Il μεταξύ fisiologico (pseudo)presocratico e il μεταξύ matematico (pseudo)platonico

Abstract

The analysis concerns the lemma μεταξύ, namely “middle” or “intermediate” entity between two different or opposite realities. Aristotle uses it in order to elaborate a metaphysical concept in a double hermeneutic- polemic context. Firstly, with reference to the Presocratic thought he speaks of three physiological types, that’s (a) between air and water, or (b) water and fire, or (c) air and fire. This description turns out to be an anachronistic interpretation of what was originally conceived as a mere “other” (ἄλλο) or “different” (ἔτερον) one from the well-known four elements (the earth and the above mentioned three). Such a beginning witness, referring no specific and explicit name of its possible author, provokes the two following traditions: the skeptical one through Sextus Empiricus who individualizes Ideus of Imera as its theorist, perhaps at the basis of a geographical Aristotle’s allusion (Ἰταλικοί); the peripatetic-neoplatonic one which is very complicated and stratified. Nikolaos of Damascus maintains the μεταξύ air/fire against that air/water, preferred by Aristotle, and appeals to Diogenes of Apollonia as its author. This thesis is totally accepted by Porphyry against Alexander of Aphrodisia, who formerly reestablished the original peripatetic tradition with the type air/water and appealed even to Anaximander so that his conception of ἄπειρον is explained through the aforesaid posterior notion. At the end Simplicius joins up the notices from Nikolaos-Porphyry and Alexander, even if he denies that Diogenes supposed the μεταξύ as exclusive principle of the entire reality in the manner, Anaximander would have determined it. According to Simplicius the epigone had described only something totally united, including every element of whichever type, whereby the same in its absolute unity continuously diversifies itself and reunifies itself. The so-called mathematical μεταξύ, attributed to Plato by Aristotle, is not attested, because in the Platonic vision there is no middle entity of this nature with the function to mediate between the intelligible and the sensible. At the end of the VI Book of Republic, especially at 511d2, the only original text, where the term is used in a mathematical context, indeed Plato exclusively deals with a methodological approach of ‘dianoetic’ sciences (mathematics, geometry, astronomy), which, in order to demonstrate their axioms, need supports of empirical representations (as a particular material drawing of triangle used by a geometer in order to deduce its universal, intelligible proprieties of geometric nature), but have no function of mediation between the two ontological dimensions (the intelligible and the sensible).