It can only serve to expose in the harshest possible light the fallacy of these analytical constructs (if we may, at least pro demonstratiu, indulge the conceit of referencing them thus) to take them to their logical conclusion; for while it is not a formally constructed axiom within the framework of the Standard Model -- though one suspects that, given Godel's theorem, it could be axiomated by the Socratic method of demonstrating the unprovability of its negation -- it is accepted as a truism among idiosyncratics and traditionalists alike that any attempted isomorphism between such constructs and any concrete system, but not necessarily a subset of a system, must result in a self-contradiction which cannot be resolved without metareferencing the conditions attendant to the self-contradiction; as is demonstrated by the classic "catalogues paradox" of Set Theory that was so anathemic to Whitehead and Russell's magnum opus, notwithstanding.
basically, yeah i agree