ora-0058

3.13 Assimilation, ordinary accommodation, and doctrinal repair

For a transcript \(T\) and doctrine \(\mathbb T\), write \(\mathsf H_{\mathbb T}(T)\) for the fiber of consistent hypotheses. New evidence \(T\to T'\) induces

\[ r_{T,T'}:\mathsf H_{\mathbb T}(T') \longrightarrow \mathsf H_{\mathbb T}(T). \]

This supports three different responses.

  1. Assimilation chooses an object of \(\mathsf H_{\mathbb T}(T')\) whose restriction is coherently related to the current hypothesis.

  2. Ordinary accommodation changes the chosen realization inside the same nonempty fiber, possibly revising cross-fragment warrants.

  3. Doctrinal accommodation moves along an admissible sketch map \(a:\mathbb T\to \mathbb T'\) because the old doctrine no longer supports an adequate realization of the evidence.

An empty fiber is decisive but not the only possible trigger for doctrinal repair. Under approximate or noisy semantics, a fiber may be formally nonempty while every object carries a persistent, observer-visible defect. Conversely, failure of the current learner to find a model does not prove that the fiber is empty.

Design principle

Revise the learned world before revising the language of possible worlds. Revise the doctrine only when a registered obstruction rules out adequate assimilation within the current hypothesis fiber.

This principle is conservative, not dogmatic. It prevents every surprising observation from rewriting the core prior, while retaining Piagetian accommodation when the prior itself blocks coherent learning.