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Reference and perspective in intuitionistic logics
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Original Paper
Reference and perspective in intuitionistic logics
John Nolt1 
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Philosophy Department, University of Tennessee, 801 McClung Tower, Knoxville, TN 37996-0480, USA |
Received: 3 April 2006 Accepted: 26 July 2006 Published online: 2 November 2006
Abstract What an intuitionist may refer to with respect to a given epistemic state depends not only on that epistemic state itself
but on whether it is viewed concurrently from within, in the hindsight of some later state, or ideally from a standpoint “beyond”
all epistemic states (though the latter perspective is no longer strictly intuitionistic). Each of these three perspectives
has a different—and, in the last two cases, a novel—logic and semantics. This paper explains these logics and their semantics
and provides soundness and completeness proofs. It provides, moreover, a critique of some common versions of Kripke semantics
for intuitionistic logic and suggests ways of modifying them to take account of the perspective-relativity of reference.
Keywords Intuitionistic logic - Intuitionism - Constructivism - Reference - Kripke semantics
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