  Parmenides generates the infinite regress as follows. Consider a plurality of large things, A, B, and C. By One-over-Many, there is a form of largeness (call it “L1”) by virtue of partaking of which A, B, and C are large. By Self-Predication, L1 is large. So there is now a new plurality of large things, A, B, C, and L1. Thus, by One-over-Many, there is a form of largeness (call it “L2”) by virtue of partaking of which A, B, C, and L1 are large. Hence L1 partakes of L2. At this point, Parmenides assumes something like the following Non-Identity assumption: