David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 176 (2):177 - 225 (2010)
The Knowability Paradox purports to show that the controversial but not patently absurd hypothesis that all truths are knowable entails the implausible conclusion that all truths are known. The notoriety of this argument owes to the negative light it appears to cast on the view that there can be no verification-transcendent truths. We argue that it is overly simplistic to formalize the views of contemporary verificationists like Dummett, Prawitz or Martin-Löf using the sort of propositional modal operators which are employed in the original derivation of the Paradox. Instead we propose that the central tenet of verificationism is most accurately formulated as follows: if φ is true, then there exists a proof of φ Building on the work of Artemov (Bull Symb Log 7(1): 1-36, 2001), a system of explicit modal logic with proof quantifiers is introduced to reason about such statements. When the original reasoning of the Paradox is developed in this setting, we reach not a contradiction, but rather the conclusion that there must exist non-constructed proofs. This outcome is evaluated relative to the controversy between Dummett and Prawitz about proof existence and bivalence
|Keywords||Knowability Paradox Fitch Verificationism Intuitionistic logic BHK interpretation Existence predicate Logic of proofs Potential proof Bivalence|
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References found in this work BETA
Sergei N. Artemov (2001). Explicit Provability and Constructive Semantics. Bulletin of Symbolic Logic 7 (1):1-36.
Sergei Artemov & Rosalie Iemhoff (2007). The Basic Intuitionistic Logic of Proofs. Journal of Symbolic Logic 72 (2):439 - 451.
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David Bell & W. D. Hart (1979). The Epistemology of Abstract Objects: Access and Inference. Proceedings of the Aristotelian Society 53:153-165.
George Boolos (1993). The Logic of Provability. Cambridge University Press.
Citations of this work BETA
Sergei N. Artemov (2012). The Ontology of Justifications in the Logical Setting. Studia Logica 100 (1-2):17-30.
Julien Murzi (2012). Manifestability and Epistemic Truth. Topoi 31 (1):17-26.
Sergei Artemov & Tudor Protopopescu (2013). Discovering Knowability: A Semantic Analysis. Synthese 190 (16):3349-3376.
Alexandru Baltag, Bryan Renne & Sonja Smets (2014). The Logic of Justified Belief, Explicit Knowledge, and Conclusive Evidence. Annals of Pure and Applied Logic 165 (1):49-81.
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