Hi Jon,
Sorry I took so long to answer. I tried to relate my question to your questions in the sense, that I tried to make a connection between the language of a statement and the meta language that describes the meaning of the statement. But did not succeed.
So finally it might just be related to the color question. Sorry that I use your forum for that!
Let the set A contain two sheep. From the point of view of A A cannot distinguish the two sheep. It is symmetric. But we can. Maybe one sheep is black, the other white. Or one is bigger, the other smaller. In a way the two sheep must have other properties, that can distinguish them, that are not defined in A or by A. If the sheep are completely identical, they have at least to different space locations, by which we can differentiate between them.
What is with space itself? What additional properties can distinguish between 2 space points?
What with a qbit? The qbit has the full SU(2) symmetry. What distinguishes two different states?
Logically speaking the set can be seen as the predicate of a proposition. Its elements are the possible subjects: "A sheep is an animal." The predicate could also be called a term. In the greek philosophy eidos. To specify what this term mean, contains, we need other term (eidos), that are not defined by the term itself. The relation between different terms (eidos) is what we call mathematics. Formally it is possible creating terms, that contain themselves, leading to the well known paradox. In the philosophy of Aristoteles the paradox do not arise, because he finally end up with the substance. He defined substance as something, that can only be the subject and not the predicate of statement. The substance is what I would call reality, or factuality.
On the way down from the eidos to the factual we face the problem how the general becomes a singular. And how we could even speak about the singular (factual), since it is singular.
In the other direction, we have Humes problem of how eidos could be derived from singular facts.
Hope this makes some sense.
Luca