I am astonished that you would stoop to feign belief in such a simple minded cavil. As I have said, the English language is a very vague means of communication. Certainly English is not a sufficiently exact mechanism to allow simple substitution as if it were mathematics. Anyone who would contend that the common use range of meaning of the word "possible" is identical in both the phrase "It is possible that ..." and the phrase "It is possible to", simply is not familiar with the language. Why are you blowing so much smoke?
I asked for a definition of "possible" which was reasonably consistent with common usage. I am of the opinion that the definition you give is both contrived and limited; being inconsistent with common usage. Under common usage, "possible" is never used (to my knowledge) to specifically refer to the situation "might not be possible" in spite of the fact that, in some very specific circumstances, such an interpretation is on occasion correct. As I said, I am using the English language as a vague rudder to steer your thoughts. The fact that you found it necessary to dig up such a basically confused presentation of its usage in order to refuse the reasonableness of my points simply enforces my impression that you are intentionally trying to misinterpret what I am saying. (When I say confused, I am referring to the issue that no one would commonly interpret "it is possible to label" as implying that it might not be possible to do so.) I find it very strange that you are so fearful of admitting that you understand what I am presenting that you have to go to such lengths to implement justification of that misunderstanding. However, in view of your concern with the question, I will alter #6 and #7 so as to be consistent with your desired definition of "possible".
***6. It is possible to label all of these "things" with the same symbols commonly used to label numbers.***
#6. Those "things" which constitute "Ultimate Reality" can be referred to via labels taken from the same set of symbols commonly used to label numbers.
***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.***
#7. That portion of true "Ultimate Reality" on which any individuals beliefs are based can be referred to via an unknown set of unknown numbers (that set of numbers being the symbols of which map into the labels referred to in point #6).
Harv: I'm sure you are seeing fireworks go off on what happens to (7) with the definition of 'possible' that I gave you. Your (7) says, in effect, that we might be able to refer to true portions of 'Ultimate Reality', but then again, we might not be able to so.
I must be getting close to convincing you my position is reasonable for you to be concentrating all your concern on such trivial cavils. Since I feel confident that you are going to find every cavil possible rather than admit that my points are reasonable, I will try and head off one obvious such cavil here and now. With regard to #7, I regard "that portion" as referring directly to the whole of "Ultimate Reality" if it is indeed the case that "Ultimate Reality" cannot be broken into separate reference-able things.
You seem to believe the English language is not near as vague as I believe it to be. I am of the opinion that the belief that English is not vague is the source of much bad reasoning. Furthermore, your ability to dig up alternate interpretations of what I say is a very good defense of that fact.
Harv: We shouldn't make the assumption since we don't know.
We shouldn't make the assumption we can refer to a portion of true "Ultimate Reality" because we don't know? Harv, you just referred to it. I should assume that what you do on a regular basis cannot be done? What kind of idiocy is that? Just more smoke?
By the way, you can think about this for a while as I will be out of town for roughly a week.
Have fun -- Dick