The knower paradox in the light of provability interpretations of modal logic
Journal of Logic, Language and Information 14 (1) (2005)
| Abstract | 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 arithmetic and in that of modal logic with fixed point operators. It is shown that the notion of a syntactical treatment of modalities is ambiguous between a self-referential treatment and a metalinguistic treatment of modalities, and that these two notions are independent. I survey and compare the provability interpretations of modality respectively given by Skyrms, B. (1978, The Journal of Philosophy 75: 368–387) Anderson, C.A. (1983, The Journal of Philosophy 80: 338–355) and Solovay, R. (1976, Israel Journal of Mathematics 25: 287–304). I examine how these interpretations enable us to bypass the limitations imposed by the Knower Paradox while preserving the laws of classical logic, each time by appeal to a distinct form of hierarchy. | |||||||||
| Keywords | No keywords specified (fix it) | |||||||||
| Categories | ||||||||||
| Options |
|
|||||||||
Download options| PhilPapers Archive |
Upload a copy of this paper Check publisher's policy on self-archival Papers currently archived: 5,664 |
| External links |
 |
| Through your library | Configure |
Similar books and articlesGeorge Boolos (1979). The Unprovability of Consistency: An Essay in Modal Logic. Cambridge University Press.
JC Beall (2000). Fitch's Proof, Verificationism, and the Knower Paradox. Australasian Journal of Philosophy 78 (2):241 – 247.
Sergei N. Artemov (2001). Explicit Provability and Constructive Semantics. Bulletin of Symbolic Logic 7 (1):1-36.
Sergei Artemov & Giorgie Dzhaparidze (1990). Finite Kripke Models and Predicate Logics of Provability. Journal of Symbolic Logic 55 (3):1090-1098.
George Boolos (1993). The Logic of Provability. Cambridge University Press.
Nicholas J. J. Smith (2000). The Principle of Uniform Solution (of the Paradoxes of Self-Reference). Mind 109 (433):117-122.
Stephen Maitzen (1998). The Knower Paradox and Epistemic Closure. Synthese 114 (2):337-354.
Konstantin N. Ignatiev (1993). On Strong Provability Predicates and the Associated Modal Logics. Journal of Symbolic Logic 58 (1):249-290.
Charles B. Cross (2001). The Paradox of the Knower Without Epistemic Closure. Mind 110 (438):319-333.
Patrick Grim (1993). Operators in the Paradox of the Knower. Synthese 94 (3):409 - 428.
Analytics
Monthly downloads |
Added to index2009-01-28Total downloads14 ( #83,035 of 549,010 )Recent downloads (6 months)1 ( #63,261 of 549,010 )How can I increase my downloads? |
My notes
Discussion
