  One way to make sense of this claim is by way of the following chain of reasoning. As we’ve seen, One-over-Many, Self-Predication, and Non-Identity together generate an infinite hierarchy of forms of largeness, each of which partakes of the forms above it in the hierarchy. Thus, L1 partakes of infinitely many forms, L2 partakes of infinitely many forms, L3 partakes of infinitely many forms, and so on. Now there are passages in which Plato appears to assume that forms are as many as the predicates that can be truly applied to them (see Philebus 14c8–d3, and Rickless (2007, 71)). And if we assume that Parmenides is still working with the Piece-of-Pie model of partaking, then the fact that a form partakes of infinitely many forms entails that it has infinitely many parts, and hence is itself infinitely many. So from the existence of an infinite regress of forms and from what appear to be dialectically appropriate assumptions, it is possible to argue that each form in the hierarchy is infinitely many. Given that the property of being one and the property of being many are contraries, it then follows directly from Purity-F that each form in the hierarchy is not one. This interpretation explains why Parmenides announces at the end of the argument that each form is no longer one, but infinitely many (see Rickless (2007, 64–75)).