20 Creativity as Compositional Theory Change

Conclusions, Limits, and Open Domains

This book began with a deliberately difficult conjunction. Creativity appears to involve a jump: a new concept, mechanism, experiment, proof strategy, or artistic technique enters a language that did not previously contain it. Infinitesimal reasoning appears to move in the opposite way, through local variations whose effects can be differentiated, compared, and controlled. The central question has been whether a disciplined interaction between these two scales can make some creative transitions intelligible without reducing them either to an unexplained leap or to optimization of a scalar novelty score.

DIAL is the book’s proposed answer, but only within a carefully bounded scope. It treats a creative system as maintaining a compositional theory, varying its models in two interacting directions, diagnosing a persistent obstruction, and admitting a finite extension when the old theory cannot express a reusable solution. This is a categorical framework for one important class of creative processes. It is not a universal definition of creativity, nor does it claim that every human discovery was produced by double involution.