All knowledge derives from postulated realities about which one has certainty, Bill. The distinction you are making is not between knowledge and belief, but between the genuine beliefs which inform one's perceptions, and the social or pretended believes one gives oral subscription to.   Believing one exists, believing in gravity, believing one is in space are all deepseated beliefs, and asserting they are not so is a pretense, like that of the faith-healer who dislikes what he fancies he feels.

Your Cartesian approach is a good one, especially for dealing with systems like geometry, math and material science, where it works to "prove by challenge" and where reason has a relatively simple role to play.

But reason is, itself, a construct in which one believes. It includes for example a premise about time, about perception, and about the nature of if-then relationships about which one must not presume ownership. They have to be postulated as externals or the sandbox falls apart.

This is the formula of success in dealing with the mechanics of things of a material nature; but these requirements are not the same as truth. And, they get much less robust when you apply them to issues of awareness, creation, perception, intentionality, and the like, none of which have any role to play in the sandbox, and are preferred to be ignored whilke operating within it.

A