Extensional Logic of Hyperintensions

  • Marie Duží
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7260)


In this paper I describe an extensional logic of hyperintensions, viz. Tichý’s Transparent Intensional Logic (TIL). TIL preserves transparency and compositionality in all kinds of context, and validates quantifying into all contexts, including intensional and hyperintensional ones. The availability of an extensional logic of hyperintensions defies the received view that an intensional (let alone hyperintensional) logic is one that fails to validate transparency, compositionality, and quantifying-in. The main features of our logic are that the senses and denotations of (non-indexical) terms and expressions remain invariant across contexts and that our ramified type theory enables quantification over any logical objects of any order. The syntax of TIL is the typed lambda calculus; its semantics is based on a procedural redefinition of, inter alia, functional abstraction and application. The only two non-standard features are a hyperintension (called Trivialization) that presents other hyperintensions and a four-place substitution function (called Sub) defined over hyperintensions.


Quantifying-in extensional/intensional/hyperintensional context transparency ramified type theory transparent intensional logic extensional logic of hyperintensions 


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  1. Anderson, C.A.: Alonzo Church’s contributions to philosophy and intensional logic. The Bulletin of Symbolic Logic 4, 129–171 (1998)CrossRefzbMATHGoogle Scholar
  2. Bealer, G.: Quality and Concept. Clarendon Press, Oxford (1982)CrossRefGoogle Scholar
  3. Carnap, R.: Meaning and Necessity. Chicago University Press, Chicago (1947)zbMATHGoogle Scholar
  4. Church, A.: Intensional isomorphism and identity of belief. Philosophical Studies 5, 65–73 (1954)CrossRefGoogle Scholar
  5. Church, A.: A revised formulation of the logic of sense and denotation. Alternative (1). Noûs 27, 141–157 (1993)CrossRefGoogle Scholar
  6. Cleland, C.E.: On effective procedures. Minds and Machines 12, 159–179 (2002)CrossRefzbMATHGoogle Scholar
  7. Cresswell, M.J.: Hyperintensional logic. Studia Logica 34, 25–38 (1975)CrossRefzbMATHGoogle Scholar
  8. Cresswell, M.J.: Structured meanings. MIT Press, Cambridge (1985)Google Scholar
  9. Duží, M.: The paradox of inference and the non-triviality of analytic information. Journal of Philosophical Logic 39(5), 473–510 (2010)CrossRefzbMATHGoogle Scholar
  10. Duží, M., Jespersen, B., Materna, P.: Procedural Semantics for Hyperintensional Logic. Foundations and Applications of Trasnsparent Intensional Logic, 1st edn. Logic, Epistemology, and the Unity of Science, vol. 17. Springer, Berlin (2010)zbMATHGoogle Scholar
  11. Duží, M., Jespersen, B.: Transparent quantification into hyperintensional contexts de re. Logique and Analyse 220 (December 2012) (to appear)Google Scholar
  12. Duží, M., Materna, P.: Can concepts be defined in terms of sets? Logic and Logical Philosophy 19, 195–242 (2010)zbMATHGoogle Scholar
  13. van Eijck, J., Francez, N.: Verb-phrase ellipsis in dynamic semantics. In: Masuch, M., Polos, L. (eds.) Applied Logic: How, What and Why?, pp. 29–60. Kluwer (1995)Google Scholar
  14. Forbes, G.: Substitutivity and the coherence of quantifying in. The Philosophical Review 105, 337–371 (1996)CrossRefGoogle Scholar
  15. Fox, C., Lappin, S.: A framework for the hyperintensional semantics of natural language with two implementations. Lecture Notes in Computational Linguistics 2009, 175–192 (2001)CrossRefzbMATHGoogle Scholar
  16. Frege, G.: Über Sinn und Bedeutung. Zeitschrift für Philosophie und philosophische Kritik 100, 25–50 (1892)Google Scholar
  17. Hyde, R.: The Art of Assembly Language Programming (1996), (retrievable)
  18. Jespersen, B.: Why the tuple theory of structured propositions isn’t a theory of structured propositions. Philosophia 31, 171–183 (2003)CrossRefGoogle Scholar
  19. Jespersen, B.: How hyper are hyperpropositions? Language and Linguistics Compass 4, 96–106 (2010)CrossRefGoogle Scholar
  20. Kaplan, D.: Quantifying in. Synthese 19, 178–214 (1968)CrossRefGoogle Scholar
  21. Kaplan, D.: Opacity. In: Hahn, L. (ed.) The Philosophy of W.V. Quine, pp. 229–289. Open Court, La Salle (1986)Google Scholar
  22. Kaplan, D.: Dthat. In: Cole, P. (ed.) Syntax and Semantics, vol. 9, Academic Press, New York (1990); reprinted in: Yourgrau (ed.) Demonstratives. Oxford University Press, Oxford Google Scholar
  23. Klement, K.C.: Frege and the Logic of Sense and Reference. Routledge, New York (2002)Google Scholar
  24. Kripke, S.: Semantical considerations on modal logic. Acta Pilosophica Fennica 16, 83–94 (1963)zbMATHGoogle Scholar
  25. Lewis, C.I.: A Survey of Symbolic Logic. University of California Press, Berkeley (1918)Google Scholar
  26. Lewis, D.: General semantics. In: Davidson, D., Harman, G. (eds.) Semantics of Natural Language, pp. 169–218. Reidel, Dordrecht (1972)CrossRefGoogle Scholar
  27. Moschovakis, Y.N.: Sense and denotation as algorithm and value. In: Väänänen, J., Oikkonen, J. (eds.) Lecture Notes in Logic, vol. 2, pp. 210–249. Springer, Berlin (1994)Google Scholar
  28. Moschovakis, Y.N.: A logical calculus of meaning and synonymy. Linguistics and Philosophy 29, 27–89 (2006)CrossRefGoogle Scholar
  29. Pierce, C.B.: Types and Programming Languages. MIT Press, London (2002)zbMATHGoogle Scholar
  30. Plotkin, G.D.: Call-by-name, call-by-value and the λ-calculus. Theoretical Computer Science 1, 125–159 (1975)CrossRefzbMATHGoogle Scholar
  31. Quine, W.v.O.: Quantifiers and propositional attitudes. Journal of Philosophy 53, 177–186 (1956)CrossRefGoogle Scholar
  32. Richard, M.: Analysis, synonymy and sense. In: Anderson, C.A., Zeleny, M. (eds.) Logic, Meaning and Computation: Essays in Memory of Alonzo Church. Synthese Library, vol. 305, pp. 545–571. Kluwer, Dordrecht (2001)CrossRefGoogle Scholar
  33. Tichý, P.: Smysl a procedura. Filosofický časopis 16, 222–232 (1968); translated as ‘Sense and procedure’ in Tichý, 77–92 (2004)Google Scholar
  34. Tichý, P.: Intensions in terms of Turing machines. Studia Logica 26, 7–25 (1969); reprinted in Tichý, 93–109 (2004)CrossRefzbMATHGoogle Scholar
  35. Tichý, P.: The Foundations of Frege’s Logic. De Gruyter, Berlin (1988)CrossRefzbMATHGoogle Scholar
  36. Tichý, P.: Collected Papers in Logic and Philosophy. In: Svoboda, V., Jespersen, B., Cheyne, C. (eds.), Filosofia, Czech Academy of Sciences, and Dunedin: University of Otago Press, Prague (2004)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Marie Duží
    • 1
  1. 1.VSB-Technical University OstravaCzech Republic

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