An axiomatic version of Fitch's paradox
Synthese 190 (12):2015-2020 (2013)
| Abstract |
A variation of Fitch’s paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundness (while still requiring he be sound), Fitch’s paradox is avoided. Provided one is willing to admit that sound knowers may be ignorant of their own soundness, this might offer a way out of the paradox
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| Keywords | Knowledge Epistemology Knowability Paradox Fitch’s paradox |
| Categories | (categorize this paper) |
| DOI | 10.1007/s11229-011-9954-0 |
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References found in this work BETA
A Logical Analysis of Some Value Concepts.Frederic B. Fitch - 1963 - Journal of Symbolic Logic 28 (2):135-142.
Taken by Surprise: The Paradox of the Surprise Test Revisited. [REVIEW]Joseph Y. Halpern & Yoram Moses - 1986 - Journal of Philosophical Logic 15 (3):281 - 304.
Knowledge, Machines, and the Consistency of Reinhardt's Strong Mechanistic Thesis.Timothy J. Carlson - 2000 - Annals of Pure and Applied Logic 105 (1--3):51--82.
The Surprise Examination Paradox and the Second Incompleteness Theorem.Shira Kritchman & Ran Raz - unknown
Citations of this work BETA
On a New Tentative Solution to Fitch’s Paradox.Alessandro Giordani - 2015 - Erkenntnis 81 (3):597-611.
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Discussion
| 2012-02-14 | |
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Bruno Maret
Université paris 1 |
notation : I use ! for 'not'
Perhaps you can avoid paradox but you have to admit this very strange proposition : K !K x -> !P K x If you know that you ignore (x) it's impossible that you know (x) I don't see how it could be compatible with the knowability principle : x -> P K x else you can't have (x) and (K !K x) (excuse me if this message is out of place, I ignore the policy of tis forum, excuse also my probable mistakes in english)
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