I hope you had a good trip by the time you read this. I'm not trying trying to needlessly cavil, I want to define our words more carefully. The definition of the word 'possible' that I gave was the classical definition used in probability theory. It states that if a situation is symmetrical, the possibility for an occurrence is one in which the outcome is equally probable with any other possibility that might occur (i.e., might be this one or might not be this one). It is based on the "principle of indifference" that states that two possibilities are equally probable if there is no reason to prefer one to the other. It is clear from your last post, that you were not using the classical definition of possibility. In any case, you were kind enough to re-state (6) and (7) in the following manner:
(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) 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)).
Thanks for revising your statements to something a little less ambiguous. Just so that I understand these clarifications, please answer the following:
a) When you say that 'can be' as in (6) and (7), who is it that can do this? How do you know this 'can be' done? For example, how do you know that 'Ultimate Reality' is constituted by 'things', and therefore how do you know this labelling can be accomplished?
b) You said: "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."
My question is that if (7) is saying that 'can be' is referring to us (i.e., you, humans, physicists,.. - you choose), then how can we know if 'Ultimate Reality' cannot be broken into separate referencable things? If you don't mean us in terms of 'can be', then who are you referring? How do you know that this other party can do what you suggest?
Warm regards, Harv