[Footnote 87: Plato, Parmenid. pp. 154 B, 155 C. [Greek: kata\ dê\ pa/nta tau=ta, to\ e(\n au)to/ te au(tou= kai\ tô=n a)/llôn presbu/teron kai\ neô/teron e)/sti te kai\ gi/gnetai, kai\ ou(/te presbu/teron ou(/te neô/teron ou(/t' e)/stin ou(/te gi/gnetai ou(/te au(tou= ou(/te tô=n a)/llôn.]] [Footnote 88: Plato, Parmenid. p. 155 C-D.] Here Parmenides finishes the long Demonstratio Secunda, which completes the first Antinomy. The last conclusion of all, with which it winds up, is the antithesis of that with which the first Demonstration wound up: affirming (what the conclusion of the first had denied) that Unum is thinkable, perceivable, nameable, knowable. Comparing the second Demonstration with the first, we see--That the first, taking its initial step, with a negative proposition, carries us through a series of conclusions every one of which is negative (like those of the second figure of the Aristotelian syllogism):--That whereas the conclusions professedly established in the first Demonstration are all in _Neither_ (Unum is neither in itself nor in any thing else--neither at rest nor in motion--neither the same with itself nor different from itself, &c.), the conclusions of the second Demonstration are all in _Both_ (Unum is both in motion and at rest, both in itself and in other things, both the same with itself and different from itself):--That in this manner, while the first Demonstration denies both of two opposite propositions, the second affirms them both. [Side-note: Startling paradox--Open offence against logical canon--No logical canon had then been laid down.] Such a result has an air of startling paradox. We find it shown, respecting various pairs of contradictory propositions, first, that both are false--next, that both are true. This offends doubly against the logical canon, which declares, that of two contradictory propositions, one must be true, the other must be false. We must remember, that in the Platonic age, there existed no systematic logic--no analysis or classification of propositions--no recognised distinction between such as were contrary, and such as were contradictory. The Platonic Parmenides deals with propositions which are, to appearance at least, contradictory: and we are brought, by two different roads, first to the rejection of both, next to the admission of both.[89] [Footnote 89: Prantl (in his Geschichte der Logik, vol. i. s. 3, pp. 70-71-73) maintains, if I rightly understand him, not only that Plato did not adopt the _principium identitatis et contradictionis_ as the basis of his reasonings, but that one of Plato's express objects was to demonstrate the contrary of it, partly in the Philêbus, but especially in the Parmenides:--