Actualism and higher-order worlds

Philosophical Studies 115 (2):149 - 178 (2003)
Abstract
It has been argued that actualism – the view that there are no non-actual objects – cannot deal adequately with statements involving iterated modality, because such claims require reference, either explicit or surreptitious, to non-actual objects. If so, actualists would have to reject the standard semantics for quantified modal logic (QML). In this paper I develop an account of modality which allows the actualist to make sense of iterated modal claims that are ostensibly about non-actual objects. Every occurrence of a modal operator involves the stipulation of a possible world, and nested modal operators require stipulation of nested possible worlds. I provide an actualistically acceptable (AA) semantics for QML wherein the nesting relation is irreflexive and intransitive and forms a tree. Despite these restrictions, AA models can beshown to be sound and complete for a wide variety of modal logics.
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Reina Hayaki (2009). Fictions Within Fictions. Philosophical Studies 146 (3):379 - 398.
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