It is not easy to find any common bearing between the demonstrations given in this dialogue respecting [Greek: E(\n] and [Greek: Polla\]--and the observations which Plato makes in the Philêbus upon [Greek: E(\n] and [Greek: Polla/]. Would he mean to include the demonstrations which we read in the Parmenides, in the category of what he calls in Philêbus "childish, easy, and irrational debates on that vexed question?" (Plato, Philêbus, p. 14 D). Hardly: for they are at any rate most elaborate as well as ingenious and suggestive. Yet neither do they suit the description which he gives in Philêbus of the genuine, serious, and difficult debates on the same question.]
Parmenides now proceeds to his second demonstration: professing to take up again the same hypothesis--_Si Unum est_--from which he had started in the first[77]--but in reality taking up a different hypothesis under the same words. In the first hypothesis, _Si Unum est_, was equivalent to, _Si Unum est Unum_: nothing besides _Unum_ being taken into the reasoning, and _est_ serving merely as copula. In the second, _Si Unum est_, is equivalent to, _Si Unum est Ens_, or exists: so that instead of the isolated _Unum_, we have now _Unum Ens_.[78] Here is a duality consisting of _Unum and Ens_: which two are considered as separate or separable factors, coalescing to form the whole _Unum Ens_, each of them being a part thereof. But each of these parts is again dual, containing both _Unum and Ens_: so that each part may be again divided into lesser parts, each of them alike dual: and so on ad infinitum. _Unum Ens_ thus contains an infinite number of parts, or is _Multa_.[79] But even _Unum_ itself (Parmenides argues), if we consider it separately from _Ens_ in which it participates, is not _Unum_ alone, but _Multa_ also. For it is different from _Ens_, and _Ens_ is different from it. _Unum_ therefore is not merely _Unum_ but also _Diversum_: _Ens_ also is not merely _Ens_ but _Diversum_. Now when we speak of _Unum_ and _Ens_--of _Unum_ and _Diversum_--or of _Ens_ and _Diversum_--we in each case speak of two distinct things, each of which is _Unum_. Since each is _Unum_, the two things become three--_Ens_, _Diversum_, _Unum_--_Unum_, _Diversum_, _Unum_--_Unum_ being here taken twice. We thus arrive at two and three--twice and thrice--odd and even--in short, number, with its full extension and properties. Unum therefore is both Unum and Multa--both Totum and Partes--both finite and infinite in multitude.[80]