ifc-0015

0.12 Two axes: Boden and Piaget

The book combines two classifications that answer different questions. Boden distinguishes how a conceptual space is used:

Combinational creativity: connects registered objects or domains.
Exploratory creativity: searches consequences generated by fixed rules.
Transformational creativity: changes the rules generating the space.

Piaget distinguishes how experience is related to a maintained schema. Assimilation interprets or repairs within the schema; accommodation revises the schema itself. These axes correlate but are not identical. A combination may be assimilatory when its interface already exists, or proto-accommodative when a new mediating type must be proposed. A long exploration can remain assimilatory. A small declaration edit can be transformational.

To keep the levels explicit, later chapters use a representational package

\[ \mathfrak R =(\mathbb S,\mathfrak D,\Lambda ,\mathcal G,\mathcal A), \]

where \(\mathbb S\) is the presentation, \(\mathfrak D\) the preservation doctrine, \(\Lambda \) the observers, \(\mathcal G\) the generative operations, and \(\mathcal A\) the admission procedures. Its differential refinement is

\[ \mathfrak R_{\mathrm{diff}} =(\mathbb S,\mathfrak D,\mathcal M,F, \Lambda ,\mathcal G,\mathcal A). \]

Assimilation keeps the relevant package fixed. Proto-accommodation probes a second local repair direction inside \(\mathfrak R_{\mathrm{dbl}}\). Accommodation changes at least one representational component through an admitted finite map and records transport to the new package.