A Leibnizian Logic of Possible Laws
A Formal Framework Motivated by Hintikka That Blocks Lovejoy's Principle of Plenitude
DOI:
https://doi.org/10.12775/LLP.2022.017Keywords
Leibnizian possible worlds, the principle of plenitude, logic of change, temporal logic, philosophical logicAbstract
The so-called Principle of Plenitude was ascribed to Leibniz by A. O. Lovejoy in The Great Chain of Being: A Study of the History of an Idea (1936). Its temporal version states that what holds always, holds necessarily (or that no genuine possibility can remain unfulfilled). This temporal formulation is the subject of the current paper. Lovejoy’s idea was criticised by Hintikka. The latter supported his criticisms by referring to specific Leibnizian notions of absolute and hypothetical necessities interpreted in a possible-worlds semantics. In the paper, Hintikka’s interpretative suggestions are developed and enriched with a temporal component that is present in the characteristics of the real world given by Leibniz. We use in our approach the Leibnizian idea that change is primary to time and the idea that there are possible laws that characterize worlds other than the real one. We formulate a modal propositional logic with three primitive operators for change, temporal constancy, and possible lawlikeness. We give its axiomatics and show that our logic is complete with respect to the given semantics of possible worlds. Finally, we show that the counterparts of the considered versions of the Principle of Plenitude are falsified in this semantics and the same applies to the counterpart of Leibnizian necessarianism.
References
Adams, R. M., Leibniz: Determinist, Theist, Idealist, Oxford University Press, 1994. DOI: http://dx.doi.org/10.1093/0195126491.001.0001
Futch, M., Leibniz’s Metaphysics of Time and Space, Springer, 2008.
Hintikka, J., “Leibniz on plenitude, relations, and the ‘reign of law’ ” in S. Knuutila (ed.), Reforging the Great Chain of Being. Studies of the History of Modal Theories, Springer, 1981.
Hintikka, J., “Was Leibniz’s deity an akrates?”, pages 85–108 in S. Knuutila (ed.), Modern Modalities, Kluwer, 1988.
Kozen, D., and R. Parikh, “An elementary proof of the completeness of PDL”, Theoretical Computer Science, 14 (1981): 113–118.
Leibniz, G. W., Leibniz-Arnauld Correspondence, ed. and transl. by H. T. Mason and G. H. R. Parkinson, Manchester University Press, 1967. DOI: http://dx.doi.org/10.1007/978-94-010-1426-7
Leibniz, G. W., Philosophical Papers and Letters, ed. II, transl. and ed. by L. E. Loemker, The New Synthese Historical Library, vol. 2, Kluwer Academic Publishers, 1989.
Leibniz, G. W., New Essays on Human Understanding, trans. and ed. (with notes) P. Remnant and J. Bennett. Cambridge, 1981.
Lovejoy, A. O., The Great Chain of Being. A Study of the History of an Idea, Harvard U. P., 22th printing 2001. DOI: http://dx.doi.org/10.4324/9781315132310
Mates, B., The Philosophy of Leibniz: Metaphysics and Language, New York: Oxford University Press, 1986.
Russell, B., A Critical Exposition of the Philosophy of Leibniz, Routledge, Taylor and Francis, 1992.
Świętorzecka, K., and J. Czermak, “A logic of change with modalities”, Logique et Analyse, 232 (2015): 511–527.
Świętorzecka, K., and J. Czermak, “Some calculus for a logic of change”, Journal of Applied Non-Classical Logics, 22, 1–2 (2012): 3–10. DOI: http://dx.doi.org/10.1080/11663081.2012.682435
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Copyright (c) 2022 Kordula Świętorzecka, Marcin Łyczak
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