Experimental philosophy is the mainstream academic field that is most directly attempting to dissolve (where possible) persistent philosophical problems by revealing the cognitive algorithms that generate old philosophical debates. Those who want to catch up with some of what these researchers have discovered already may want to read this July 2011 review of the field.
Also see my post Are Deontological Moral Judgments Rationalizations?
Upvoted for drawing my attention to an interesting field that was largely off my radar and providing useful links on the topic.
-edit hmm. my upvote doesn’t seem to registering, but the sentiment stands.
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In that case, see also my discussion post on formal epistemology.