Revamping the restriction strategy
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press (2009)
This study continues the anti-realist’s quest for a principled way to avoid Fitch’s paradox. It is proposed that the Cartesian restriction on the anti-realist’s knowability principle ‘ϕ, therefore 3Kϕ’ should be formulated as a consistency requirement not on the premise ϕ of an application of the rule, but rather on the set of assumptions on which the relevant occurrence of ϕ depends. It is stressed, by reference to illustrative proofs, how important it is to have proofs in normal form before applying the proposed restriction. A similar restriction is proposed for the converse inference, the so-called Rule of Factiveness ‘3Kϕ therefore ϕ’. The proposed restriction appears to block another Fitch-style derivation that uses the KK -thesis in order to get around..
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Paolo Maffezioli, Alberto Naibo & Sara Negri (2013). The Church–Fitch Knowability Paradox in the Light of Structural Proof Theory. Synthese 190 (14):2677-2716.
Sergei Artemov & Tudor Protopopescu (2013). Discovering Knowability: A Semantic Analysis. Synthese 190 (16):3349-3376.
Martin Fischer (2013). Some Remarks on Restricting the Knowability Principle. Synthese 190 (1):63-88.
Julien Murzi (2010). Knowability and Bivalence: Intuitionistic Solutions to the Paradox of Knowability. [REVIEW] Philosophical Studies 149 (2):269 - 281.
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