Then you present me with a brilliant lemma Y, which clearly seems like a likely consequence of my mathematical axioms, and which also seems to imply X—once I see Y, the connection from my axioms to X, via Y, becomes obvious.
Seems a lot like learning a proof of X. It shouldn’t surprise us that learning a proof of X increases your confidence in X. The mugger genie has little ground to accuse you of inconsistency for believing X more after learning a proof of it.
Granted the analogy isn’t exact; what is learned may fall well short of rigorous proof. You may have only learned a good argument for X. Since you assign only 90% posterior likelihood I presume that’s intended in your narrative.
Nevertheless, analogous reasoning seems to apply. The mugger genie has little ground to accuse you of inconsistency for believing X more after learning a good argument for it.
Seems a lot like learning a proof of X. It shouldn’t surprise us that learning a proof of X increases your confidence in X. The mugger genie has little ground to accuse you of inconsistency for believing X more after learning a proof of it.
Granted the analogy isn’t exact; what is learned may fall well short of rigorous proof. You may have only learned a good argument for X. Since you assign only 90% posterior likelihood I presume that’s intended in your narrative.
Nevertheless, analogous reasoning seems to apply. The mugger genie has little ground to accuse you of inconsistency for believing X more after learning a good argument for it.