Truth as a Logical Connective

  • Shunsuke YatabeEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10091)


Some truth theories allow to represent and prove generalized statements as “all that you said is true” or “all theorems of \({\mathbf {PA}}\) are true” in the sense of deflationism.


  1. [B63]
    Belnap, N.D.: Tonk, plonk and plink. Analysis 22(6), 130–134 (1963)CrossRefGoogle Scholar
  2. [B08]
    Beal, J.: Spandrels of Truth. Oxford University Press, Oxford (2008)Google Scholar
  3. [C93]
    Coquand, T.: Infinite objects in type theory. In: Barendregt, H., Nipkow, T. (eds.) TYPES 1993. LNCS, vol. 806, pp. 62–78. Springer, Heidelberg (1994). doi: 10.1007/3-540-58085-9_72 CrossRefGoogle Scholar
  4. [D73]
    Dummett, M.: Frege: Philosophy of Language. Duckworth, London (1973)Google Scholar
  5. [D93]
    Dummett, M.: The Logical Basis of Metaphysics (The William James Lectures, 1976). Harvard University Press, Cambridge (1993)Google Scholar
  6. [Fl08]
    Field, H.: Saving Truth From Paradox. Oxford University Press, Oxford (2008)CrossRefzbMATHGoogle Scholar
  7. [FS87]
    Friedman, H., Sheared, M.: An axiomatic approach to self-referential truth. Ann. Pure Appl. Logic 33, 1–21 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  8. [Gl16]
    Galinon, H.: Deflationary truth: conservativity or logicality? Philos. Q. (to appear)Google Scholar
  9. [GB]
    Gupta, A., Belnap, N.: The Revision Theory of Truth. MIT Press, Cambridge (1993)zbMATHGoogle Scholar
  10. [Gt34]
    Gentzen, G.: Untersuchungen über das logische Schließen. I. Math. Z. 39(2), 176–210 (1934). Translated in: Investigations concerning logical deduction. In: Szabo, M. (ed.) The Collected Papers of Gerhard Gentzen, pp. 68–131. North-Holland, Amsterdam (1969)MathSciNetzbMATHGoogle Scholar
  11. [HPS00]
    Hájek, P., Paris, J.B., Shepherdson, J.C.: The liar paradox and fuzzy logic. J. Symbolic Logic 65(1), 339–346 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  12. [Ha11]
    Halbach, V.: Axiomatic Theories of Truth. Cambridge University Press, Cambridge (2011)CrossRefzbMATHGoogle Scholar
  13. [HH05]
    Halbach, V., Horsten, L.: The deflationist’s axioms for truth. In: Beal, J.C., Armour-Garb, B. (eds.) Deflationism and Paradox. Oxford University Press, Oxford (2005)Google Scholar
  14. [Hj12]
    Hjortland, O.: HARMONY and the context of deducibility. In: Insolubles and Consequences. College Publications (2012)Google Scholar
  15. [Hr12]
    Horsten, L.: Tarskian Turn. MIT Press, Cambridge (2012)zbMATHGoogle Scholar
  16. [LgR12]
    Leigh, G.E., Rathjen, M.: The Friedman-Sheard programme in intuitionistic logic. J. Symbolic Logic 77(3), 777–806 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  17. [Lt01]
    Leitgeb, H.: Theories of truth which have no standard models. Stud. Logica. 68, 69–87 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  18. [M85]
    McGee, V.: How truthlike can a predicate be? A negative result. J. Philos. Logic 17, 399–410 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  19. [Pr65]
    Prawitz, D.: Natural Deduction: A Proof-Theoretical Study. Dover Publications, New York (2006)zbMATHGoogle Scholar
  20. [P60]
    Prior, A.: The runabout inference ticket. Analysis 21, 38–39 (1960–61)Google Scholar
  21. [R93]
    Restall, G.: Arithmetic and Truth in Łukasiewicz’s Infinitely Valued Logic. Logique et Analyse 36, 25–38 (1993)MathSciNetGoogle Scholar
  22. [S12]
    Setzer, A.: Coalgebras as types determined by their elimination rules. In: Dybjer, P., Lindström, S., Palmgren, E., Sundholm, G. (eds.) Epistemology versus Ontology, pp. 351–369. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  23. [Yb93]
    Yablo, S.: Paradox without self-reference. Analysis 53, 251–252 (1993)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Graduate School of Letters, Center for Applied Philosophy and EthicsKyoto UniversityKyotoJapan

Personalised recommendations