Today’s developments in morphometry through pattern recognition tools developed for deep learning offer us the elements of a “geometry” obtained a posteriori from the analysis of vast data sets of objects; it is a geometry constructed by “abductive” reasoning, which is very different from the a priori hypothetico-deductive reasoning of geometry tout court. The applications of this abductive morphometric geometry are verifiable retrospectively – in its statistical adaptation to the facts it describes – and prospectively, when used to generate new forms that have a semiotic status comparable to that of “asemic writings”.