 Now, what is the place of mathematics in Stumpf’s classification of sciences? This question was left open in our earlier remarks because the classification criteria we used were based on the cardinal distinction between phenomena and psychical functions, which underlies the main division between natural and social sciences. But as Stumpf pointed out in his paper “On the Classification of Sciences”, contrary to the method with which most classifications that are meant to be normative proceed, a classification that describes the state of a science as it is practiced at a given time in the history cannot rely on a single criterion of classification, and its task is to show how several criteria are intertwined in many ways (C. Stumpf, 1906a, p. 88). This is why one must rely on a new criterion based on the distinction between a priori and a posteriori methods in order to delineate mathematics, including geometry, from the other sciences. Indeed: