On Sharon and Spectre’s argument against closure
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Sharon and Spectre give the best argument against closure that I know of, and they are to be commended for bringing clarity to a discussion often enmeshed in obscurity. Nevertheless, I think that their argument proves less than they advertise.
(CP) Necessarily, if S knows p, competently deduces q from p, and thereby comes to believe q, while retaining knowledge of p throughout, then S knows q.
Crucial to their argument against CP is another closure principle about evidence (I omit qualifications that won’t matter for our purposes):
(CE) Necessarily, if e is evidence for p for S and p entails q, then e is evidence for q for S.
CE is false.
If CE is false, then CP is false.
CP is false.
KeywordsRational Confidence Alternative Conception Atomic Proposition Gettier Case Contingent Truth
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