Gettier cases are not cases where erroneous logic leads to a correct conclusion. The reasoning in a Gettier case can be perfectly fine; this is why the belief of Gettierized subjects remains justified. The issue is, rather, that because of "luck" there is a risk for reasoning/belief formation mechanism to go wrong, at the same time that it turns out to have produced a correct/true belief. The issue derives from there being a gap between a proposition being justified and it being true (Linda Zagzebski has a great paper that shows that whenever that is the case, you will end up with an analogous problem).
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