Abstract
It has been claimed that counterpart theory cannot support a theory of actuality without rendering obviously invalid formulas valid or obviously valid formulas invalid. We argue that these claims are not based on logical flaws of counterpart theory itself, but point to the lack of appropriate devices in first-order logic for “remembering” the values of variables. We formulate a mildly dynamic version of first-order logic with appropriate memory devices and show how to base a version of counterpart theory with actuality on this. This theory is, in special cases, equivalent to modal first-order logic with actuality, and apparently does not suffer from the logical flaws that have been mentioned in the literature.
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References
Blackburn, P., de Rijke, M., Venema, Y. (2001). Modal logic. Cambridge: Cambridge University Press.
Braüner, T., & Ghilardi, S. (2006). First-order modal logic. In P. Blackburn, J.F.A.K. van Benthem, F. Wolter (Eds.), Handbook of modal logic. Studies in logic and practical reasoning (Vol. 3, pp. 549–620). New York: Elsevier Science Inc.
Corsi, G. (2002). Counterpart semantics: A foundational study on quantified modal logics. Technical Report ILLC 2002 PP-2002-20, ILLC/Department of Philosophy. University of Amsterdam, Amtsterdam.
Cresswell, M.J. (2004). Adequacy conditions for counterpart theory. Australasian Journal of Philosophy, 82(1), 28–41.
Fara, M., & Williamson, T. (2005). Counterparts and actuality. Mind, 114(453), 1–30.
Forbes, G. (1982). Canonical counterpart theory. Analysis, 42(1), 33–37.
Garson, J.W. (1984). Quantification in modal logic. In D. Gabbay & F. Guenther (Eds.), Handbook of philosophical logic, volume II: extensions of classical logic (pp. 249–307). Dordrecht: D. Reidel Publishing Co.
Hazen, A.P. (1976). Expressive completeness in modal language. Journal of Philosophical Logic, 5(1), 25–46.
Hazen, A.P. (1979). Counterpart-theoretic semantics for modal logic. Journal of Philosophy, 76, 319–338.
Hodes, H.T. (1984). Axioms for actuality. Journal of Philosophical Logic, 13(1), 27–34.
Kaplan, D. (1978). On the logic of demonstratives. Journal of Philosophical Logic, 8, 81–98.
Lewis, D.K. (1968). Counterpart theory and quantified modal logic. Journal of Philosophy, 69, 26–39.
Ramachandran, M. (1989). An alternative translation scheme for counterpart theory. Analysis, 49(3), 131–141.
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Rigoni, A., Thomason, R.H. The Logic of Counterpart Theory with Actuality. J Philos Logic 43, 1–31 (2014). https://doi.org/10.1007/s10992-012-9248-0
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DOI: https://doi.org/10.1007/s10992-012-9248-0