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      Intuitionistic Epistemic Logic

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          Abstract

          We outline an intuitionistic view of knowledge which maintains the original Brou\-wer-Heyting-Kolmogorov semantics for intuitionism and is consistent with the well-known approach that intuitionistic knowledge be regarded as the result of verification. We argue that on this view co-reflection \(A \rightarrow {\bf{K}} A\) is valid and the factivity of knowledge holds in the form \({\bf{K}} A \rightarrow \neg\neg A\) `known propositions cannot be false'. We show that the traditional form of factivity \({\bf{K}} A \rightarrow A\) is a distinctly classical principle which, like {\it tertium non datur} \(A\vee\neg A\), does not hold intuitionistically, but, along with the whole of classical epistemic logic, is intuitionistically valid in its double negation form \(\neg\neg({\bf{K}} A\rightarrow A)\). Within the intuitionistic epistemic framework the knowability paradox is resolved in a constructive manner. We argue that this paradox is the result of an unwarranted classical reading of constructive principles and as such does not have the consequences for constructive foundations traditionally attributed it.

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          Author and article information

          Journal
          2014-06-06
          2016-01-16
          Article
          10.1017/S1755020315000374
          1406.1582

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          03B20, 03B42
          40 pages. Pre-print of version to appear in the Review of Symbolic Logic
          math.LO

          Logic & Foundation

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