There are two dialogues in which Plato refers to Polemarchus. In the Phaedrus he is referred to as a man turned to philosophy. In the Republiche he enters the discussion on justice, the only discussion in which he takes part. If the Phaedrus was written after the Republic, as the modern Platonic scholarship has maintained, Polemarchus’ performance ought to enlighten us as to what Plato saw in him, so that he referred to him in the Phaedrus as he did.
Socrates broaches the theme of justice by rejecting Cephalus’ limited conception of it: ‘This then is not a definition of justice: to speak truth and to give back what one receives’ (Ouk ara houtos horos estin dikaiosunȇs, alȇthȇ te legein kai ha an labȇi tis apodidonai). ‘Yes it is (Panu men oun)’, interposes Polemarchus, ‘if Simonides is to be believed’ (eiper ge ti chrȇ Simȏnidȇi peithesthai). (331d2-5) – Socrates: ‘Tell me then (Lege dȇ), O thou heir of the argument (su ho tou logou klȇronomos) – [Polemarchus claimed to be the heir of Cephaus’ argument as his eldest son and ‘heir of all his things’] – what did Simonides say, and according to you truly say (ti phȇis ton Simȏnidȇn legonta orthȏs legein), about justice (peri dikaiosunȇs)?’ – Pol. ‘He said that the repayment of the debt is just (Hoti to ta opheilomena hekastȏi apodidonai dikaion esti), and in saying so he appears to me to be right (touto legȏn dokei emoige kalȏs legein).’ – Soc. ‘I should be sorry to doubt the word of such a wise and inspired man (Alla mentoi Simȏnidȇi ge ou raidion apistein – sophos gar kai theios anȇr), but his meaning (touto mentoi hoti pote legei), though probably clear to you (su men, ȏ Polemarche, isȏs gignȏskeis), is the reverse of clear to me (egȏ de agnoȏ).’ (331e1-4, tr. Jowett)
Jowett’s ‘clear to you’ stands for Socrates’ su gignȏskeis ‘you know’, his ‘is the reverse of clear to me’ stands for Socrates’ egȏ de agnoȏ ‘I do not know’. By pointing to Polemarchus’ thinking (isȏs) that he knows (su gignȏskeis) what Socrates does not know (egȏ de agnoȏ), Socrates indicates that Polemarchus suffers from the most disgraceful ignorance (amathia eponeidistos), that of a man thinking that he knows what he does not know (hȇ tou oiesthqi eidenai ha ouk oiden, Pl. Apology 29b2-3).
The first Book of the Republic ends with Socrates reemphasising his own ignorance: ‘And the result of the whole discussion has been that I know nothing at all (hȏste moi nuni gegonen ek tou dialogou mȇden eidenai). For I know not what justice is (hopote gar to dikaion mȇ oida ho estin), and therefore I am not likely to know whether it is or is not a virtue (scholȇi eisomai eite aretȇ tis ousa tunchanei eite kai ou), nor can I say whether the just man is happy or unhappy (kai poteron ho echȏn auto ouk eudaimȏn estin ȇ eudaimȏn).’ Plato’s two brothers, Glaucon and Adeimantus, compel Socrates in the second Book to transcend his philosophic ignorance. In the ensuing discussion Polemarchus plays no part; the significance of his exclusion is underlined by the eagerness with which he entered the discussion in Book I, and by the fact that the whole discussion takes place in his house.