Quantified Modal Logic and the Plural De Re

Midwest Studies in Philosophy 14 (1):372-394 (1989)
Abstract
Modal sentences of the form "every F might be G" and "some F must be G" have a threefold ambiguity. in addition to the familiar readings "de dicto" and "de re", there is a third reading on which they are examples of the "plural de re": they attribute a modal property to the F's plurally in a way that cannot in general be reduced to an attribution of modal properties to the individual F's. The plural "de re" readings of modal sentences cannot be captured within standard quantified modal logic. I consider various strategies for extending standard quantified modal logic so as to provide analyses of the readings in question. I argue that the ambiguity in question is associated with the scope of the general term 'F'; and that plural quantifiers can be introduced for purposes of representing the scope of a general term. Moreover, plural quantifiers provide the only fully adequate solution that keeps within the framework of quantified modal logic.
Keywords Logic  Modal Logic  Quantification  Plural Logic
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    Peter Fritz (2013). Modal Ontology and Generalized Quantifiers. Journal of Philosophical Logic 42 (4):643-678.
    Gabriel Uzquiano (2011). Plural Quantification and Modality. Proceedings of the Aristotelian Society 111 (2pt2):219-250.
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