Deductive closure and the sorites

I argue against unqualified acceptance of the principle of deductive closure (DC): that, if p follows deductively from premises that are already known, we are in a position to know p. DC, I claim, is a sorites premise; it seems intuitively irresistible, but indiscriminate application of it leads to absurd conclusions. Furthermore, a theory on which the application of DC is restricted explains our practice of deriving new knowledge from old knowledge better than a theory on which our application of DC is unrestricted. This restriction on the application of DC allows contextualists to meet an argument of Hawthorne’s that contextualism must lead either to absurd knowledge attributions or to constant shifting of the standards for knowledge. Even if the standard of knowledge remains constant, the absurd knowledge attribution is the conclusion of a sorites argument and should be rejected.
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