All the kinds of knowledge you describe are subclasses of rational knowledge. Is there irrational knowledge?
In response to
Scientific Evidence, Legal Evidence, Rational Evidence
In response to
Guardians of the Truth
Perhaps the difference between the Inquisition and Feynman is that science specifically claims it has nothing to say about morality, so it can't justify killing anyone in its name.
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Believe stuff for crazy reasons (biased instincts, poor processing of data, etc). That's irrational knowledge - even if it happens to be wrong.
I was thinking more something like ethics.