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Reference and perspective in intuitionistic logics

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Abstract

What an intuitionist may refer to with respect to a given epistemic state depends not only on that epistemic state itself but on whether it is viewed concurrently from within, in the hindsight of some later state, or ideally from a standpoint “beyond” all epistemic states (though the latter perspective is no longer strictly intuitionistic). Each of these three perspectives has a different—and, in the last two cases, a novel—logic and semantics. This paper explains these logics and their semantics and provides soundness and completeness proofs. It provides, moreover, a critique of some common versions of Kripke semantics for intuitionistic logic and suggests ways of modifying them to take account of the perspective-relativity of reference.

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References

  • Aczel P. H. G. (1968). Saturated intuitionistic theories. In: Schmidt H. A., Schütte K., Thiele H.-J. (eds) Contributions to mathematical logic. North Holland, Amsterdam

    Google Scholar 

  • Dummett, M., & Lemmon, E. J. (1959). Modal logics between S4 and S5. Zeitschrift für mathematishe Logik und Grundlagen der Mathematik, 5, 250–64.

    Google Scholar 

  • Fitting M. C. (1969). Intuitionistic logic, model theory and forcing. North Holland, Amsterdam

    Google Scholar 

  • Fitting M. C. (1983). Proof methods for modal and intuitionistic logics. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  • Gabbay D. (1981). Semantical investigations in Heyting’s intuitionistic logic. Reidel, Dordrecht

    Google Scholar 

  • Heyting A. (1966). Intuitionism: An introduction, 2nd revised ed. North Holland, Amsterdam

    Google Scholar 

  • Kleene S. C., Velsey R. (1965). Foundations of intuitionistic mathematics. North Holland, Amsterdam

    Google Scholar 

  • Kripke S. (1963). Semantical analysis of intuitionistic logic I. In: Crossley J., Dummett M. (eds.) Formal systems and recursive functions. North Holland, Amsterdam, pp 92-129

    Google Scholar 

  • Leblanc H., Gumb R.D. (1983). Soundness and completeness proofs for three brands of intuitionistic logic. In: Leblanc, Gumb Stern, (eds) Essays in epistemology and semantics. Haven, New York

    Google Scholar 

  • Morscher, E., & Hieke, A. (Eds.) (2001). New essays in free logic: In honour of Karel Lambert. Applied Logic Series, vol. 23. Dordrecht: Kluwer.

  • Posy C. (1974). Brouwer’s constructivism. Synthese. 27, 125-59

    Article  Google Scholar 

  • Posy, C. (1982). A free IPC is a natural logic. Topoi, 1, 30–43; reprinted In Karel Lambert (Ed.), Philosophical Applications of Free Logic, (pp. 49–81) (1991). (Oxford: Oxford University Press, 1991), (My page references are to the reprint.)

  • Thomason R. (1968). On the strong semantical completeness of the intuitionistic predicate calculus. Journal of Symbolic Logic 33, 1-7

    Article  Google Scholar 

  • Troelstra, A. S., & van Dalen, D. (1988). Constructivism in mathematics, vol. 1. Amsterdam: North Holland.

  • Van Dalen D. (1983). Intuitionistic logic. In: Gabbay D., Guenther F. (eds.) Handbook of philosophical logic, vol. III: Alternatives to classical logic. D. Reidel, Dordrecht, pp 225-339

    Google Scholar 

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Correspondence to John Nolt.

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Nolt, J. Reference and perspective in intuitionistic logics. JoLLI 16, 91–115 (2007). https://doi.org/10.1007/s10849-006-9024-z

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  • DOI: https://doi.org/10.1007/s10849-006-9024-z

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