Abstract
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.
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REFERENCES
Black, M. (1952): ‘The identity of indiscernibles’, Mind 61(242), 153–164.
Bull, R. and Segerberg, K. (1984): ‘Basic Modal Logic’, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic (pp. 1–88), Dordrecht: Kluwer Academic Publishers, ii.
Dummett, M.A.E. and Lemmon, E.J. (1959): ‘Modal Logics between S4 and S5’, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 5, 250–264.
Garson, J.W. (1984): ‘Quantification in Modal Logic’, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic (pp. 249–308), Dordrecht: Kluwer Academic Publishers.
Geach, P.T. (1967): ‘Intentional Identity’, Journal of Philosophy 64(20), 627–632.
Geach, P.T. (1969): ‘The Perils of Pauline’, Review of Metaphysics 23, 287–300.
Hazen, A.P. (1996): ‘Actualism Again’, Philosophical Studies 84, 155–181.
Hughes, G.E. and Cresswell, M.J. (1984): A Companion to Modal Logic, London: Methuen.
Kripke, S. (1963): ‘Semantical Considerations on Modal Logic’, Acta Philosophica Fennica 16, 83–94.
Kripke, S. (1980): Naming and Necessity, Cambridge, MA: Harvard University Press.
Lewis, D. (1968): ‘Counterpart Theory and Quantified Modal Logic’, Journal of Philosophy 65, 113–126.
Lewis, D. (1986): On the Plurality of Worlds, Oxford: Basil Blackwell.
Linsky, B. and Zalta, E. (1994): ‘In Defense of the Simplest Quantified Modal Logic’, in Philosophical Perspectives, vol. 8: Logic and Language (pp. 431–458), Atascadero: Ridgeview.
Linsky, B. and Zalta, E. (1996): ‘In Defense of the Contingently Nonconcrete’, Philosophical Studies 84, 283–294.
Marcus, R.B. (1946): ‘A Functional Calculus of First Order Based on Strict Implication’, Journal of Symbolic Logic 11, 1–16.
McMichael, A. (1983): ‘A Problem for Actualism about Possible Worlds’, Philosophical Review 92, 49–66.
Plantinga, A. (1974): The Nature of Necessity, Oxford: Oxford University Press.
Plantinga, A. (1976): ‘Actualism and Possible Worlds’, Theoria 42, 139–160.
Quine, W.V. (1956): ‘Quantifiers and Propositional Attitudes’, Journal of Philosophy 53, 177–187.
Sahlqvist, H. (1975): ‘Completeness and Correspondence in the First and Second Order Semantics for Modal Logic’, in S. Kanger (ed.), Proceedings of the Third Scandinavian Logic Symposium (pp. 110–143), Amsterdam: North-Holland.
Salmon, N. (1989): ‘The Logic ofWhat Might Have Been’, Philosophical Review 98, 3–34.
Williamson, T. (1998): ‘Bare Possibilia’, Erkenntnis 48(2 and 3), 257–273.
Williamson, T. (2000): ‘Existence and Contingency’, Proceedings of the Aristotelian Society 100(1), 117–139.
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Hayaki, R. Actualism and Higher-Order Worlds. Philosophical Studies 115, 149–178 (2003). https://doi.org/10.1023/A:1025050806424
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DOI: https://doi.org/10.1023/A:1025050806424