They are truisms - in principle they are statements that are entirely redundant as one could in principle work out the truth of them without being told anything. However, principle and practice are rather different here - just because we could in principle reinvent mathematics from scratch doesn't mean that in practice we could. Consequently these beliefs are presented to us as external information rather than as the inevitable truisms they actually are.
Nice to have you here. Those are some cool names you dropped.
I approve of attending the Quaker meeting: I don't think there's any better way to quickly meet good people than to find religious groups.
Did you take the 2011 Less Wrong survey, out of curiosity?