Annals of Pure and Applied Logic 165 (1):199-224 (2014)

Hidenori Kurokawa
City University of New York
Walter Dean
University of Warwick
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 Knower. We will suggest this debate sheds new light on the concept of knowledge which is at issue in the paradox – i.e. is it a “thin” notion divorced from concepts such as evidence or justification, or is it a “thick” notion more closely resembling mathematical provability? We will argue that a number of features of the paradox suggest that the latter option is more plausible. Along the way, we will provide a reconstruction of the paradox using a quantified extension of Artemovʼs [2] Logic of Proofs, as well as a series of results linking the original formulation of the paradox to reflection principles for formal arithmetic. On this basis, we will argue that while the Knower can be understood to motivate a distinction between levels of knowledge, it does not provide a rationale for recognizing a uniform hierarchy of knowledge predicates in the manner suggested by Anderson
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/j.apal.2013.07.010
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 65,683
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
Discrimination and Perceptual Knowledge.Alvin I. Goldman - 1976 - Journal of Philosophy 73 (November):771-791.
The Concept of Truth in Formalized Languages.Alfred Tarski - 1936 - In A. Tarski (ed.), Logic, Semantics, Metamathematics. Oxford University Press. pp. 152--278.
Proof Theory.Gaisi Takeuti - 1975 - Elsevier.

View all 38 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

The Knower Paradox Revisited.Byeong D. Lee - 2000 - Philosophical Studies 98 (2):221-232.
Operators in the Paradox of the Knower.Patrick Grim - 1993 - Synthese 94 (3):409 - 428.
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.
Truth, Omniscience, and the Knower.Patrick Grim - 1988 - Philosophical Studies 54 (1):9 - 41.
Fitch's Proof, Verificationism, and the Knower Paradox.J. C. Beall - 2000 - Australasian Journal of Philosophy 78 (2):241 – 247.
The Paradox of the Knower.C. Anthony Anderson - 1983 - Journal of Philosophy 80 (6):338-355.
The Paradox of the Knower.Fred Feldman - 1989 - Philosophical Studies 55 (1):93 - 100.


Added to PP index

Total views
48 ( #227,317 of 2,462,427 )

Recent downloads (6 months)
2 ( #299,176 of 2,462,427 )

How can I increase my downloads?


My notes