A Multimodal Pragmatic Treatment of the Knowability Paradox

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.