Abstract
Frege overlooked the role of quantifiers as expressing, by their formal dependence on each other, the actual dependences between variables bound to them. The resulting flaw in Frege’s and other logicians’ logic began to be corrected only in IF logic. The dependence relations are codified in the Skolem functions that correspond to existential-force quantifiers. Their existence is the natural truth condition. Such functions are not adequately handled in first-order predicate logic. In any adequate logic, a fixed mode of identification is presupposed. The frameworks of identification can be perspectival or public. Kripke makes the same mistake about quantifiers as Frege and in addition assumes that only perspectival indentification is needed in the last analysis. He also overlooks dependence relations between modal operators and quantifiers.
Jaakko Hintikka—deceased
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References
Frege, G. (1893–1903a). Grundgesetze der Arithmetik, begriffsschriftlich abgeleitet. Jena: Herman Pohle.
Frege, G. (1893–1903b) The basic laws of arithmetic (M. Furth (Ed.) [partial translation of Frege 1893–1903], Trans.), Berkeley and Los Angeles: University of California Press.
Hintikka, J. (1996). The principles of mathematics revisited. Cambridge: Cambridge University Press.
Hintikka, J. (2004). On the different identities of identity: A historical and critical essay. In G. Fløistad (Ed.), Language, meaning, interpretation (pp. 117–139). Dordrecht: Kluwer Academic Publishers.
Hintikka, J. (forthcoming) If logic, definitions and the vicious circle principle.
Kripke, S. (1963). Semantical considerations on modal logic. Acta Philosophica Fennica, 16, 83–94.
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Hintikka, J. (2016). Identity in Frege’s Shadow. In: Costreie, S. (eds) Early Analytic Philosophy - New Perspectives on the Tradition. The Western Ontario Series in Philosophy of Science, vol 80. Springer, Cham. https://doi.org/10.1007/978-3-319-24214-9_2
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