The Hubble Tension and the Limits of Framework-Level Appraisal: Double Non-Termination in Cosmology

After more than a decade and over a hundred proposed resolutions, the Hubble tension has neither been absorbed by the standard cosmological model nor forced its replacement or abandonment. Standard accounts of theory change predict no such state: Kuhnian crisis resolves into revolution, Lakatosian degeneration into displacement. The state, this paper argues, is structural rather than transitional. Framework-level cosmological claims, whose assessment takes the universe as a whole as its domain, admit no external evaluative standpoint; being empirical, they have no proof-theoretic route to closure; and the discriminating evidence that once settled such claims has been consumed as the framework matured. Under these three conditions epistemic closure and the formation of performance verdicts fail together, both being forms of independent component evaluation. Such an inquiry can neither answer its questions nor stop for reasons: a condition here called double non-termination. Validation is where the failure shows, since validating a framework-level model requires a comparison standard the framework itself supplies. The argument is developed against the noetic account of progress, with evidence from episodes across the distance ladder, the dark sector, and modified gravity in which adjudicating strategies fail. The diagnosis explains why proliferation without adjudication appears in mature cosmology and not in the contrast cases examined, predicts that adjudication displaces competition upward rather than ending it, and states its own falsification conditions.