SocratessaysThis is not the definition of justice, to speak thetruth, and to give back whatever one has received.’(I 330b) Polemarchos says ‘gives back benefits to friends and hurts to enemies’.(I.331e)He interpret the dictum as meaningthat one should benefit one’s friends and harmone’s enemy: the merit or desert concept of justice: return good for good and evil for evil: that iswhat is due. Thrasymachos says ‘Ideclare justice is nothing but the advantage of thestronger’.(I.337c) a similarpoint more elaborated made by Callicles inthe Gorgias, he argues that nature justice is theright of the strongman and the legal justice is merely the barrier which themultitude of weaklings puts up to save itself.
In AncientGreeks, expressions of practical wisdom in the poets cited asauthoritative; in Oresteia: we learn by suffering;what you do shall be done to you; in one of thepoets: justice is ‘randering to everyman hisdue’. Which become definition of justice in Roman Law; Justice is rendering to each man what is his (whatbelongs to him, is due to him).
Plato defined justiceas “giving to every men his due”. Forwhat is the due to him, is that he should be treated as what he is, in thelight of his capacities and his training, while what is due from him is thehonest performance of those tasks which the place accorded him requires.Platoargued that The Guardians need the virtue of Wisdom to carry out soundly theirfunction of governing; the auxiliaries needthe virtue of courage for the specificfunction of maintaining security and order; all three classes need the virtue of temperance to accept their experienceroles; the virtues of justice is the balance or harmony of each class performing its proper role.  Platoasserted that The just city must reduce the opportunity for selfish errors. Sorulers not allow have any private property, wife, children. Just means doingfor common, not individual, advantage, those most devoted to the common goodare most worthy of respect. InGorgias, Plato’s theory of justice observed that ‘ naturehimself intimates that it is just for the better to have more than the worse,the stronger than the weaker, and in many way she shows that among man as wellas among animals justice consists in the superior ruling over and having morethan the inferior’.  Plato was not considering any altruistic virtue such as kindness,sympathy, benevolence, generosity, but only what natural indicates to bethe essential condition of successful association. In laws, Plato to the notion of justice ‘gives to the greatermore, and to the inferior less, and in proportion to the nature of each;greater honor always to the greater virtue, and to the less less; and to eitherin proportion to their respective measure of virtue and eduction, and this isjustice. Blitz commentson Plato that Honesty might lead to bad results; justice depends on knowingwhat is good. To procure any good one would prefer an expert to a just man,justice seems useless. Honesty, law-abidingness, good character, morality, in aword, justice is seeing or doing what is good as awhole; becausejustice is the heart of a good political community,to explore it is to explore the merits of different forms of government.The justice of the whole is that each minds or does only his own job. The bestpolitical community is the just one, where each, and especially the rulers,enjoys the virtue or combinations of virtues, the moderation, courage, andwisdom, to act well. 
Aristotle terselydefined justice as ‘that virtue of the soul which is distributive according todesert’. He declared that
“politicalscience is the most excellent of all the arts and sciences, and the end soughtfor in political science is the greater good for men,which is justice, for justice is the interest of all.” He said that justice in treatingequals equally and unequal unequally, but in proportion to their relevantdifferences. One more familiar quotation on this theme by Aristotle: “God, then, as the old stonyhas it, holding the beginning and the end and the middle of all things thatexist, Proceeding by a straight path in the course of nature, brings them toaccomplishment; with him ever follow justice, the avenger of all that fallshort of the divine law-justice, in whom may he that is to be happy be from thefirst a blessed and happy partaker. The essence of law is justice, which all existinglaws should endeavour to embody as perfectly as possible ,‘ justice is the most excellent of virtues… more gloriousthan either the evening or Moring star.’ Aristotle said in Ethics BookV.Since Aristotle time, that justice involves suppression of the arbitrarydestination. ‘ the core of justice I talk to be the exclusion of arbitrages.’
Right-wing political parties tent tostress the merit conception, while left-wingpolitical parties stress the equality conception. Aristotle gave a (weak) argument forrejecting the equalitarian conception ofdistributive justice. John Rawlsingenious argument for acceptation equality needsconception and has added a less impressive argument for rejecting the merit conception.
Glauconregardsthe system of law and government as the result of social contract made in orderto avoid the worse alternative of being oppressed by tyrannical regime. Heasserts ‘all man believe in their hearts that injustice is far more profitableto the individual than justice. The injustice man has a reputation for justice. For if a man is merely just butnot also thought just, he gain nothing. Man have historically praised justiceand condemned injustice only because of their consequences. Glaucon says I know ‘most people thinkjustice is and whence it comes; all who practise it practise unwillingly, as anecessary thing but not
as a good; forthe life of the unjust is much better than the life of the just.’(II.357a) ‘Ihave never heard any account of justice such as I want to show it is betterthan injustice’.(II.357b) ‘to be unjust is good, and to suffer injustice isbad, and the excess of evil in suffering injustice is greater than the excessof good in being unjust;’.(II.357b) ‘down to present generation of men, not oneof you has ever praised justice or dispraised injustice except in terms of thereputations and honours and gifts which come from them.’(II.366a) ‘ no one hasshown that injustice is the worst evil that the soul has in itself, and justicethe greatest good.’(II.366b)
Epicureans and Sophists,with theory of the nature of virtue, maintained that justicewas merely a name for such convention among men as they should adjudgebest for their own utility and happiness. Thisis the earliest social contract. Greekphilosopher Carneades ( 2 B.C.) argued that the orthodox view of justice,assumed and demonstrate that justice was not avirtue at all, as virtue was defined by the philosophers, but was merely a convention; was what men shouldagree to be a sound basis for the maintain of civil society, and hence that it varied with times places, circumstances and even opinions.Sophists put it morality is man-made convention. The result of separating the‘ought’ from the ‘is’.
Chrysippus who excelledin logic, the theory of knowledge, ethic, and physics said: you cannot find any other beginning of justice than thatfrom Zeus and from common nature; for from this source all such must have itsbeginning, if we are to take any ground on boons and evils. 
The famous passage from Hesiod:
“ the better path to go by on the other side towards Justice; forJustice beats outrage when she comes at length to the end of the race. But onlywhen he has suffered, does the fool learn this. For oath keeps pace with wrongjudgement. There is noise when justice is being dragged in the way where thosewho devour bribes and give sentence with crooked judgements take...they whogive straight judgements to strangers and to the man of the land, and thepeople prosper in it... neither famine nor disasterever haunt men who do true justice; but light heartedly they tend thefields which are all their care.