This system can only be useful to someone who thinks strong agnosticism is incorrect, and is willing to impose their definitions upon others without their acceptance.

Read what i dais. And understand it. Playing word games is not funny.

I'm not playing word games. I'm questioning your epistemology. You seem to begin with the assumptions certain knowledge (i.e. PNC, Causality) which quantitative testing cannot falsify and based on those assumptions (of science) you put forth the claim the only way to gain knowledge is to fit within the criteria of that epistemology of science. To which I have no problem if what you are testing were a scientific question. But God is not a scientific question per se. Science doesn't exist independent of God, rather God sustains the laws of nature as to produce said presuppositions and a rational world. So in other words, you've smuggled in an atheistic presupposition into the epistemology of your knowledge gathering criteria which I deny or any classical theist would deny that antecedent. Additionally this particular epistemology cannot be used to assign truth value to other types of knowledge such as qualitative knowledge. This is what is colloquially known as scientism. There are ways to assign truth value to claims without the epistemology of science. There are ways to assign truth value to the presuppositions of science, but that requires a different set of tools which you seem to deny are useful.

You're playing word games here. You know what is meant above. The word 'know' is just there to convey a degree of confidence. We say we know something (colloquially) when certain criteria has been met. In physics normally referring to statistical methods and sigma values applied to commonly agreed upon data sets. Being able to show thing to be false is a tool that's nice to have in this to show whether or not a hypothesis is valid for the findings. In other areas other methods can occur. No one (colloquially) in this process pretends that 'knowing' refers to an absolute knowing. But the lack of absolute level of knowing doesn't mean we cant say that we know a thing with a very, very high confidence level, to the point where the practical distinction is not really worth haggling about.

In short the tools in the toolbox for scientific understanding are there to make up for our biases and various shortcomings. A rock falls with 9.82m2 regardless of whether you are a hindu, jew, christian or atheist. A genome changes over time in a measurable way regardless of your favourite mythology. And that goes for radioactive decay, geological strata and so forth. Can anything of this be proven in the philosophical absolute sense? No, not really, but none of us can show that we even exists in the absolute sense either. But then again that's not a practical way to tackle life as we didnt...

Better tool or correct tool?

Correct me if I'm wrong, but you just explained how it practical to assume certainty of a knowledge with a knowing that cannot be falsifiable or tested empirically. You are just finding the conclusions of an empiricism assumptions that exist without cause, which is begging the question if you are positing it is "practical" to assume they are causeless. I'm sure you'd reject any theist that told you it was practical to assume God because that's how they "know" thow shall not kill.

I don't agree the principle of causality assumes time. Just the opposite. According to the special theory of relativity, "the notion of causality can be used as a prior foundation from which to construct notions of time and space."

https://en.wikipedia.org/wiki/Causality

Non contradiction can be assumed as it is a definition we have made up, we have no examples of it not being true and we have no actual reasons to believe it isn't, at least not in the universe we inhabit. So for all practical purposes and intent we can treat it as an absolute even though we can't really be 100% about the universality of that ssumption. In treat realism in more or less the same way. Causality is a more thorny question. As we define it currently causality implies a time axle. And we have good reason, from available evidence to believe that its not necessarily so that time has existed at all states of the universe. So the question on how to define such a principle in all circumstances remains to be seen. but yes, in the current instantiation of the universe we inhabit it makes sense to treat is an an absolute.

In short there is a difference of certainty here. We can define frameworks that are self contained and where absolutes can reign but they are merely abstractions of a messy reality which may or may not rely on absolutes. But even so it may be reasonable to treat them as absolutes from an practical point of view even if they arent. Its not much use to expect my glas of milk to float upwards when I drop it even if it potentially could given the circumstances I am in.

Supply with a better tool and we can discuss it.

Sorry, I was editing when you responded. I'll let you respond to my edits if you feel so inclined.

Sure. We all could be a brain in a vat. Doesnt mean its particularly meaningful to act in that way. As you point out we can only really act on our sensory input. The fact that this sensory input is or can be faulty doesnt mean its useless, but it does require us to devise various safe guards increase our likelihood of making objectively good assessments. The fact that its not perfect doesnt mean it isn't useful.