TheAncientGeek comments on No Universally Compelling Arguments in Math or Science - Less Wrong
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But that's a universal defense of any free-floating belief.
For that matter: do you really think the degrees of justification for the rules of induction are similar to those of your moral beliefs?
If you can pin down the fundamentals of rationality, I'd be glad to hear how.
Side conditions can be added, eg that intuitions need to be used for something else.