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Thrasymachus (Θρασύμαχος) (c 459-400 BCE) was a sophist of Ancient Greece best known as a character in Plato's Republic.
In real life
Thrasymachus was a citizen of Chalcedon, on the Bosphorus. His career appears to have been spent as a sophist, at Athens as far as we know. He is credited with an increase in the rhythmic character of Greek oratory, especially the use of the paeonic rhythm in prose; also a greater appeal to the emotions through gesture.
A fragment of his work On Constitutions survives, which contains the maxim that the ancestral constitution is common to all. The meaning of this is debatable; one suggestion is that every orator can claim to speak for it, no matter what he is advocating.
There is a man by the same name mentioned in Aristotle's Politics (V.5.4) who overthrew the democracy at Cyme, but nothing is known of this event, nor can it be said with any degree of certainty that they are the same man.
In Plato
Thrasymachus' current importance derives mainly from his being a character in Plato's dialogue. He is noted for his unabashed, even reckless, defense of injustice and for his famous blush at the end of Book 1, after Socrates has tamed him. The meaning of this blush, like that of Socrates' statement in Book 6 that he and Thrasymachus "have just become friends, though we weren't even enemies before" (498c), is a source of some dispute.
There is a long philosophical tradition of exploring what exactly Thrasymachus meant in Republic I, and of taking his statements as a coherent philosophical assertion, rather than as Plato's straw man.
In the Republic I, Thrasymachus violently disagreed with the outcome of Socrates' discussion with Polemarchus about justice. Demanding payment before speaking, he claims that "justice is the advantage of the stronger" (338c) and that "injustice, if it is on a large enough scale, is stronger, freer, and more masterly than justice'" (344c). Socrates counters by forcing him to admit that there is some standard of wise rule — Thrasymachus does claim to be able to teach such a thing — and then arguing that this suggests a standard of justice beyond the advantage of the stronger. The rest of the dialogue is occasioned by Glaucon's dissatisfaction with Socrates' refutation.
His name means fierce fighter, which may have influenced his role in the dialogue.
In Leo Strauss's interpretation, Thrasymachus and his definition of justice represent the city and its laws, and thus are in a sense opposed to Socrates and to philosophy in general. As an intellectual, however, Thrasymachus shared enough with the philosopher to potentially act to protect philosophy in the city.
Quotes
338c: φημὶ γὰρ ἐγὼ εἰ̂ναι τὸ δίκαιον οὐκ ἄλλο τι ἢ τὸ του̂ κρείττονος συμφέρον.* (“Thus I say that justice is nothing other than the advantage of the stronger.”)
344c: οὕτως, ὠ̂ Σώκρατες, καὶ ἰσχυρότερον καὶ ἐλευθεριώτερον καὶ δεσποτικώτερον ἀδικία δικαιοσύνης ἐστὶν ἱκανω̂ς γιγνομένη*, καὶ ὅπερ ἐξ ἀρχη̂ς ἔλεγον, τὸ μὲν του̂ κρείττονος συμφέρον τὸ δίκαιον τυγχάνει ὄν, τὸ δ' ἄδικον ἑαυτῳ̂ λυσιτελου̂ν τε καὶ συμφέρον. * ("Thus, Socrates, injustice on a sufficiently large scale is a stronger, freer, and a more masterful thing than justice, and, as I said in the beginning, it is the advantage of the stronger that is the just, while the unjust is what profits man's self and is for his advantage.")
External links
"Thrasymachus"