Like much of creativity research, possibility studies faces two philosophical challenges: the homunculus problem, in which switches in mental activity cannot depend on an internal autonomous decision-making device (which itself would need such a device, ad infinitum); and the frame problem, in which choices of where to explore fruitfully for new ideas in a potentially infinite space of possibilities must somehow be constrained to areas of relevance that cannot be pre-determined prior to commencing exploration. In this talk, I will present PRODIGI (Progress and Discovery of Ideas In Generating Insights), a computational model implemented in ACT-R that seeks new possibilities in the products of its own failures to solve, comparing the properties of failed attempts, extracting dimensions of variability that differentiate alternative failures, and using these dimensions to discover new possibilities. The model is the first computational implementation that can find solutions to an insight problem without being provided with solution-relevant knowledge from the outset.  I will illustrate how PRODIGI addresses the homunculus and frame problems with computational and behavioural data from two puzzles: the Nine-Dot problem and the Cards problem, the latter an analogue of the challenge faced by Mendeleev in creating the periodic table of chemical elements.