6.2 Conceptual spaces and transformations

Boden’s distinction among combinational, exploratory, and transformational creativity is the closest direct precursor to the book’s organization [ Boden , 1998 , 2004 ] . It shifts attention from the surface novelty of an answer to the conceptual space that makes the answer possible. Wiggins develops a formal framework for describing and comparing creative systems in this spirit, making the rules, traversal mechanism, and evaluation functions explicit [ Wiggins , 2006 ] .

This tradition contributes two lasting lessons. First, novelty is relative to a repertoire and a set of generative rules. Second, changing the rules is a different operation from searching them more effectively. Those lessons align with the distinction between models of a fixed sketch and a map \(\mathbb S\to \mathbb S^+\) that changes the presentation itself.

The categorical formulation adds a semantic test to the geometric metaphor. A conceptual space is not only a region of possible artifacts. It can be a presented theory whose admissible realizations are models and whose legal transformations preserve a declared doctrine. A transformation can then be examined through restriction, extension, equivalence of presentations, and the transport of old results. This is particularly useful when two syntactically different spaces generate equivalent model categories: textual novelty alone should not be mistaken for theoretical transformation.