ora-0074

4.12 Two levels of accommodation

Let

\[ \mathsf{Lift}_u(M)= \{ M'\in \mathsf H_{\mathbb T}(T'): u^*M'\simeq M\text{ on }\mathcal Q_0\} \]

be the compatible-assimilation fiber.

Proposition 4.11 Assimilation obstruction

If \(\mathsf{Lift}_u(M)\) is empty, the new evidence cannot be conservatively assimilated into \(M\) relative to \(\mathcal Q_0\).

This obstruction does not yet say which accommodation is warranted. Ordinary accommodation chooses another object of \(\mathsf H_{\mathbb T}(T')\): the realization changes but the doctrine does not. Doctrinal accommodation changes \(\mathbb T\) along an admissible sketch morphism and transports the surviving interpretation into a different hypothesis fibration. The first response says “my theory of this world was wrong.” The second says “my language of possible worlds was too restrictive or wrongly typed.”

An empty compatible-assimilation fiber is evidence against the current realization, not automatically against the core doctrine. Doctrinal repair requires the stronger finding that adequate models remain absent, or retain a persistent observable defect, throughout the relevant old-doctrine fiber.