Aristotele e le sfide delle matematiche del suo tempo: una “scepsi anti-scettica”

The focus is on the way how Aristotle was challenged by the complex of disciplines called by him «mathematics»: arithmetic, geometry, astronomy, harmonics, optics, and even mechanics, display according to him a precise order (taxis; cf. Metaph. M 3, 1078 a 9-16; An. Post. I 27, 87 a 31-37), culminating in «universal mathematics», that is to be identified with the general theory of proportions of Euclid’s Elem. V (cf. An. Post. I 5, 74 a 17-25). They are presented as disciplines in progress – in their terminology and definitions, as well as in their epistemological status and ontology –, that already raised “skeptical” reactions like Protagoras’ one (cf. Metaph. B 2, 997 b 34-998 a 6; 80 B 7a Diels-Kranz). Aristotle’s debate – is in his words: a skepsis (cf. Metaph. M 1, 1076 a 22) – against mathematical Platonism follows consequently an anti-skeptical line, which consists in the defense of the existence of mathematical objects so as they are defined by the experts (cf. Metaph. M 3, 1077 b 31-34).