4.15 A grounded research program

The categorical Spelke–Piaget proposal can now be evaluated through a common protocol for each core system.

1. Specify the weakest fragment sketch that expresses the hypothesized competence.

2. Define the presentations realistically available to the learner and the observers converting interaction into typed evidence.

3. State the equivalences under which competence should remain invariant.

4. Exhibit queries for which the fragment provides a presentation-stable identification gain over a weaker ambient class.

5. Specify overlaps with other systems and test whether their local models admit effective or approximate descent.

6. Predict which new evidence should be assimilated, which should revise a realization, and which would count against the doctrine itself.

This is primarily a theoretical book, so these items are theorem obligations rather than an experimental protocol implemented here. They nevertheless anchor the formalism in developmental claims. A categorical model that cannot state these contrasts has not yet captured the truth of the core-knowledge hypothesis; it has only supplied notation for it.

Guiding question.

Is there a smallest core sketch whose realizations explain the observed early invariances, whose overlaps reconstruct later compositional competence, and whose weakening provably destroys identifiable developmental queries?