seem to be objects that may fail to exist, collections containing them are taken to exist at any world. We discuss several forms of necessitism that accommodate this problem.
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