On the later Platonic dialogue (ca. 360 BC). What is a sophist? Historically, these were foreign teachers in Ancient Greece who taught young people the tools of philosophy and rhetoric, among other things, and especially they claimed to teach virtue.
In this dialogue, "the Eleatic Stranger" (i.e., not Socrates, who is present but wholly silent after the first couple of pages) is trying to figure out what a sophist really is, and in the process is showing us a new procedure for defining a word, which he calls the method of division. This is sort of like 20 questions, where you start with "animal, vegetable, or mineral?" The difference, of course, being that in 20 questions, one player already knows the answer, and you might ask whether it makes any sense at all to use such a method when you really don't know what the thing is that you're looking for. If you don't know what a gastopod is, then you can't start to answer that by asking yourself what general type of thing it is. But with "sophist," or any other term (e.g., justice, knowledge) that Plato concerns himself with, of course you know enough to start the inquiry, and the point is to get more philosophically precise. So a better example might be "what is a whale," where you start with the animal you can see and end up classifying it as mammal as opposed to fish.
The Stranger ends up classifying the sophist in several ways corresponding to various properties ascribed to sophists (Is he someone who hunts for the souls and money of young people? Is he someone who divides people from their confused beliefs? Is he someone who creates false beliefs in people's heads?) but ends up having to explore the concept of falsity, and its metaphysical correlate, non-being. The "Eleatic" in "Eleatic Stranger" is supposed to connote Parmenides, a Presocratic philosopher who famously claimed that all existence is really One, with no real change. This means that all the variation among the things we see is really illusion: all is Being, and there can be no real thing as a lack of Being. Among the many paradoxes for language coming out of this view is that we can't even rationally say that "non-being does not exist," because in doing so we're using "non-being" as the subject of the sentence—i.e., as an object, i.e., as something that in some sense exists and has this property of not existing. And this property of "not existing" of course means "partakes of non-being." So, saying that unicorns don't exist is a matter of attributing this paradoxical property to these non-things.
If Plato/the Stranger wants to claim that the sophist is a liar, then he has to make sense contra Parmenides of the idea that a sentence can be false, i.e., can refer to a state of affairs that IS NOT, that lacks being. Non-being has to in some sense be a real thing. The eventual solution in this difficult dialogue is that the concept of "other" makes talking about non-being make sense. A unicorn is not really a non-thing; it's just a thing that's different than any of the things that are in the world, or a better way of putting it is that the situation of there existing a unicorn is other than any of the situations that hold. Falsity just means "other than truth."
So, how does all this talk of sophistry vs. philosophy relate to our intellectual climate today? Why would anyone believe Parmenides in the first place, such that it's worth our time to refute him? And is this definition by the method of division just a gimmick, where for you to come up with appropriate grounds for division, you really already have to know the answer to your question in advance? Mark, Wes, and Dylan try to ferret their way through these issues in this fast-paced, comparatively difficult discussion. This means that you will likely wish to listen to most or all of our previous Plato episodes before you bother with this one, and hearing us tussle with non-Being in Hegel's Logic or with Heraclitus (a counterpoint view to Parmenides) might also help. In some ways, you might see this dialogue and other supposedly "late" Platonic works (meaning we really don't, for the most part, know what order these were written in) as a bridge between Plato and Aristotle, as this method of division and the style of the dialogue are much more dry than one might expect from Plato.
Buy the book or follow along in this online version. Dylan's fancy new Eva Brann translation is Plato : Sophist: The Professor of Wisdom (Focus Philosophical Library).
Plato picture by Genevieve Arnold.