To begin with, you and I are in perfect agreement that no explanations can be created to explain things one is unaware of. As you say, to correctly explain A would require an infinite amount of information. I am perfectly aware of the limitations imposed by that difficulty. This is exactly why I so carefully assembled the structures A, B and C. When we attempt to explain something, we are generally dealing with less than all the available information: i.e., we only have some part of A. That is why I "define" B to be a finite collection of elements of A (this is done to provide a reference to that part of A which is available to us). I do this in order to explicitly handle the limitations implied by the fact that we cannot ever know that we are missing some information.
I also define C to be a finite collection of sets B for reasons more subtle (having to do with the issue of testing an explanation). You make much the issue of A not being what you "want" to explain. So what; the concept you are trying to force on the discussion is totally spurious and has utterly nothing to do with what can be explained. Essentially, you keep distorting things in that direction in order to build a straw man which is convenient and easy to destroy.
I am constructing a model of the concept an explanation; not providing an explanation. It should be clear to you that no explanation is possible until after C is provided. If I am going to create a model of all explanations, exactly what A, B, and C is has to be kept entirely open.
The issue of what I can and can not explain has no bearing whatsoever on this conversation. What I said was that I could model any explanation. If you can explain something to me in its entirety (for mental convenience go ahead and think in terms of a twenty questions type conversation), I can provide what turns out to be a very useful model of your explanation.
And yes, explanation is a very human thing! I have defined it to be a method of coming up with expectations perfectly consistent with what you know: i.e., perfectly consistent with C. That is to say, it will perfectly correlate with the sets B which make up C. You give me a B and it will tell you exactly the probability of that B being in C (if I have both B and C you should not find that a difficult statement to accept). Now will it give you what the next B taken from A will be? No, it will not! Not unless the probability of that B obtained from C is identical with the probability of B in A. Now that is something to be learned and it will eventually adjust your expectations.
You claim that "Something that which is to be explained does not mean that this something is explainable". Harv, anything can be explained by the explanation, "that's a bunch of Bull!"
"Rather than say 'true', then why not say 'as applicable'? I prefer this term since 'true' has ontological implications which I'd like to avoid."
Oh Harv, get off my back! I didn't say "True"; I said "as true as" which is quite a different statement. And yes, no one ever has the slightest idea if any explanation is "ontologically true". All one can concern one's self with is the usefulness of that explanation: i.e., how dependable are the expectations obtained from that explanation. And my model does not concern itself with the validity of the explanation; only with the consistency of the expectations (and particularly, the consistency with C, what is known). This lies entirely with the interpretation of the elements of B: you must realize that there are a myriad of interpretations available to us! (Actually infinitely more than are dreamt of in your philosophy.)
Another quote from Harv:
"What you do not apparently see is that set C has no proven relationship to set A."
Again you are working on setting up that straw man. The only reason A is even in the discussion is to provide elements for B. The relationship with C is defined!
"But, if we can model anything, then let's just say we are modeling goblins and fairies, and you can see how it sounds to those who read this." So you now stoop to ridicule?
But I have made an exact definition of what I am modeling: "A method of obtaining expectations from the set C." I have defined that to be an explanation. If you have complaints with that, point out an explanation which does not "provide expectations from what is known".
"On the other hand, your model has absolutely no practical merit except by which to discuss here on astronomy.net as an excellent case study for the debate on the philosophy of science (which is why I debate this issue). I don't consider that enough practical merit to justify your model as legitimate since the pool of possible models that could perform the same function are innumerable."
Innumerable are they? Ok Harv, give me one alternate model of the concept of "explanation"! And, when you do that, lay out the predictions that model sets out. (And being wrong is not an acceptable prediction as my model covers that issue: i.e., you had better come up with some testable predictions.
I have put forth a model and it makes a very specific prediction. That no explanation of anything which is consistent with what is known will violate my fundamental equation. I think that is a pretty strong prediction.
Harv, one thing which you (and everyone else) seems to neglect to think about is the fact that what is presumed to exist is a function of the rules you believe must be obeyed. Likewise, the rules which you presume must be obeyed are a function of what you believe exists. There is a trade off here which allows an infinite number of explanations of anything. People are invariably convinced that their personal interpretation of the issues is the only possible explanation. That is the issue I am fighting and you, as a philosopher, should be interested.
Have fun -- Dick