Abstract
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.
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Notes
- 1.
- 2.
Notice that Frege’s analysis is extendable to other speech acts such as asking, questioning, etc. So is \(\mathcal {L}^{P}\) . Languages where \(\mathcal {L}^{P}\) is expanded so to give rise of other pragmatics acts have been studied. See, for example, [3].
- 3.
Where ’proof’ has to be understood in its intuitive sense.
- 4.
The fusion \(\mathcal {L}_{1} \oplus \mathcal {L}_{2}\) of two modal languages, \(\mathcal {L}_{1}\) and \(\mathcal {L}_{2}\), endowed with two independent boxes, \(\Box _{1}\) and \(\Box _{2}\), is the smallest modal language generated by both boxes. Note also that the fusion of modal languages is commutative.
- 5.
BPs can be equivalent to conditions on the relations between accessibility relations [5].
- 6.
On (KPPI) see [11].
- 7.
On (KPPI’) and (KPPI”) see [7].
References
Artemov, S., & Protopopescu, T.(2013). Discovering knowability: a semantic analysis. Synthese, 190(16), 3349–3376.
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.
Bellin, G., & Biasi, C. (2004). Towards a logic for pragmatics. Assertions and conjectures. Journal of Logic and Computation, 14, 473–506.
Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal Logic. Cambridge: Cambridge University Press.
Carnielli, W., Coniglio, M.E. (2011). Combining logics. In Edward N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. Winter 2011 edition.
Carnielli, W., Pizzi, C., & Bueno-Soler, J. (2008). Modalities and multimodalities (vol. 12). Springer.
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.
Costa-Leite, A. (2006). Fusions of modal logics and Fitch’s paradox. Croatian Journal of Philosophy, 17, 281–290.
Dalla Pozza C., & Garola, C. (1995). A pragmatic interpretation of intuitionistic propositional logic. Erkenntnis, 43, 81–109.
De Vidi, D., & Solomon, G. (2001). Knowability and intuitionistic logic. Philosophia, 28(1), 319–334.
Dummett, M. (2009). Fitch’s paradox of knowability. In J. Salerno, (Ed.), New essays on the knowability paradox, (pp. 51–52). Oxford: OUP Press.
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.
Fischer, M. (2013). Some remarks on restricting the knowability principle. Synthese, 190(1), 63–88.
Fitch, F. B. (1963). A logical analysis of some value concepts. The Journal of Symbolic Logic, 28(2), 135–142.
Gabbay, D.M., & Shehtman, V.B. (1998). Products of modal logics, part 1. Logic Journal of IGPL, 6, 73–146.
Gödel, K. (1933). Eine interpretation des intuitionistischen aussagenkalkuls. Ergebnisse Eines Mathematischen Kolloquiums, 4, 39–40.
Salerno, J. (2009). New essays on the knowability paradox. Oxford: OUP.
Troelstra, A.S., & Schwichtenberg, H. (2000). Basic proof theory (No. 43). Cambridge: Cambridge University Press.
Wansing, H. (2002). Diamonds are a philosopher’s best friends. Journal of Philosophical Logic, 31(6), 591–612.
Williamson, T. (1992). On intuitionistic modal epistemic logic. Journal of Philosophical Logic, pp. 63–89.
Acknowledgements
\(^*\) 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.
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Carrara, M., Chiffi, D., Sergio, D. (2017). A Multimodal Pragmatic Analysis of the Knowability Paradox. In: Urbaniak, R., Payette, G. (eds) Applications of Formal Philosophy. Logic, Argumentation & Reasoning, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-58507-9_9
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