  The evidence in Simplicius indicates that Zeno then transitioned to  the antinomy’s other arm, the unlimited largeness of things, via the  following lemma: since what has no magnitude would be nothing, each  of the many must have some magnitude. Simplicius’s report of how Zeno specifically argued for the second arm’s conclusion, that each of the many is of unlimited magnitude, pertains primarily to its apparent  sub-argument for the interim conclusion that each thing has  limitlessly many parts, which ran as follows. Each of the many has  some magnitude and thickness (from the lemma). Whatever has some  magnitude and thickness will have (distinguishable) parts, so that  each of the many will have parts. If x is one of the many,  then x will have parts. Since each of these parts of  x has some magnitude and thickness, each of these parts will have its own parts, and these parts will in turn have parts of their  own, and so on, and so on, without limit. Thus each of the many will  have a limitless number of parts. Whether or not Zeno then made  explicit how the antinomy’s final conclusion followed from this, here is a plausible reconstruction of the rest of the reasoning was  presumably supposed to go: Every part of each thing has some  magnitude; the magnitude of any object is equal to the sum of the  magnitudes of its parts; and the sum of limitlessly many parts of  some magnitude is a limitless magnitude. Therefore, the magnitude of  each of the many is limitless. 