I'm torn from wanting to move forward, and wanting to be intellectually honest. If I were to be fully intellectually honest, then I don't think we can know if labels can identify 'things' actually part of Ultimate Reality or not. However, to be consistent with my acceptance of (6), I will allow it like I would allow someone to scratch their fingernails against glass as long as it is necessary that I do so. Since I'd like to see your argument from first principles, I am accepting the glass scratching out of necessity.
Regarding (7), this only moves from one hand scratching the glass to two hands scratching the glass.
***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.***
It is possible... What does that mean? Does it mean that of all the possibilities in Ultimate Reality that none of those possibilities entail individuals whose beliefs are not based via a set of unknown numbers? How do we know that? What if Ultimate Reality is not guided by logical principles? It seems to me that the logic of Ultimate Reality is unknowable.
Perhaps you have a different meaning of the word 'possible'.
***These "labels" do not identify these "things". They are merely attached labels and no more. As I said earlier, all that #6 says is that it is possible to attach labels consisting of the same symbols used to represent numbers. No mention was ever made that these labels provided any information at all, only that it was possible to attach them.***
The reason I accepted (6) is because we weren't trying to separate the labels between the URW and the world as it appears to us (i.e., 'things' that we think exist but does not exist. By trying to separate the labels, you are adding to your assumptions. Let me state those hidden assumptions:
(6) It is possible to label all of these "things" with the same symbols commonly used to label numbers.
* In other words, if we have a human concept of false conception of Ultimate Reality, then we can label this human concept by a label (symbol, number, color, etc). If we are referring to something that is a 'thing' of Ultimate Reality, then it is either a differentiated manifold or non-differentiated manifold. If the former is true, then the differentiated sections of the manifold represent a number. If the latter is true, then the whole differentiated manifold can be labeled by one number. Either case, (6) is presumably true given our current state of knowledge (which isn't much - but heck let's just go with it to go through Dick's presentation - we're probably okay in accepting (6)).
(6a) Since beliefs either point to falsely conceived things or Ultimate Reality 'things', those beliefs can only point to one or the other, but not both and not neither.
* 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? This is not your standard classical logic, but even you have denied the principle of bivalence (i.e., a logical statement must be either true or false). Different possibilities come to mind, and I wonder why a (6a) would be assumed to be true.
(6b) There exists an algorithm that distinguishes beliefs that point to either falsely conceived things or Ultimate Reality 'things'.
* Again, very problematical. In (6) we don't care if we can identify a particular falsely conceived belief, or a particular 'Ultimate Reality' correct belief. We are only concerned about the possibility that a label can exist to a particular section of a manifold. That doesn't mean that we know what that number identifies, nor that there exists an algorithm to know what that is. For all we know, there might be a manifold section having an attached label but no algorithm exists by which to identify it. What that means is that we could hold a belief that it is not possible to decipher whether it is true or not as pertaining to Ultimate Reality. When I say "is not possible" I mean that there is no algorithm that exists which establishes the possibility.
Based on these 2 problematic assumptions, I see (7) as an invalid assumption. Now, I could be intellectually dishonest and just accept what you are saying, but let's be clear here. You have surpassed your knowledge of what we know or can know, and I find that this exercise is tenuous at best.
Warm regards, Harv