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].
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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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