The reason that I said go ahead and hide me is because you said you were thinking of doing so, and my response to someone who says that is to just do it. I would say it to anyone.
As I have tried to explain to you many times, from an abstract perspective, any solution of any problem consists of three parts: the basic information which is to be explained, the explanation which will be found acceptable after the problem is solved, and the other things implied by the explanation.
Fair enough. Now, Dick, there is a classification in problem solving that depends on the method by which you solve a problem. There is logical problem solving (i.e., first and second order logics, etc), mathematical problem solving, epistemic problem solving, and ontic problem solving. Each depends on the situation. For example, you don't solve a crime by writing a mathematical equation on the chalkboard. Likewise, you don't solve a mathematical problem by looking for physical clues.
When I look at your method to solve your problem, you use certain methods. It is quite clear that you use a mathematical approach. That's a given. Once you formulate a math problem, you are free to solve the problem mathematically as you have done. No one should complain about that.
But, it's how you arrive at the math problem that requires other methods. This is where you need to rely on either logical methods, epistemic methods, or ontic methods. We know it is not a logical method (e.g., Goedel's first completeness theorem) since you are not using any first or second order logic, nor are you using any other logics (e.g., deontic logic, paraconsistent logic, fuzzy logic, etc). So, you must either utilize epistemic methods and/or ontic methods.
It is very important to distinguish which method that you are using at each point in the construction of your argument that leads up to your mathematical argument. The reason is that your list of assumptions will depend on the method that you take to solve whatever problem that you are confronting.
So, would you agree that the problem that you are trying to solve is an epistemic problem? If you agree, then would you also agree that it is important to use an epistemic method to a epistemic problem?
The reason that you should agree is that unlike epistemic methods, an ontic method makes certain claims about reality that we think need to be true in order for things to present themselves just like they happen to do. For example, believing in God's existence and providing an argument for God is traditionally such an ontic approach.
Hence, unless you want to avoid the issue of making extraordinary claims which ontic arguments often entail, you are forced into an epistemic method of argument. Which raises the ugly question, "why is it that you do not feel compelled to avoiding an ontic appeal in your paper?"
The reason I gave the three very different examples of what I was talking about was because none of them specifically denote the circumstance I want you to think about. Instead, it is the characteristic which the three have in common which establishes the meaning of the division between "knowable" and "unknowable" I am trying to convey. If you cannot see any similarity between the circumstances, then I have failed to communicate the concept (not at all an unexpected phenomena).
I see the parallel of what you are communicating. I do. What you are not addressing, however, is that each criteria has a different epistemic and/or ontic distinction, which does not answer the question on whether you are truly keeping in line with an epistemic solution to arrive at the set-up of your math problem. You see, those two terms (knowable and unknowable data) are key to your math, and without those terms you cannot formulate the model. I understand what you are trying to convey in the meaning of those terms, but keep in mind that you are doing more than conveying meaning. You are trying to show from the point of an observer, how they can construct a model such as your's if they make very few correct epistemic assumptions and know mathematics. But, the epistemic assumptions they have to make is in regards to the knowable and unknowable data. This is fundamental! What goes into those categories makes no difference from the point of this bystander, all that matters is that they are willing to make these two designations and are willing to follow through on the math based on these delineations in terms (i.e., knowable and unknowable).
However, here's the catcher. If they cannot make those delineations without a valid epistemic distinction, then they cannot take that right epistemic step in the direction of setting up your math problem. You have, in effect, asked them to take a step in a direction that they cannot go. You have asked them to accept an epistemic assumption that they are not warranted into accepting (i.e., the existence of knowable and unknowable data) since the meaning of those terms, as you have defined it, is beyond their ability to know as a valid dichotomy of their knowledge.
All I am trying to do is to come up with an abstract reference which will refer to that information which (in the final analysis) will turn out to be valid.
And, you are welcome to do so! BUT, the condition is that you must lead the bystander (with mathematical background) at each point with conditions that they can easily accept. For example, if one of the requirements to set up your math was to accept that there is spiritual and evil data in the world, notice how troubling that would be for your paper. The question this bystander would immediately ask is what is spiritual and evil data. If they were told that spiritual data was what God saw as 'spiritual' and evil data was what God saw as 'evil', then a whole slew of problems should prevent someone from proceeding with the math set-up. It doesn't matter if all you are doing is setting up an abstract reference that only refers to spiritual or evil data, the whole point is that this bystander cannot needlessly accept that there is spiritual and evil data in the first place!! Your paper, of course, isn't so overt as this, but it makes the same mistake. It tries to define knowledge in a manner that this bystander should reject since it is not clear beyond a shadow of a doubt that the bystander can make the delineation of knowledge that you are making - especially when you reference 'God' whom the bystander could be an atheist or agnostic (and, I know that you might lock-in on this particular statement since you will say it is not belief in God that matters, but the hypotheticalness of God having such knowledge that you seek by mentioning God, but the point is that you cannot ask a bystander to accept a hypothetical situation such as this in order to justify the knowable and unknowable data as a proper delineation).
The concept must apply to any and all solutions, whether the "final analysis" refers to a solution handed to us by god, one obtained by a scientist a million years from now or the resolution of a single conundrum solved by a scientist tomorrow. I have discovered a rather astonishing solution to the general problem of solving problems. Comprehending that solution requires comprehending the difference between "the basic information which is to be explained" and "the implied information which is a consequence of believing the explanation".
You are jumping ahead of yourself. Prior to talking about your results or even the math of abstract references, you first have to justify the moves you take to get to the math set-up. The person who must be justified in taking those steps is the bystander who is following your instructions as to what is valid steps to take in the situation that they are in with regards to their subconscious/conscious state. Remember, you are dealing with a bystander who cannot trust their subconscious. You are dealing with someone who is not sure if they should believe in the accuracy of their perceptions, etc. All they know is that mathematics is a valid assumption of self-consistent reasoning and that they should accept an abstract approach. However, you also have to get them to accept your first steps in the direction of setting up the math problem. Here's where you lose your bystander.
That issue is a direct consequence of the particular problem being solved and what is known when the attempt is made. It is completely immaterial to the logic I am trying to present. My logic relies only on the recognition of the difference and the existence of both categories. If you say the first category does not exist than there is nothing to be explained; if you say the second category does not exist then the explanation implies nothing exists which can not be known without any explanation at all.
You are making false dichotomies again. Things may not be so simple. The bystander could object and say that only pragmatic knowledge exists and that explanations can serve pragmatic purposes. Last week I gave Mike a set-up in which truth is not an external thing, but only an internal thing. Your paper doesn't work if there are no external 'truths' per se. Here is the statement I provided to him:
T2': "P contextually obtains and not P contextually obtains for every possible proposition depending on the conceptual scheme Cx used to determine P and not P. Conceptual schemes Cx(1-n) may be incommensurable between each other"
Now, if T2' is what we actually call truth. That is, if we say P 'is true' and P contextually obtains in that situation of reference, then our knowledge is P. Your model fails under T2' where P is our knowledge. Your model has no means by which to classify P as either 'knowable data' or 'unknowable data'. The reason is that P is both and neither in situation by situation, context by context.
This implies the explanation serves no purpose.
Explanation might serve pragmatic purposes. Purpose enough. I'm not saying that is the case, but the way your paper is set-up, it automatically rejects this possibility without justification in doing so. In that way, you restrict the answers and thereby make your bystander very unhappy.