The remaining fragments of Thrasymachus’ writings provide few clues about his philosophical ideas. They either deal with rhetorical issues or they are excerpts from speeches (DK 85b1 and b2) that were (probably) written for others and thus can hardly be seen as the expression of Thrasymachus’ own thoughts. The most interesting fragment is DK 85b8. It contains the claim that the gods do not care about human affairs since they do not seem to enforce justice. Scholars have, however, been divided whether this claim is compatible with the position Plato attributes to Thrasymachus in the first book of the Republic. Plato’s account there is by far the most detailed, though perhaps historically suspect, evidence for Thrasymachus’ philosophical ideas.

In the first book of the Republic, Thrasymachus attacks Socrates’ position that justice is an important good. He claims that ‘injustice, if it is on a large enough scale, is stronger, freer, and more masterly than justice’ (344c). In the course of arguing for this conclusion, Thrasymachus makes three central claims about justice.

Justice is nothing but the advantage of the stronger (338c)
Justice is obedience to laws (339b)
Justice is nothing but the advantage of another (343c).
There is an obvious tension among these three claims. It is far from clear why somebody who follows legal regulations must always do what is in the interest of the (politically) stronger, or why these actions must serve the interests of others. Scholars have tried to resolve these tensions by emphasizing one of the three claims at the expense of the other two.

First, there are those scholars (Wilamowitz 1920, Zeller 1889, and Strauss 1952) who take (1) as the central element of Thrasymachus’ thinking about justice. According to this view, Thrasymachus is an advocate of natural right who claims that it is just (by nature) that the strong rule over the weak. This interpretation stresses the similarities between Thrasymachus’ arguments and the position Plato attributes to Callicles in the Gorgias.

A second group of scholars (Hourani 1962, and Grote 1850) emphasizes the importance of (2) and contends that Thrasymachus advocates a form of legalism. According to this interpretation, Thrasymachus is a relativist who denies that justice is anything beyond obedience to existing laws.

A third group (Kerferd 1947, Nicholson 1972) argues that (3) is the central element in Thrasymachus’ thinking about justice. Thrasymachus therefore turns out to be an ethical egoist who stresses that justice is the good of another and thus incompatible with the pursuit of one’s self-interest. Scholars in this group view Thrasymachus primarily as an ethical thinker and not as a political theorist.

In addition, there is a group of scholars (A.E. Taylor 1960, and Burnet 1964) who read Thrasymachus as an ethical nihilist. According to this view, Thrasymachus’ project is to show that justice does not exist. Burnet writes in this context: ‘[Thrasymachus] is the real ethical counterpart to the cosmological nihilism of Gorgias.’

Others (Barney 2004 and Johnson 2005) have stressed that Thrasymachus should not be read as a philosopher who offers precise definitions of justice, but rather as a sociologist or political scientist who offers empirical observations that amount to a cynical commentary on those who follow a traditional, Hesiodic conception of justice.

Finally, there are a number of scholars who claim that Thrasymachus is a confused thinker. Cross and Woozley (1964) contend, for example, that Thrasymachus advances different criteria for justice ‘without appreciating that they do not necessarily coincide.’ This claim has been renewed by Everson (1998). J.P. Maguire (1971) argues that only some of the arguments in book I of the Republic are Thrasymachus’ own, while other ideas are falsely attributed to Thrasymachus by Plato in order to prepare the ground for his own arguments.

3. Influence
In spite of the