ifc-0054

3.9 The three modes in differential form

Leung’s scaffolding does not replace Boden’s modes. It clarifies the geometry within which they operate.

Mode	Differential reading	Characteristic risk
Combinational	Compose registered objects, operations, or probe shapes using the available monoidal structure.	A formally legal tensor or composition may have no semantic value.
Exploratory	Traverse and compare variations realized by \(F(A)\) while the ambient category and probe semantics remain fixed.	Local reachability can be mistaken for completeness of the conceptual space.
Transformational	Use persistent defects in local profiles to motivate a finite change of ambient theory, interpretation, or tangent action.	The local evidence underdetermines the global extension.

Table 3.1 Boden’s three creativity modes interpreted through tangent structure. The correspondence is diagnostic, not an identification of creativity with differentiation.

Combinational creativity is especially compatible with the monoidal picture: probe shapes and admissible constructions can be composed. Exploratory creativity studies the neighborhood structure generated by those probes. Transformational creativity begins when the neighborhood is persistently inadequate. It may alter the base declaration, enlarge the observer family, or replace the available differential structure.