But believing one’s own beliefs to come from a source that systematically produces correct beliefs is a coherence condition.
This is only if you have some kind of completeness or logical omniscience kind of condition, requiring us to have beliefs about reflective statements at all. It’s entirely possible to only have beliefs over a limited class of statements—most animals don’t even have a concept of reflection, yet they have beliefs which match reality. One need not have any beliefs at all about the sources of one’s beliefs.
As for the proof, seems like the interesting part would be providing deeper foundations for axioms 4 and 5. Those are the parts which seem like they could fail.
This is only if you have some kind of completeness or logical omniscience kind of condition, requiring us to have beliefs about reflective statements at all. It’s entirely possible to only have beliefs over a limited class of statements—most animals don’t even have a concept of reflection, yet they have beliefs which match reality. One need not have any beliefs at all about the sources of one’s beliefs.
As for the proof, seems like the interesting part would be providing deeper foundations for axioms 4 and 5. Those are the parts which seem like they could fail.