Thank you for that informative exposition. I do have to say that I decry the comingling of the rational and the non-rational in referring to any candidate for ‘true’ knowledge as a “belief.”

I think a belief is best thought of as an extra-rational, purely subjective assertion of a ‘truth’ — or Truth. As such, it is not amenable in any way to being validated or invalidated within material existence (though people will surely argue — and fight — even kill/get killed over beliefs). [Ideology is to secular beliefs what theology is to religious beliefs.]

Rational knowledge is contingent — as Russell would have it, on ‘external facts’. Russell’s definition of ‘truth’ can only be applied to that.