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Diamonds Are a Philosopher's Best Friends: The Knowability Paradox and Modal Epistemic Relevance Logic

Heinrich Wansing
Journal of Philosophical Logic
Vol. 31, No. 6 (Dec., 2002), pp. 591-612
Published by: Springer
Stable URL: http://www.jstor.org/stable/30226775
Page Count: 22
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Diamonds Are a Philosopher's Best Friends: The Knowability Paradox and Modal Epistemic Relevance Logic
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Abstract

The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is derived that all truths are, in fact, known. Nevertheless, the solution offered is in the spirit of the constructivist attitude usually maintained by defenders of the anti-realist premise. In order to avoid the paradoxical reasoning, a paraconsistent constructive relevant modal epistemic logic with strong negation is defined semantically. The system is axiomatized and shown to be complete.

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