 The first is an argument from the assumed simplicity of the One. This corresponds to things we can find in Plato. In what is frequently referred to as the ‘first hypothesis’ of Plato’s Parmenides (137c-142a), Parmenides begins (137c) by laying it down that the One cannot be many; he then argues, first (137cd), that if the One is, it must be without parts, since otherwise it would be many. Subsequent argumentation makes this a proscription against all attempts to predicate anything positive of the One: any such predicate would pluralize the One, make it consist of parts. Ultimately that will include even the predicate ‘being’: it is supposed to follow that the One “in no way is” (141e9–10), that it is not; that is to say, that it is not a being (e11). It is difficult to believe that Plato himself would have bought this argument and its conclusion. He did buy into some of the train of thought: see Sophist 244b-245e. But both Plato (even in the Sophist) and Aristotle seem prepared to infer from a predication of the form ‘S is P’ a conclusion of the form ‘S is’, whereas in the first hypothesis of the Parmenides and in DCMS iv we have an argument that goes from a predication of the form ‘the One is F’ to the conclusion ‘the One is not’. This is not the place to attempt to sort out the relationship between the Platonic passages and Speusippus, but the interesting suggestion has been made (Graeser 1997, 1999; see also Halfwassen 1993) that Plato is responding to Speusippus in the Parmenides. At any rate, the Argument from Simplicity for the One’s not-being goes back to the Academy.