[Footnote 26: The scope of the Zenonian dialectic, as I have here described it, is set forth clearly by Plato, in his Parmenides, c. 3-6, p. 127, 128. [Greek: Pô=s ô)= Zê/nôn, tou=to le/geis? _ei) polla/ e)sti ta\ o)/nta,_ ô(s a)/ra dei= au)ta\ o(/moia/ te ei)=nai kai\ a)no/moia, tou=to de\ dê\ a)du/naton.--Ou)kou=n ei) a)du/naton ta/ te a)no/moia o(/moia ei)=nai kai\ ta\ o(/moia a)no/moia, _a)du/naton dê\ kai\ polla\ ei)=nai?_ ei) ga\r polla\ ei)/ê, pa/schoi a)\n ta\ a)du/nata. A)=ra _tou=to/ e)stin o(\ bou/lontai/ sou oi( lo/goi?_ ou)k _a)llo ti ê)\ diama/chesthai para\ pa/nta ta\ lego/mena, ô(s ou) polla/ e)stin?_] Again, p. 128 D. [Greek: A)ntile/gei ou)=n tou=to to\ gra/mma pro\s tou\s ta polla\ le/gontas, kai\ a)ntapodi/dôsi tau=ta kai\ plei/ô, tou=to boulo/menon dêlou=n, ô(s e)/ti geloio/tera pa/schoi a)\n _au)tô=n ê( u(po/thesis, ê( ei) polla/ e)stin--ê)\ ê( tou= e(\n ei)=nai--ei)/ tis i(kanô=s e)pexi/oi_].
Here Plato evidently represents Zeno as merely proving that contradictory conclusions followed, _if you assumed a given hypothesis_; which hypothesis was thereby shown to be inadmissible. But Plato alludes to Zeno in another place (Phædrus, c. 97, p. 261) under the name of the Eleatic Palamedes, as "showing his art in speaking, by making the same things appear to the hearers like and unlike, one and many, at rest and in motion". In this last passage, the impression produced by Zeno's argumentation is brought to view, apart from the scope and purpose with which he employed it: which scope and purpose are indicated in the passage above cited from the Parmenides.
So also Isokrates (Encom. Helen. init.) [Greek: Zê/nôna, to\n tau)ta\ dunata\ kai\ pa/lin a)du/nata peirô/menon a)pophai/nein.]]
[Footnote 27: Plato, Parmenides, p. 128 D.]
[Side-note: Mistake of supposing Zeno's _reductiones ad absurdum_ of an opponents doctrines to be generalisations of data gathered from experience.]
But the purport of Zeno's reasoning is mistaken, when he is conceived as one who wishes to delude his hearers by proving both sides of a contradictory proposition. Zeno's contradictory conclusions are elicited with the express purpose of disproving the premisses from which they are derived. For these premisses Zeno himself is not to be held responsible, since he borrows them from his opponents: a circumstance which Aristotle forgets, when he censures the Zenonian arguments as paralogisms, because they assume the Continua, Space, and Time, to be discontinuous or divided into many distinct parts.[28] Now this absolute discontinuousness of matter, space, and time, was not advanced by Zeno as a doctrine of his own, but is the very doctrine of his opponents, taken up by him for the purpose of showing that it led to contradictory consequences, and thus of indirectly refuting it. The sentence of Aristotle is thus really in Zeno's favour, though apparently adverse to him. In respect to motion, a similar result followed from the Zenonian reasonings; namely, to show That motion, as an attribute of the Real and Absolute, was no less inconsistent with the hypothesis of those who opposed Parmenides, than with the hypothesis of Parmenides himself:--That absolute motion could no more be reconciled with the doctrine of the discontinuous Many, than with that of the Continuous One:--That motion therefore was only a phenomenal fact, relative to our sensations, conceptions, and comparisons; and having no application to the absolute. In this phenomenal point of view, neither Zeno nor Parmenides nor Melissus disputed the fact of motion. They recognised it as a portion of the world of sensation and experience; which world they tried to explain, well or ill, by analogies and conjectures derived from itself.