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More on the paradox of the knower without epistemic closure

Charles B. Cross

Mind 113 (449):109-114 (2004)

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The Paradox of the Knower without Epistemic Closure -- Corrected.C. B. Cross - 2012 - Mind 121 (482):457-466.details This essay corrects an error in the presentation of the Paradox of the Knowledge-Plus Knower, which is the variant of Kaplan and Montague’s Knower Paradox presented in C. Cross 2001: ‘The Paradox of the Knower without Epistemic Closure,’ MIND, 110, pp. 319–33. The correction adds a universally quantified transitivity principle for derivability as an additional assumption leading to paradox. This correction does not affect the status of the Knowledge-Plus paradox as a rebuttal to an argument against epistemic closure, since the (...) Download Export citation Bookmark 4 citations
Non‐Classical Knowledge.Ethan Jerzak - 2017 - Philosophy and Phenomenological Research 98 (1):190-220.details The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory validating (...) Download Export citation Bookmark 5 citations
The knower paradox in the light of provability interpretations of modal logic.Paul Égré - 2004 - Journal of Logic, Language and Information 14 (1):13-48.details This paper propounds a systematic examination of the link between the Knower Paradox and provability interpretations of modal logic. The aim of the paper is threefold: to give a streamlined presentation of the Knower Paradox and related results; to clarify the notion of a syntactical treatment of modalities; finally, to discuss the kind of solution that modal provability logic provides to the Paradox. I discuss the respective strength of different versions of the Knower Paradox, both in the framework of first-order (...) Download Export citation Bookmark 13 citations
Is ‘Knowing that P’ Identical with ‘Knowing that “P” Is True’?Changsheng Lai - 2021 - Philosophia 48 (3):1075-1092.details It is epistemological orthodoxy that the object of propositional knowledge is the truth of propositions. This traditional view is based on what I call the ‘KT-schema’, viz, ‘S knows that p, iff, S knows that “p” is true’. The purpose of this paper is to reject the KT-schema. By showing the paradoxical upshot of the KT-schema and providing counterexamples to the KT-schema, this paper argues that ‘knowing that p’ is more than ‘knowing that “p” is true’. Consequently, we shall rethink (...) Download Export citation Bookmark
The Paradox of the Knower revisited.Walter Dean & Hidenori Kurokawa - 2014 - Annals of Pure and Applied Logic 165 (1):199-224.details The Paradox of the Knower was originally presented by Kaplan and Montague [26] as a puzzle about the everyday notion of knowledge in the face of self-reference. The paradox shows that any theory extending Robinson arithmetic with a predicate K satisfying the factivity axiom K → A as well as a few other epistemically plausible principles is inconsistent. After surveying the background of the paradox, we will focus on a recent debate about the role of epistemic closure principles in the (...) Download Export citation Bookmark 3 citations

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