A Multimodal Pragmatic Analysis of the Knowability Paradox

Part of the Logic, Argumentation & Reasoning book series (LARI, volume 14)


The Knowability Paradox starts from the assumption that every truth is knowable and leads to the paradoxical conclusion that every truth is also actually known. Knowability has been traditionally associated with both contemporary verificationism and intuitionistic logic. We assume that classical modal logic in which the standard paradoxical argument is presented is not sufficient to provide a proper treatment of the verificationist aspects of knowability. The aim of this paper is both to sketch a language \(\mathcal {L}_{\Box ,K}^{P}\), where alethic and epistemic classical modalities are combined with the pragmatic language for assertions \(\mathcal {L}^{P}\), and to analyse the result of the application of our framework to the paradox.


Knowability Logic for pragmatics Multimodality 



\(^*\) We would like to thank the referees of the volume for their helpful comments and suggestions. The research of Daniele Chiffi is supported by the Estonian Research Council, PUT1305 2016-2018, PI: Pietarinen. Massimiliano Carrara’s research was conducted while he was in his sabbatical year.


  1. 1.
    Artemov, S., & Protopopescu, T.(2013). Discovering knowability: a semantic analysis. Synthese, 190(16), 3349–3376.Google Scholar
  2. 2.
    Beall, J.C. (2005). Knowability and possible epistemic oddities. In J. Salerno, (Ed.), New essays on the knowability paradox, (pp. 105–125). Oxford: OUP Press.Google Scholar
  3. 3.
    Bellin, G., & Biasi, C. (2004). Towards a logic for pragmatics. Assertions and conjectures. Journal of Logic and Computation, 14, 473–506.Google Scholar
  4. 4.
    Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal Logic. Cambridge: Cambridge University Press.Google Scholar
  5. 5.
    Carnielli, W., Coniglio, M.E. (2011). Combining logics. In Edward N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. Winter 2011 edition.Google Scholar
  6. 6.
    Carnielli, W., Pizzi, C., & Bueno-Soler, J. (2008). Modalities and multimodalities (vol. 12). Springer.Google Scholar
  7. 7.
    Carrara, M., & Chiffi, D. (2014). The knowability paradox in the light of a logic for pragmatics. In R. Ciuni, H. Wansing, & C. Willkommen (Eds.), Recent Trends in Philosophical Logic, (pp.33–48). Springer.Google Scholar
  8. 8.
    Costa-Leite, A. (2006). Fusions of modal logics and Fitch’s paradox. Croatian Journal of Philosophy, 17, 281–290.Google Scholar
  9. 9.
    Dalla Pozza C., & Garola, C. (1995). A pragmatic interpretation of intuitionistic propositional logic. Erkenntnis, 43, 81–109.Google Scholar
  10. 10.
    De Vidi, D., & Solomon, G. (2001). Knowability and intuitionistic logic. Philosophia, 28(1), 319–334.Google Scholar
  11. 11.
    Dummett, M. (2009). Fitch’s paradox of knowability. In J. Salerno, (Ed.), New essays on the knowability paradox, (pp. 51–52). Oxford: OUP Press.Google Scholar
  12. 12.
    Fine, K., & Schurz, G. (1991). Transfer theorems for stratified multimodal logics. In B. J. Copeland (Ed.), Logic and Reality (pp. 169–213). Oxford: Clarendon Press.Google Scholar
  13. 13.
    Fischer, M. (2013). Some remarks on restricting the knowability principle. Synthese, 190(1), 63–88.Google Scholar
  14. 14.
    Fitch, F. B. (1963). A logical analysis of some value concepts. The Journal of Symbolic Logic, 28(2), 135–142.CrossRefGoogle Scholar
  15. 15.
    Gabbay, D.M., & Shehtman, V.B. (1998). Products of modal logics, part 1. Logic Journal of IGPL, 6, 73–146.Google Scholar
  16. 16.
    Gödel, K. (1933). Eine interpretation des intuitionistischen aussagenkalkuls. Ergebnisse Eines Mathematischen Kolloquiums, 4, 39–40.Google Scholar
  17. 17.
    Salerno, J. (2009). New essays on the knowability paradox. Oxford: OUP.CrossRefGoogle Scholar
  18. 18.
    Troelstra, A.S., & Schwichtenberg, H. (2000). Basic proof theory (No. 43). Cambridge: Cambridge University Press.Google Scholar
  19. 19.
    Wansing, H. (2002). Diamonds are a philosopher’s best friends. Journal of Philosophical Logic, 31(6), 591–612.Google Scholar
  20. 20.
    Williamson, T. (1992). On intuitionistic modal epistemic logic. Journal of Philosophical Logic, pp. 63–89.Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.FISPPA Department - Section of PhilosophyUniversity of PaduaPaduaItaly
  2. 2.Ragnar Nurkse Department of Innovation and GovernanceTallinn University of TechnologyTallinnEstonia
  3. 3.Freelance LogicianLecceItaly

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