  Returning to the Parmenides passage, it should also be noted that Socrates’ description of Zeno’s book, which Plato has Zeno  endorse, indicates that its arguments had a certain structure and  purpose. Specifically, the passage indicates that all Zeno’s  arguments opposed the common-sense assumption that there are many  things. It might also suggest that these arguments took the form of  antinomies like the one Socrates specifically cites, so that the  general pattern of Zeno’s argumentation would have been: if there are many things, these must be both F and not-F; but  things cannot be both F and not-F; therefore, it  cannot be the case that there are many things. Although this  description has inspired some to attempt to accommodate the extant  paradoxes (of motion, plurality, and place) within a unified  architecture that would have provided the plan for Zeno’s original  book, if in fact he wrote only one, none of these attempts have  proved convincing. Since Plato’s description is in a number of  respects difficult to square with what we know from other sources of  Zeno’s actual arguments, one should be wary of making it the basis  for hypotheses regarding the book’s plan of organization. For one  thing, the paradoxes of motion reported by Aristotle do not evidently target the assumption that there are many things, nor do they take  the form of antinomies. Moreover, only one of the arguments against  plurality elsewhere reported, the antinomy of limited and unlimited,  conforms to the pattern of argumentation exemplified in the antinomy  of like and unlike described by Plato’s Socrates (see below, 2.1.1).  The remaining argument, the antinomy of large and small (see 2.1.2),  purports to show not only that the assumption that there are many  things leads to an apparent contradiction, but, rather more  ambitiously, it purports to reduce each of the contradictory  consequences to absurdity. Plato does not actually state, of course,  that all Zeno’s arguments took the form of antinomies. In the end, if the characterization of Zeno’s treatise by Plato’s Socrates in the  passage above is not quite accurate, there remains no more plausible  view from antiquity regarding the general thrust of his arguments, to the extent that there may have been a single one. One can, moreover,  easily broaden Socrates’ specification of the target to encompass the arguments against motion and place by changing it to the slightly  more complex thesis that there are many things that move from place  to place. Socrates might easily have been taking it for granted that, for Zeno, such motion goes along automatically with plurality. What  we know of Zeno’s arguments certainly accords with the notion that  they were meant to challenge ordinary assumptions about plurality and motion. His arguments are quite literally  “para-doxes”—from the Greek para  (“contrary to” or “against”) and  doxa (“belief” or  “opinion”)—arguments for conclusions contrary to  what people ordinarily believe. What more there might be to say about Zeno’s purposes will be discussed below, after presentation of what  we know of his actual arguments.