We know the reasonings of Zeno and Melissus only through scanty fragments, and those fragments transmitted by opponents. But it is plain that both of them, especially Zeno, pressed their adversaries with grave difficulties, which it was more easy to deride than to elucidate. Both took their departure from the ground occupied by Parmenides. They agreed with him in recognising the phenomenal, apparent, or relative world, the world of sense and experience, as a subject of knowledge, though of uncertain and imperfect knowledge. Each of them gave, as Parmenides had done, certain affirmative opinions, or at least probable conjectures, for the purpose of explaining it.[14] But beyond this world of appearances, there lay the real, absolute, ontological, ultra-phenomenal, or Noumenal world, which Parmenides represented as _Ens unum continuum_, and which his opponents contended to be plural and discontinuous. These opponents deduced absurd and ridiculous consequences from the theory of the One. Herein both Zeno and Melissus defended Parmenides. Zeno, the better dialectician of the two, retorted upon the advocates of absolute plurality and discontinuousness, showing that their doctrine led to consequences not less absurd and contradictory than the _Ens unum_ of Parmenides. He advanced many distinct arguments; some of them antinomies, deducing from the same premisses both the affirmative and the negative of the same conclusion.[15] [Footnote 14: Diog. Laert. ix. 24-29. Zeller (Phil. d. Griech. i. p. 424, note 2) doubts the assertion that Zeno delivered probable opinions and hypotheses, as Parmenides had done before him, respecting phenomenal nature. But I see no adequate ground for such doubt.] [Footnote 15: Simplikius, in Aristotel. Physic. f. 30. [Greek: e)n me/ntoi tô=| suggra/mmati au)tou=, polla\ e)/chonti e)picheirê/mata, kath' e(/kaston dei/knusin, o(/ti tô=| polla\ ei)=nai le/gonti sumbai/nei ta\ e)nanti/a le/gein], &c.] [Side-note: Consequences of their assumption of Entia Plura Discontinua. Reductiones ad absurdum.] If things in themselves were many (he said) they must be both infinitely small and infinitely great. _Infinitely small_, because the many things must consist in a number of units, each essentially indivisible: but that which is indivisible has no magnitude, or is infinitely small if indeed it can be said to have any existence whatever:[16] _Infinitely great_, because each of the many things, if assumed to exist, must have magnitude. Having magnitude, each thing has parts which also have magnitude: these parts are, by the hypothesis, essentially discontinuous, but this implies that they are kept apart from each other by other intervening parts--and these intervening parts must be again kept apart by others. Each body will thus contain in itself an infinite number of parts, each having magnitude. In other words, it will be infinitely great.[17]