Actualism and Higher-Order Worlds

It has been argued that actualism – the view that there are no non-actual objects – cannot deal adequately with statementsinvolving iterated modality, because such claims require reference, either explicit or surreptitious, to non-actualobjects. 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 tomake sense of iterated modal claims that are ostensibly aboutnon-actual objects. Every occurrence of a modal operatorinvolves the stipulation of a possible world, and nestedmodal operators require stipulation of nested possible worlds.I provide an actualistically acceptable (AA) semantics for QMLwherein 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.