  Parmenides sets up the argument by pointing out that, according to the theory of forms, Oneness is supposed to follow from One-over-Many. (Some, e.g., Fine (1993, 204), claim that Plato means the sentence “each form is one” to express Uniqueness, not Oneness. But this is certainly not what a relevantly similar sentence expresses at Republic 476a2–6 and 524b7–11—see above.) From the existence of a plurality of F things and the fact that, for any such plurality P, there is a form of F-ness by virtue of partaking of which each member of P is F, it follows that there is one form “over” the many members of P (in the sense of being that by virtue of partaking of which each member of P is F). And given that anything that is one “over” many is (in some sense) one, it follows that any form that has participants is one.