ora-0066

4.6 Cross-system composition is the decisive test

Spelke’s systems are often described as distinct, but human knowledge is not a permanent disjoint union of six modules. Infants and children learn that a bounded object occupies a place, that several objects have a magnitude, that an agent moves an object, and that another person can use a word to direct attention toward it. The categorical proposal is strongest precisely here: typed composition and descent should explain how partial systems form a coherent world without erasing their local invariants.

Let \(\mathbb T_i\) be the fragment sketches and \(\mathbb T_{ij}\) their interfaces. The comparison

\[ \mathsf{Mod}(\mathbb T_{\mathrm{core}}) \longrightarrow \lim \bigl( \prod _i\mathsf{Mod}(\mathbb T_i) \rightrightarrows \prod _{i,j}\mathsf{Mod}(\mathbb T_{ij}) \rightrightarrows \cdots \bigr) \]

is therefore not just technical packaging. Its failure modes distinguish three possibilities: a fragment was learned incorrectly; the overlap warrant was learned incorrectly; or the proposed core sketch does not admit the observed composition. Chapter 3 proved that effective descent turns local and overlap identification into global identification. The empirical question is whether the developmental systems actually exhibit the compatibility and uniqueness that such descent predicts.