Abstract
Rosenkranz has recently proposed a logic for propositional, non-factive, all-things-considered justification, which is based on a logic for the notion of being in a position to know (Rosenkranz Mind, 127(506), 309–338 2018). Starting from three quite weak assumptions in addition to some of the core principles that are already accepted by Rosenkranz, I prove that, if one has positive introspective and modally robust knowledge of the axioms of minimal arithmetic, then one is in a position to know that a sentence is not provable in minimal arithmetic or that the negation of that sentence is not provable in minimal arithmetic. This serves as the formal background for an example that calls into question the correctness of Rosenkranz’s logic of justification.
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Acknowledgements
Earlier versions of this paper have been presented at the Third Leuven-Bristol Workshop (Leuven, 15 September 2017) and the First Flemish Epistemology Workshop (Leuven, 18–19 May 2018). I would like to thank the audiences at those events for their comments and questions. I would like to thank Sven Rosenkranz, who was present at the First Flemish Epistemology Workshop, in particular. In addition, I would also like to thank Felipe Morales Carbonell, Harmen Ghijsen and Lars Arthur Tump for their feedback. Last but not least, I would like to thank the editor and two anonymous reviewers.
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Heylen, J. Rosenkranz’s Logic of Justification and Unprovability. J Philos Logic 49, 1243–1256 (2020). https://doi.org/10.1007/s10992-020-09556-7
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DOI: https://doi.org/10.1007/s10992-020-09556-7