Abstract
It has been argued that a combination of game-theoretic semantics and independence-friendly (IF) languages can provide a novel approach to the conceptual foundations of mathematics and the sciences. I introduce and motivate an IF first-order modal language endowed with a game-theoretic semantics of perfect information. The resulting interpretive independence-friendly logic (IIF) allows to formulate some basic model-theoretic notions that are inexpressible in the ordinary quantified modal logic. Moreover, I argue that some key concepts of Kripke’s new theory of reference are adequately modeled within IIF. Finally, I compare the logic IIF to David Lewis counterpart theory, drawing some morals concerning the interrelation between metaphysical and semantic issues in possible-world semantics.
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References
Blackburn P. (2006) Arthur prior and hybrid logic. Synthese 150(3): 329–372
Blackburn, P., Marx, M. (2002). Tableaux for quantified hybrid logic. In Proceedings of the international conference on automated reasoning with analytic tableaux and related methods, Lecture notes in computer science, (Vol. 2381). Berlin: Springer.
Correia F.: (2007) Modality, quantification and many vlach-operators. Journal of Philosophical Logic, 36: 473–488.
Corsi, G. (2002). Counterpart semantics. A foundational study on quantified modal logics (pp. 2002–2020). ILLC Prepublications/ILLC.
Fara, D. G. Dear Haecceitism. Erkenntnis (forthcoming).
Fara, M., Williamson, T. (2005). Counterparts and actuality. Mind, 114, 1–30.
Fitting M., Mendelsohn R. L. (1998) First-order modal logic. Kluwer, Dordrecht
Forbes G. (1989) Languages of possibility. Blackwell, Oxford
Garson J. (1984) Quantification in modal logic. In: Gabbay D. M., Guenthner F. (eds) Handbook of philosophical logic. Reidel, Dordrecht, pp 249–307
Haukioja J. (2006) Proto-rigidity. Synthese 150(2): 155–169
Hazen A.: (1976a) Expressive completeness in modal language. Journal of Philosophical Logic. 5: 25–46.
Hazen A.: (1976b) Actuality and quantification. Notre Dame Journal of Formal Logic. 31(4): 498–508.
Henkin, L. (1961). Some remarks on infinitely long formulas. In Infinistic methods. Proceedings of the symposium on foundations of mathematics, Warsaw, Panstwowe (2–9 September 1959) (pp. 167–183). New York: Pergamon Press
Hintikka, J. (1969). Existential presuppositions and their elimination. In J. Hintikka (Ed.) Models for modalities. Dordrecht: Reidel.
Hintikka J. (1996) The principles of mathematics revisited. Cambridge University Press, Cambridge
Hintikka J., Sandu G. (1995) The fallacies of the new theory of reference. Synthese 104: 245–283
Hintikka J., Sandu G. (1997) Game-theoretical semantics. In: van Benthem J., ter Meulen A. (eds) Handbook of logic and language. Elsevier, Amsterdam
Kripke S.: (1963) Semantical considerations on modal logic. Acta Philosophica Fennica. 16: 83–94.
Kripke S. (1971) Identity and necessity. In: Munitz M. (eds) Identity and individuation. New York University, New York
Kripke S. (1980) Naming and necessity. Harvard University Press, Cambridge
LaPorte J. (2000) Rigidity and kind. Philosophical Studies 97(3): 293–316
Lewis, D. (1979). Counterpart theory and quantified modal logic. In: M. J. Loux (Ed.), The possible and the actual. Readings in the metaphysics of modality. Ithaca: Cornell University Press
Lewis D. (1986) On the plurality of worlds. Blackwell, Oxford
Peacocke C.: (1978) Necessity and truth theories. Journal of Philosophical Logic. 7: 473–500
Pietarinen, A.-V. (2004). Semantic games in logic and epistemology. In S. Rahman, J. Symons, D. M. Gabbay & J. P. van Bendegem (Eds.), Logic, epistemology, and the unity of science. Dordrecht: Kluwer.
Pietarinen, A.-V., Sandu, G. (2004). IF Logic, Game-theoretical semantics and the philosophy of science. In S. Rahman, J. Symons, D. M. Gabbay & J. P. van Bendegem (Eds.), Logic, epistemology, and the unity of science. Dordrecht: Kluwer.
Pietarinen, A.-V., Tulenheimo, T. (2004). An Introduction to IF Logic. ESSLLI.
Saarinen E. (1979) Backwards-looking operators in tense logic and in natural language. In: Saarinen E. (eds) Game-theoretical semantics. Springer, Dordrecht
Sandu, G., & Tulenheimo, T. (2005). Logics of Imperfect Information. Proceedings of CombLog’04.
Schwartz S. P. (2002) Kinds, general terms, and rigidity: A reply to LaPorte. Philosophical Studies 109: 265–277
Soames S. (2002) Beyond rigidity: The unfinished semantic agenda of naming and necessity. Oxford University Press, New York
Stalnaker, R. (2003). Reference and necessity. In Ways a world might be metaphysical and anti-metaphysical essays. Oxford: Oxford University Press
Stanley, J. (1997). Names and rigid designation. In B. Hale & C. Wright (Ed.) A companion to the philosophy of language (pp. 555–585). Oxford: Blackwell.
Varzi, A. (2006). Strict identity with no overlap. Studia Logica, 82(3), 371–378.
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Torza, A. How to Lewis a Kripke–Hintikka. Synthese 190, 743–779 (2013). https://doi.org/10.1007/s11229-012-0201-0
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DOI: https://doi.org/10.1007/s11229-012-0201-0