One can never explain a dogma is correct - for the very specific reasons that I’ve covered.
Yet operating without a dogma is always either baseless or circular, as I’ve covered, and the only way to reconcile this with the fact that some knowledge is better than others is to have a founding dogma, as I’ve covered.
In this way, we know a dogma exists by trying to explain around it or without it. This doesn’t mean we’ve explained the dogma, because the dogma necessarily has to be void of explanation. If it wasn’t void, it would be part of the explanation and not the inevitable dogma that all knowledge must necessarily regress back towards. You cannot require then that the dogma must be explainable by its implications, because this inverts the dogma to discrete experiences that premise Continuous Experience: committing the fallacy of reverse causation.
Explaining presupposes a dissection, so cannot be a fundmental: explanation can only exist after the existence of a fundamental to ground it. This is why Epistemology must follow Ontology, because knowledge must first of all exist before it can develop. Continuous unity therefore has to be the nature of a fundamental axiom.
It’s not an arbitrary decision of mine that experience is this axiom - as I’ve covered. It’s the only possible conclusion. And due to the nature of inevitable dogma, it defies terms and implications itself. And only due to the axiomatic imposition of an unaccountable dogma can you proceed to divide it up into concepts and conceptual models.
What does “all” abstract from? There’s nothing greater than “all” from which to abstract “all” or it wouldn’t be “all”. The best you can do is describe “all” tautologously, which is to say “meaninglessly” - simply rephrasing in terms of synonyms - or you can describe it as the sum of its constituent parts: in terms of discrete experiences and losing out on its gestalt. As such, “Continuous Experience” by itself doesn’t tell us anything meaningful - it is tautology to meaninglessly rephrase it in terms of synonyms. The words “continuous” and “experience” only function as the remainders of all possible equations that we can construct from discrete experiences - the words may as well be “unabstractable/undefinable existence” or “all”. Concretely, “all existence” directly and immediately confronts us as experience, which is unbroken such that nothing can be said about it. But is saying that nothing can be said about it through the word “continuous” really saying anything about it? And is using the concrete term of “experience” saying it’s an abstraction? Words are circularly defined terms of discrete experiences, so can never suffice to encompass what they aren’t, but “Continuous Experience” is just about the best you can do given the necessity of words to communicate meaningful knowledge. It’s a problem even to give “Continuous Experience” a name at all, but to do so exactly fits the problem shaped hole left by dealing solely in discrete experiences - as its inevitable remainder. It doesn’t need a name, as it’s immediately inevitable with or without having a dissected discrete term to describe. The point is you get to “that which Continuous Experience refers” from either and any direction inevitably.
So your mention of classical philosophy where no one premise can stand alone is false. Philosophy since then, as I covered with mention of Russell, the Zermelo and Fraenkel guys who resolved his paradox, and Godel who poked a hole even in the ZF resolution, has advanced beyond classical philosophy. We already knew about circular reasoning before then (no premise standing alone requires infinite premises - “turtles all the way down” - or circular premises that all try to stand on each other and thereby stand on nothing as a whole). You have to advance on from classical philosophy once you realise its flaws. We already knew tautologies are meaningless and logic cannot exist without premises etc., but those guys formalised this whether they intended to do so or not. I’m simply coining the result as “Experientialism”.
Your 3 premises of valuator logic are fine as just another way to have pre-dissected Continuous Experience into discrete experiences and connect them back together into a conceptual model. Let it do battle with other conceptual models of discrete experiences. I’m staying back a step further to address a fundamental problem of Epistemology that it cannot fundamentally be either baseless or circular, with each term relying on a previous premise either indefinitely along a line or indefinitely around a circle, and at the same time have a fundamental starting point. You need an axiom or whatever you say is either linearly or circularly baseless.