Provability logic meets the knower paradox

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Abstract

The 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 Egré discusses three possible solutions that modal provability logic provides for the paradox by surveying and comparing three different provability interpretations of modality, including one by Solovay. To check whether this solution is satisfactory, we use the criteria for solutions to paradoxes defined by Susan Haack. This extended abstract aims to describe to what extent the knower paradox can be solved using provability logic and to what extent a solution proposed in the literature satisfies Haack's criteria. Finally, the extended offers some reflections on the relation between knowledge, proof, and provability, as inspired by the knower paradox.
Original languageEnglish
Title of host publicationAdvances in Modal Logic 2018
Subtitle of host publication Accepted Short Papers
EditorsG. D’Agostino, G. Bezhanishvilii
PublisherRijksuniversiteit Groningen
Pages31-35
Number of pages5
Publication statusPublished - 31-Aug-2018
EventAdvances in Modal Logic - University of Bern, Bern, Switzerland
Duration: 27-Aug-201831-Oct-2018
http://www.aiml2018.unibe.ch

Conference

ConferenceAdvances in Modal Logic
Abbreviated titleAIML 2018
CountrySwitzerland
CityBern
Period27/08/201831/10/2018
Internet address

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