Since I can't determine how to quantify it, my response has been to treat all other beliefs as conditioned on "my reasoning process is basically sound", which makes a fair number of my beliefs having tacit probability 1; if I find reason to question any of these beliefs, I will have to rederive every belief from the original evidence as much as possible, because it's exposed a significant flaw in the means by which I determine what beliefs to hold. Largely this consists of mathematical proofs, but also things like "there is not currently a flying green elephant in this room" and "an extant rain god is mutually incompatible with reductionism".

This is an amazingly apt description of the mind-state that Robert Anton Wilson called "Chapel Perilous".