When Updating Becomes Canonical: A No-Go Theorem for Expressive Observational Theories

In sufficiently expressive observational settings, sharpening observation into a globally unramified architecture forces a choice: one cannot preserve both conservativity of extension and decisive completeness of the observational calculus. We call this the Unramified observation–Conservativity–Observational decisiveness (UCO) trilemma. The key mechanism is that removing observational ramification turns updating on observation from a choice among admissible rules into a canonical internal operator. Once such an update calculus is internalized in an arithmetic-interpreting fragment, Gödel-Rosser incompleteness produces undecidable observational sentences; conservativity then reflects this pressure back into the base theory, contradicting decisiveness. Philosophically, UCO sharpens Quine–Duhem holism and neo-Kantian views of framework change: resolving structural underdetermination often requires principled site enrichment, but global attempts to make observation fully lossless while preserving inherited commitments run into logical ceilings.