Parmenides holds that the purpose of inquiry is either to determine the existence of something (so as to say that whatever is, is indeed the case) or the nonexistence of something (so as to say that something is not the case). He then points out that the former mode of inquiry is justified in that it seeks that which is, while the latter is a matter of illusion, since we cannot determine or find that which is not. This thus leads Parmenides to conclude that there is only 'the one' that is constant and continuous.
But is Parmenides himself not assuming knowledge of that which 'is not', namely knowledge about the mode of inquiry that seeks that which is not? For in order to justifiably categorize such thought as illusion rather than his own thought, which he assumes to be truth, Parmenides must possess a comparative knowledge of that which is (namely the truth he possesses) and that which is not (namely the illusion that beguiles those whom he criticizes). But such comparative knowledge unavoidably is a knowledge that posseses sense of being and nonbeing. If Parmenides would counter with a point so as to say that the knowledge he possess about such nonexistence or nonbeing is indirect, as to be an inherent aspect of the 'one' ( though this would contradict Parmenides's rejection of pluarality), than his argument would become entirely trivial, in that those who speculate about that which is in terms other than Parmenides's could likewise be speaking of such nonbeing in an indirect way, and as such needn't be subject to the main criticism offered by Parmenides.