I’ve been thinking more about closure, and what leads epistemologists to accept it in a theory of knowledge or justification. A standard way in which closure is defended is by appeal to something like intuitions. You consider all the examples you can think of, and note how closure is preserved. You also make some point about extending knowledge through competent deduction. All of this culminates in a predilection to explain away apparent counterexamples to closure, such as Dretske’s zebra/mule case.
Each of these steps can be questioned, especially when we consider how various deductive principles for first-order logic have to be abandoned when thinking about the logic of subjunctives. For a broad variety of subjunctives, hypothetical syllogism is just fine; but it only takes a good counterexample or two to undermine the rule. And notice that if you really want to preserve such principles for subjunctives, it is not that hard to see how to go contextual about them to preserve them (UPDATE: probably the best example here would be that of strengthening the antecedent, which is the example Heller uses). Moreover, extending knowledge through competent deduction doesn’t require a closure principle. It only requires that the method is justification-preserving or highly reliable, in a way that doesn’t normally introduce gettierization.
So the psychology of closure affirmation still puzzles me.
I think I understand why evidentialists affirm closure. Evidence for a claim is information that gives one a reason to think the claim is true, and there is no better reason to think a claim is true than one that logically guarantees that it is true. All other evidence should be envious of this exalted status.
I think we can say something of the same sort for non-modal versions of reliabilism. After all, if we want to use methods and procedures that get us reliably to the truth, what better method than one guaranteed to preserve truth?
The puzzling case, though, is modal epistemologists. If you think of knowledge in terms of possible worlds and closeness relations between them, then you think of knowledge in much the same way that fans of Lewis/Stalnaker semantics think of subjunctives. In such a case, you’ll have a high degree of motivation to deny closure, since the class of worlds relative to which the truth value of a knowledge claim is assessed can shift between premises and conclusion of a deductive argument.
This is the conclusion that some modal epistemologists embrace, but not all. It’s the remainder that I don’t quite understand. For example, consider Sosa. Sosa proposes safety rather than sensitivity as a condition for knowledge, and a large part of the motivation is because (he thought) safety preserves closure. Turns out he was wrong, which he now realizes; but instead of abandoning closure, he adjusts the safety view even further to try to come up with a principle that will preserve closure.
But why this attachment to closure? I would have expected an attachment to closure to derive from one’s inclinations in the theory of knowledge, but that can’t explain the attraction of modal epistemologists to closure. The case for closure, if it goes as in the first paragraph above, is far from conclusive. If I add in an attraction for certain kinds of epistemology, I can see the attraction. But not for modal epistemologists. Anyone have ideas here?