Excellent post! I had to reread what "goals" were again to make sure I had everything right. Back then I was not criticizing word choices, because we weren't to that level yet. However, now that we're at the point that the basic definitions are so important, I think a better term instead of goals would be to separate the word goals, and your approach to solving goals as a "Hypothesis".
A repost:
1. A goal initiates the inquiry because the search for truth is a goal.
2. Goals parameterise our enquiry because they determine the point at which a given endeavour can be deemed to be satisfactorily achieved and the criteria by which this point is to be reached.
3. Therefore, if goals set the beginning and the end of the enquiry, they set the parameters for how or when our understanding of the truth is satisfactory. — TVCL
This is due to a few factors. A goal is seen in common vernacular as "the end". Something like, "I want to find out if this apple is edible." How we approach pursuing a goal is not the same as arriving at the goal itself.
When you speak about goals, you imply that it is how we approach the goal which is just as important. If I want to fly by using my arms, then it would be silly to approach that goal without using my arms. Further, we wish to use logic, like the law of non-contradiction in our goals. That requires that our equation to discover Y must be falsifiable in some way. If we do not have this restriction, then someone could introduce a non-falsifiable belief, and state because it is not contradicted by reality, it is therefore provisional knowledge per your definition.
This is because the argument itself requires the use of logic to progress and progress in necessary relation to an aim — TVCL
Without defining our approach to obtaining goals as necessarily being falsifiable, your above claim will not hold. If we split your goal an end result, and the approach to that goal as a hypothesis, I think your approach is communicated with greater clarity, and security in its definition. If you disagree with the inclusion of a "hypothesis", this is fine. But your definition of "goal" as I understand it currently makes some assumptions that are not proven such as point 2.
e) Applying these criteria, we are left with:
i) beliefs that cannot be regarded as knowledge.
ii) beliefs that have the potential to be knowledge — TVCL
One problem here is the exclusion of knowledge itself as a viable definition. If we are to say there is a potential for knowledge, we must be able to show what knowledge is first. You even state this at the end.
As such, what comes to be regarded as knowledge is not "That which has been demonstrated to accord with reality" but "That which has been demonstrated to not be contradicted by reality." — TVCL
We cannot analyze the potential of something without first knowing what that something is. I would think that if you hold a goal, a hypothesized belief, and cannot contradict it, then you have knowledge. Now this assumes that knowledge is something which could be changed at a later time if new information arises that contradicts your claims. That is fine, but that would be knowledge itself, not provisional. What you might be doing here is thinking that knowledge needs to be truth. In doing so, you run into the problems that truth brings to epistemology. It is fine if you decide to go this route, but you'll have to address those problems as they rise up.
Of course, I have not addressed your arguments about discrete experience in here and this is because they were not needed to get the argument to this point. However, if you think that they can intersect with the argument above/are required for it or can build off from it, please do say. — TVCL
This is fine. The arguments I proposed were only used to give you a basis of how to approach the idea of knowledge from a foundational level. I am more eager to see your own approach. The only lesson to be drawn from my approach is to see how to make as few assumptions as possible in constructing an argument. Our arguments are also serving two different approaches. My argument comes from a fundamental construction of epistemology like Descartes, which admittedly is unnecessary for many people. Your epistemology is more a logical approach based on assumed precepts which few would nave need to question. We are not questioning what the "I" is, proving that thought is knowable, or other such concepts. Your goal is an applicable epistemology within our normative understanding of reality, which is useful and easy to grasp for daily use. And I think its going very well so far!
Feel free to confirm or deny any points I've made. If we are in general agreement with this base, then we can continue with the further branches from this I'm sure you're ready to get to!