Intuitionistic Epistemic Logic, Kripke Models and Fitch’s Paradox

Journal of Philosophical Logic 41 (5):877-900 (2012)
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Abstract

The present work is motivated by two questions. (1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it? In what follows we outline an answer to (2) and give a model-theoretic definition of the operator K. This will shed some light also on (1), since it turns out that K, defined as we do, fulfills the properties of a necessity operator for a normal modal logic. The interest of our construction also lies in a better insight into the intuitionistic solution to Fitch's paradox, which is discussed in the third section. In particular we examine, in the light of our definition, De Vidi and Solomon's proposal of formulating the verification thesis as Φ → ¬¬KΦ. We show, as our main result, that this definition excapes the paradox, though it is validated only under restrictive conditions on the models

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Carlo Proietti
University of Amsterdam

References found in this work

Knowledge and belief.Jaakko Hintikka - 1962 - Ithaca, N.Y.,: Cornell University Press.
The taming of the true.Neil Tennant - 1997 - New York: Oxford University Press.
Intuitionism Disproved?Timothy Williamson - 1982 - Analysis 42 (4):203--7.
Mathematical modal logic: A view of its evolution.Robert Goldblatt - 2003 - Journal of Applied Logic 1 (5-6):309-392.

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