One minor but representative issue sticks out at me immediately:
Were he to have access to Twitter, one could easily imagine Thrasymachus engaging furiously in late-night tweet battles.
But Thrasymachus is the person who literally demands that people pay him in order to hear his views; having erupted in incredulity, he then has to be pressed to to explain his outburst given that he is not receiving anything for it. This sort of doubtful claim would be just minor, except that the argument turns on what it means to be like Thrasymachus, the man who advocates that might makes right and that real justice is the will of the stronger, and so building up the similarities requires getting a plausible profile.
Williams notes that two claims in Trump's responses are similar to two claims in Thrasymachus's argument that injustice (in the usual sense of the word) is more beneficial to the one who can commit it than justice (in the usual sense of the word) is:
Thrasymachus defends the life of the unjust over that of the just because it is more profitable and pleasurable. Specifically, he cites two instances where the unjust life proves superior — and in ways strikingly similar to Trump’s own habits. First, “when there is an income tax, the just man will pay more and the unjust less on the same amount of income.” And second, “in private contracts . . . wherever the unjust is the partner of the just you will find that, when the partnership is dissolved, the unjust man has always more and the just less.” Thus the “smart” person, as Trump might have it, would be wise to avoid paying taxes and fulfilling contractual agreements wherever it is possible to do so with impunity. It is not difficult to recognize the Thrasymachian echoes in last week’s debate.
But we have to be quite careful here. From the fact that Thrasymachus says that the unjust pay fewer taxes it's an illicit conversion to suggest that everyone who in fact pays fewer taxes is unjust, for instance; it's quite clear that Thrasymachus does not have in mind paying the minimum taxes required of you but not paying even that. A definition in the background here is the idea that justice might be paying what is owed (the definition of Simonides that was previously discussed in the Republic), and Thrasymachus is claiming that paying what you owe leaves you worse off (because you no longer have what you paid) if you could have gotten away with not paying. It would generally be absurd to suggest, for instance, that people can't be just unless they always pay more taxes than they are legally required to pay or let themselves be cheated in business dealings. The obvious question is what is the actual obligation, what is in fact owed -- and one cannot determine whether Trump's claims fit Thrasymachus's description unless one has determined this.
The greatest difficulty with Williams's argument, though, is that there is no candidate who is likely to be a serious contender for the Office of the President of the United States who shows up very well against Plato's standards. Williams puts a lot of emphasis on wealth, but presidential candidates in general are quite wealthy. Trump as a real estate billionaire is unusually so, with a net worth of about $5 billion. But Hillary Clinton has a net worth of about $30 million; Gary Johnson has a net worth of about $7 million; and Jill Stein, far and away the poorest of the most visible presidential candidates of 2016, has a net worth of around $2 or 3 million. (Estimates from here and here.) People who can run for a major office usually can do so because they already are making at least six figures. If wealth is the problem, it is so regardless of candidate.
And it's not just wealth that is an issue. Anyone who is actively seeking office comes under some kind of suspicion in Plato's account. In a society of perfectly just people, Plato's Socrates says only half-jokingly, people would compete not to rule. We would have to go about forcing the best of us to rule us, Cincinnatus-style, and politicians would run reluctantly because they didn't see any other course available that would preserve justice. In reality, of course, this is not what we get; we get the people most eager for rule, and it's mostly a contest between people whose thirst for rule is based on a craving for power and those for whom it is based on a craving for something else, like attention. The Athenian politician who was most like a modern politician was Themistocles, and Themistocles is treated very dismissively throughout Plato's work, as the kind of politician who panders to the people and feeds them with junk.
One can also see the oddness by stepping back a moment and recognizing that Williams's argument involves a pre-selection of what will count for the similarity. For instance, you can imagine another article just like this one, pointing out that Hillary Clinton makes almost all of her rather considerable income from speeches, which is exactly the sort of thing Thrasymachus does, and that in a national security scandal she has escaped all and any punishments for actions that would get civil servants or soldiers in very serious trouble despite the fact that she in principle had greater official responsibilities on precisely those points, and that she has been dogged continually by suggestions that she indulged in pay-to-play politics, which is very much like one of the other things that Thrasymachus attributes to the unjust. One could then point out that Plato thinks all of these things tend toward tyranny, which he certainly does, and finish exactly as Williams does, with just a change of pronouns: "This is the Thrasymachian worldview. In choosing a president, Americans are now confronted with either embracing a Thrasymachus for our times or rejecting her." The same general problems would still be true, but the root of the argument, the apparent similarity, is easy to create for most politicians -- you just have to pick what to emphasize. This ties back to what I've already noted, that pretty much all modern politicians will come out looking bad, in at least some ways, on Plato's analysis of good and bad politics. One could equally turn Williams's argument into an argument not to vote; if we should be wary of voting for a Thrasymachus, what should we do when pretty much every choice is a Thrasymachus?
The argument isn't awful in every respect -- the brief discussion of pleonexia in Plato's philosophy is quite nicely done -- but the basic core of the argument simply doesn't work; it is wax-nose reasoning.
