Re Nav. Just let it go. Its not worth it.

Contradictory belief systems can not exist alongside one another in one person's mind, but they can exist alongside one another in society.
I'd challenge even the first part of that. In my experience doublethink is a common phenomenon.

IMHO the problem with the first post is it treats belief systems as if they were like maths, an internally consistent way to develop/uncover knowledge. Whereas most of what actually goes on in the wet and messy place between our ears has little resemblance to the neatly ordered arguments of a "system".

And after all, even maths has had to abandon any claim to be complete. And if the most rigourous belief system known to us has to admit there are true statements beyond its power to prove, (and IIRC this is a generalisable result for ANY system, can anyone confirm that for us) then belief system tolerance certainly should be possible.

QED and thank you Godel.