An observation is not an explanation.
The limits of inferring a learner’s understanding from an observed response.
One answer.
More than one possible explanation.
A selected response is compatible with more than one generative explanation. Similar performance can arise from different strategies, and different performance can arise without a corresponding difference in the latent attribute of interest.
The central issue is not whether a model can produce an explanation. It is whether the available observations discriminate that explanation from plausible alternatives. Model expressiveness and evidential identifiability are separate properties.
Where observational equivalence persists, a fitted account can be determined partly by regularization, prior structure, or representational convention. Those commitments may be useful, but usefulness does not transform them into information supplied by the observations.
Instrument-relative observability and transportability
Observability is relative to an instrument and an admissible observation regime. A latent contrast may be distinguishable under one regime and unresolved under another. The same estimator can consequently operate in identified, partially identified, and effectively unidentified regions without an obvious change in its output format.
Transportability introduces a further separation between the stability of a fitted relation and the stability of the interpretation attached to it. A relation that persists across generated examples or simulated response structures need not preserve its meaning across human populations, instructional contexts, or exposure histories.
The relevant epistemic object is thus not a point estimate in isolation, but the set of interpretations compatible with the observation regime and its maintained assumptions. Shrinking a computational uncertainty measure does not, by itself, shrink that interpretive set.
This perspective describes a research problem and its interpretive commitments. It is not a claim of calibrated difficulty, demonstrated learning gains, or deployment of each formalism discussed.