The Lesser Hippias is a short and peculiar dialogue. Because Aristotle mentions it, evidently everyone accepts that Plato wrote it, but they like to make it very early, which I guess is a different way of accounting for its radical differences from other Socratic dialogues.
In this dialogue, Socrates is encouraged by the young Eudicus to question Hippias, who has just given a long speech. The audience has wandered off, and now just a few remain. Eudicus presses Hippias to answer to Socrates (evidently he’s supposedly still a little irritated because of the run-in they had in the Greater Hippias, but I haven’t read that one yet). The question Socrates sets is which is the greater hero, Achilles or Odysseus?
The conversation that follows leads to a very curious conclusion. First Hippias declares that Achilles is the bravest, Nestor is the wisest, and Odysseus is the “wiliest” (polutropotatos). This leads to a discussion of Odysseus as one who lies, and Achilles as one who (as he famously declares in Iliad 9) hates liars.
It’s at this point that I have come to expect the weird argument about falsehood not existing on account of the impossibility of not-being. But not here! Instead Socrates gets Hippias to agree that it’s actually the man who knows the most about truth who is the best liar (the expert mathematician is most able to lie about numbers, etc.). Returning to Achilles, Socrates suggests that he’s such a good liar that even Odysseus doesn’t notice when he says first that he’s going straight home to Phthia, but next that he’ll wait until Hector burns the ships. At this point Hippias says that Achilles lied unintentionally, and thus is better than Odysseus, who lied on purpose.
Here things get really wacky, as the Socrates who just (in the Protagoras) made the argument that nobody ever does evil intentionally, makes the argument that intentional wrong-doers are better than unintentional ones! He gets there by way of athletics (the good runner who runs slowly on purpose is better than the guy who runs slowly involuntarily, etc.). This of course seems plausible, but less so when he broadens the argument to finally conclude that “It is, then, in the nature of the good man to do injustice voluntarily, and of the bad man to do it involuntarily, that is, if the good man has a good soul… then he who voluntarily errs and does disgraceful and unjust acts, Hippias, if there be such a man, would be no other than the good man” (376b).
Clearly Socrates is mainly having a good time here, proving himself to be more polutropos than Hippias, the fan of Achilles. He does, at the end, admit that he doesn’t “agree with himself” on this conclusion, but “wanders” (planomai) — something Odysseus does a lot of as well. But can we salvage anything from the conclusion? That “the bad man does injustice involuntarily” is actually pretty much exactly what he says elsewhere. And in the Protagoras he claimed that it was impossible to be good (he does here qualify his statement with the conditional “if there be such a man”). But frankly it’s pretty weird.