 Thrasymachus, it turns out, is passionately committed to this ideal of the rational ruler ‘in the strict sense’, construed as the intelligently exploitative tyrant, and Socrates’ arguments against him soon zero in on it. Moreover, the ideal of the wholly rational ruler is the keystone of Plato’s own political philosophy, soon to be elaborated as the ‘philosopher-king’ of Republic V-VII (and again later in his dialogue Statesman). So it is very striking that it is first introduced in the Republic not as a Socratic concept but as a Thrasymachean one. Plato thus seems to mark it as an idea appropriated from the sophistic enemy; it is at any rate a precious piece of common ground which can provide a starting-point for arguments between Socrates and Thrasymachus, who otherwise agree on so little. 