We analyze a minimal formal setting in which distinguishability is induced bydescriptions, modeled as equivalence relations on a nonempty carrier and ordered byrefinement. Within this setting, we isolate two extremal totalizations: total indiscrimination and total specification. We show that these extremal regimes admit onlytrivial quotient structure and are absorbing with respect to all operations internal tothe refinement order. The results are elementary but unavoidable consequences of theformal setup. They are recorded explicitly in order to fix structural constraints thatwill be assumed, without re-derivation, in subsequent work. No assumptions are maderegarding dynamics, topology, probability, ontology, or domain-specific interpretation.
Swarup (Thu,) studied this question.