From mathematical intermediates to an intermediate position? The case of Speusippus’ soul

This paper aims at understanding if any notion of “intermediate” is at play within Speusippus’ system. I begin by investigating this question vis-à-vis mathematical objects. Given that I subscribe to an episodic understanding of Speusippus’ world, I explain that the only possible meaning of μεταξύ in his system is that of a mere positional marker. This is because in an episodic world, the radical ontological distinction that marks off each layer of reality demands that μεταξύ mean no more than the location of an item within a ranking. This conclusion, however, provides us with an unusual candidate for the role of “intermediate”: the soul. If taken as a heuristic concept, in fact, the notion of “intermediate” allows us to see Speusippus’ soul in a different light. More specifically, given that the soul is a specific kind of substance, I argue that its intermediateness lies neither in its mixed pies in the hierarchy of beings. Rather, the soul may be regarded as an intermediary being insofar as it is that which grants human beings with their cognitive functions via interaction with the body.