I simply don’t think the concept of the “crux” (as CFAR & co. use it) is nearly as universally applicable to disagreements as you (and others here) seem to imply.
This is surprising to me. A crux is a thing that if you didn’t believe it you’d change your mind on some other point—that seems like a very natural concept!
Is your contention that you usually can’t fine any one statement such that if you changed your mind about it, you’d change your mind about the top-level issue? (Interestingly, this is the thrust of top comment by Robin Hanson under Eliezer’s Is That Your True Rejection? post.)
This is surprising to me. A crux is a thing that if you didn’t believe it you’d change your mind on some other point—that seems like a very natural concept!
Is your contention that you usually can’t fine any one statement such that if you changed your mind about it, you’d change your mind about the top-level issue? (Interestingly, this is the thrust of top comment by Robin Hanson under Eliezer’s Is That Your True Rejection? post.)