Creative model-based diagrammatic cognition: The discovery of the “imaginary” non-euclidean geometry

The present article is devoted to illustrate the issue of the model-based and extra-theoretical dimension of cognition from the perspective of the famous discovery of non-Euclidean geometries. This case study is particularly appropriate because it shows relevant aspects – creative – of diagrammatic cognition, which involve intertwined processes of both explanatory and non-explanatory abduction. These processes act at the model-based level taking advantage of what I call mirror and unveiling diagrams. A description of important abductive heuristics is also provided: expansion of scope strategy, Euclidean/non-Euclidean model matching strategy, consistency-searching strategy.