I took a few days to consider your post. Let me backtrace a little here, since I see the problem.
"(6). It is possible to label all of these "things" with exactly the same symbols commonly used to label numbers."
After some thought, I realize the problem which you made realize in (7). When we refer to 'things' of 'Ultimate Reality', we aren't talking about plural objects since we don't know enough about 'Ultimate Reality' to know if plurality of objects even makes sense. All we know about 'Ultimate Reality' is the concept of 'Ultimate Reality' which we must assume is a valid concept.
Therefore, the term 'things' is entirely misleading (and perhaps the reason why you don't always put quotes around the term - thinking that we are actually talking and referring to things). To get away from this, we cannot identify the true concepts underlying Ulimate Reality as anything more basic than the concept itself. Hence, all we can say about 'Ultimate Reality' is the label 'Ultimate Reality'. The term 'things' only inserts in our discussion a very subtle misconception which I now see that your (7) is based on. However, I can still accept (6), but it should be reworded as:
(6). It is possible to label 'Ultimate Reality' with exactly the same symbols commonly used to label numbers. This requires only one number.
Now, the misconception of (7) is much easier to see:
(7) It is possible to refer to that portion of true "Ultimate Reality" on which any individuals beliefs are based via a set of unknown numbers.
The phrase "that portion of true 'Ultimate Reality'" is meaningless since we cannot talk about 'portions' or 'true' with respect to our concept which we labeled 'Ultimate Reality' (or by a number as in (6)).
Any further breakdown of 'Ultimate Reality' is an assumption based on our experience of the world we experience, and we have no way to know if this experience extends to the concept of 'Ultimate Reality'.
This, I hope, more clearly clarifies where I am coming from. The term 'things' is not wrong in the way that I was using it, but I see how that term was being abused (over and over again you even removed the quote marks from that term showing that my definition was probably different than your definition).
Okay, now let me reply a few key remarks.
***In many respects, an attempt to understand "Ultimate Reality" is very analogous to the decoding problem and techniques applicable to that problem should be applicable to the problem of understanding anything.***
I don't think understanding 'Ultimate Reality' is as analogous as you think. We have no premises to assume are true about 'Ultimate Reality', we have no rules of inference to assume are true, nor do we have any right to assume that our conclusions are true. Hence, we cannot say anything that is in any way formally 'proven' with regard to 'Ultimate Reality'. Nothing I know of is like this. Our experience of the world around us gives us the distinct impression that the world operates on logic and having certain basic premises is not out of the question.
****H: If we are referring to something that is a 'thing' of Ultimate Reality, then it is either a differentiated manifold or non-differentiated manifold. D: What does the "it" refer to? The thing or "Ultimate Reality".***
This is not saying there is a particular thing in 'Ultimate Reality', only that whatever is actually 'out there' is classifiable as 'Ultimate Reality' (not necessarily plural objects). You can label 'it', but it is one label or one number. You can use '1', '0', 'things', etc.. etc...
****H: Very problematical. What about the possibility of beliefs that are both true and false in Ultimate Reality, or conversely, both not-true and not-false? D: If they are part of "Ultimate Reality" then I wish to include them in my reference. If they are not then I don't want to include them. Once again, you are trying to put meaning into what I am saying which is not there. All I am saying is that "it is possible to label the things which make up 'Ultimate Reality'": i.e., it is possible to refer to the "things which make up 'Ultimate Reality'". We can use a language to think about these things. All I want to do is view the language as an abstract construct: i.e., as a collection of symbols for some unknown references.***
Dick, you are using classical logic to decipher Ultimate Reality, but we don't know if classical logic applies to 'Ultimate Reality'! This is the reason we cannot say more about 'Ultimate Reality' than the label itself implies. Can't you see the obstacle in what you are doing?
Sorry for the re-clarification, but as I said, I didn't realize that the term 'things' of 'Ultimate Reality' would be the focus of your misunderstanding. Hence, it was necessary to eliminate that term altogether.
Warm regards, Harv