[Footnote 16: Aristotel. Metaphys. B. 4, p. 1001, b. 7. [Greek: e)/ti ei) a)diai/reton au)to\ to\ e(/n, kata\ me\n to\ Zê/nônos a)xi/ôma, ou)the\n a)\n ei)/ê. o(\ ga\r mê/te prostithe/menon mête\ a)phairou/menon poiei= ti mei=zon mêde\ e(/latton, ou)/ phêsin ei)=nai tou=to tô=n o)/ntôn, ô(s dê=lon o(/ti o)/ntos mege/thous tou= o)/ntos]. Seneca (Epistol. 88) and Alexander of Aphrodisias (see the passages of Themistius and Simplikius cited by Brandis, Handbuch Philos. i. p. 412-416) conceive Zeno as having dissented from Parmenides, and as having denied the existence, not only of [Greek: ta\ polla\], but also of [Greek: to\ e(/n]. But Zeno seems to have adhered to Parmenides; and to have denied the existence of [Greek: to\ e(/n], only upon the hypothesis opposed to Parmenides--namely, that [Greek: ta\ polla\] existed. Zeno argued thus:--Assuming that the Real or Absolute is essentially divisible and discontinuous, divisibility must be pushed to infinity, so that you never arrive at any ultimatum, or any real unit ([Greek: a)kribô=s e(/n]). If you admit [Greek: ta\ polla\], you renounce [Greek: to\ e(/n]. The reasoning of Zeno, as far as we know it, is nearly all directed against the hypothesis of _Entia plura discontinua_. Tennemann (Gesch. Philos. i. 4, p. 205) thinks that the reasoning of Zeno is directed against the world of sense: in which I cannot agree with him.] [Footnote 17: Scholia ad Aristotel. Physic. p. 334, a. ed. Brandis.] Again--If things in themselves were many, they would be both finite and infinite in number. _Finite_, because they are as many as they are, neither more nor less: and every number is a finite number. _Infinite_, because being essentially separate, discontinuous, units, each must be kept apart from the rest by an intervening unit; and this again by something else intervening. Suppose a multitude A, B, C, D, &c. A and B would be continuous unless they were kept apart by some intervening unit Z. But A and Z would then be continuous unless they were kept apart by something else--Y: and so on ad infinitum: otherwise the essential discontinuousness could not be maintained.[18] [Footnote 18: See the argument cited by Simplikius in the words of the Zenonian treatise, in Preller, Hist. Philos. Græc. ex font. context. p. 101, sect. 156.] By these two arguments,[19] drawn from the hypothesis which affirmed perpetual divisibility and denied any Continuum, Zeno showed that such _Entia multa discontinua_ would have contradictory attributes: they would be both infinitely great and infinitely small--they would be both finite and infinite in number. This he advanced as a _reductio ad absurdum_ against the hypothesis. [Footnote 19: Simplikius ad Aristot. Physic. f. 30. [Greek: kai\ ou)/tô me\n to\ kata\ to\ plê=thos a)/peiron e)k tê=s dichotomi/as e)/deixe, to\ de\ kata\ to\ me/gethos pro/teron kata\ tê\n au)tê\n e)pichei/rêsin]. Compare Zeller, Phil. d. Griech. i. p. 427.]