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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Citations of this work BETA
The Ontology of Justifications in the Logical Setting.Sergei N. Artemov - 2012 - Studia Logica 100 (1-2):17-30.
The Logic of Justified Belief, Explicit Knowledge, and Conclusive Evidence.Alexandru Baltag, Bryan Renne & Sonja Smets - 2014 - Annals of Pure and Applied Logic 165 (1):49-81.
On a New Tentative Solution to Fitch’s Paradox.Alessandro Giordani - 2015 - Erkenntnis 81 (3):597-611.
Discovering Knowability: A Semantic Analysis.Sergei Artemov & Tudor Protopopescu - 2013 - Synthese 190 (16):3349-3376.
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