Solutions to the Knower Paradox in the Light of Haack’s Criteria

Author:

de Vos Mirjam,Verbrugge RinekeORCID,Kooi Barteld

Abstract

AbstractThe knower paradox states that the statement ‘We know that this statement is false’ leads to inconsistency. This article presents a fresh look at this paradox and some well-known solutions from the literature. Paul Égré discusses three possible solutions that modal provability logic provides for the paradox by surveying and comparing three different provability interpretations of modality, originally described by Skyrms, Anderson, and Solovay. In this article, some background is explained to clarify Égré’s solutions, all three of which hinge on intricacies of provability logic and its arithmetical interpretations. To check whether Égré’s solutions are satisfactory, we use the criteria for solutions to paradoxes defined by Susan Haack and we propose some refinements of them. This article aims to describe to what extent the knower paradox can be solved using provability logic and to what extent the solutions proposed in the literature satisfy Haack’s criteria. Finally, the article offers some reflections on the relation between knowledge, proof, and provability, as inspired by the knower paradox and its solutions.

Funder

Netherlands Organization for Scientific Research

Publisher

Springer Science and Business Media LLC

Subject

Philosophy

Reference47 articles.

1. Anderson, C. A. (1983). The paradox of the knower. The Journal of Philosophy, 80(6), 338–355.

2. Åqvist, L. (2014). Deontic tense logic with historical necessity, frame constants, and a solution to the epistemic obligation paradox (the “knower”). Theoria.

3. Beklemishev, L. D. (1994). On bimodal logics of provability. Annals of Pure and Applied Logic, 68(2), 115–159.

4. Bilu, Y. F. (2005). Catalan without logarithmic forms (after Bugeaud, Hanrot and Mihăilescu. Journal de Théorie des Nombres de Bordeau, 17(1), 69–85.

5. Boolos, G. (1995). The logic of provability. Cambridge: Cambridge University Press.

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