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] [Footnote 77: Plato, Parmenid. p. 142 A. [Greek: Bou/lei ou)=n e)pi\ tê\n u(po/thesin pa/lin e)x a)rchê=s e)pane/lthômen, e)a/n ti ê(mi=n e)paniou=sin a)lloi=on phanê=|?]] [Footnote 78: This shifting of the real hypothesis, though the terms remain unchanged, is admitted by implication a little afterwards, p. 142 B. [Greek: _nu=n de\_ ou)ch au(/tê e)/stin ê( u(po/thesis, _ei) e(\n e(\n_, ti/ chrê\ sumbai/nein, a)ll' _ei) e(\n e)/stin_.]]