Journal of Logic, Language and Information

, Volume 16, Issue 1, pp 91–115 | Cite as

Reference and perspective in intuitionistic logics

Original Paper

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.

Keywords

Intuitionistic logic Intuitionism Constructivism Reference Kripke semantics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aczel P. H. G. (1968). Saturated intuitionistic theories. In: Schmidt H. A., Schütte K., Thiele H.-J. (eds) Contributions to mathematical logic. North Holland, AmsterdamGoogle Scholar
  2. 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
  3. Fitting M. C. (1969). Intuitionistic logic, model theory and forcing. North Holland, AmsterdamGoogle Scholar
  4. Fitting M. C. (1983). Proof methods for modal and intuitionistic logics. Kluwer Academic Publishers, DordrechtGoogle Scholar
  5. Gabbay D. (1981). Semantical investigations in Heyting’s intuitionistic logic. Reidel, DordrechtGoogle Scholar
  6. Heyting A. (1966). Intuitionism: An introduction, 2nd revised ed. North Holland, AmsterdamGoogle Scholar
  7. Kleene S. C., Velsey R. (1965). Foundations of intuitionistic mathematics. North Holland, AmsterdamGoogle Scholar
  8. Kripke S. (1963). Semantical analysis of intuitionistic logic I. In: Crossley J., Dummett M. (eds.) Formal systems and recursive functions. North Holland, Amsterdam, pp 92-129Google Scholar
  9. 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 YorkGoogle Scholar
  10. Morscher, E., & Hieke, A. (Eds.) (2001). New essays in free logic: In honour of Karel Lambert. Applied Logic Series, vol. 23. Dordrecht: Kluwer.Google Scholar
  11. Posy C. (1974). Brouwer’s constructivism. Synthese. 27, 125-59CrossRefGoogle Scholar
  12. 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.)Google Scholar
  13. Thomason R. (1968). On the strong semantical completeness of the intuitionistic predicate calculus. Journal of Symbolic Logic 33, 1-7CrossRefGoogle Scholar
  14. Troelstra, A. S., & van Dalen, D. (1988). Constructivism in mathematics, vol. 1. Amsterdam: North Holland.Google Scholar
  15. 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 225-339Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Philosophy DepartmentUniversity of TennesseeKnoxvilleUSA

Personalised recommendations