The overt argument against conceptualism in the Parmenides and the covert argument for conceptualism in the Sophist (with a particular focus on the being of not-being)

This contribution begins by analysing the argument against conceptualism in the Parmenides and then extends it to “the not-being” (to mê on) in the Sophist, or that which “is what is not” (258c2-3). It concludes with the puzzle that, in this case, the being of “the not-being” also has “understanding (nous), life (zôê) and soul (psychê)” (249a9). The main new points are (1) if “the not-being” has understanding (nous), “the not-being” –according to the ontological argument of the Parmenides – also has thought (noêma), which has a second “not-being” as its object and (2) the question of wether Plato would have interpreted Fragment 3 of Parmenides, to gar auto estin noein te kai einai, not only in the sense that thinking implies being, but also in the sense that being implies thinking.