If justice is assumed to mean the doctrine of giving man what he deserves, then the central problem for Ajax is that he is not given what he feels he deserves-- the armor of Achilles. No one in the play offers a convincing argument that Ajax is unworthy of this tribute. Yet, the armor is given to men that are less worthy. In this respect, Ajax feels slighted. Next to Achilles, he is the greatest warrior in the Greek camp, and the armor should belong to him. So, even before the play begins, there has occurred an action that is embarrassing and demeaning to Ajax.
Later, we learn that in the heat of battle while besieging Troy, Ajax had offended Athena by suggesting that her assistance was not needed by him, and that she should go elsewhere to help others. Now, in terms of proper relations between mortals and gods, this was a foolish thing to say. No god wants to hear that they are unnecessary. Athena was offended, and in Greek literature when gods are offended, mortal men suffer.
Thus, when the pride of Ajax collides with the pride of Athena:
Well then, now you've seen his arrogance, make sure you never speak against the gods, or give yourself ideas of your own grandeur, if your strength of hand or heaped up riches should outweigh some other man's. A single day pulls down any human's scale of fortune or raises it once more. But the gods love men who possess good sense and self-control and despise the ones who are unjust.[164]In other words, justice implies having good sense and self-control, for the gods cannot love that which is unjust.
Here is the essential meaning of justice as it applies to men: that justice equals the will of the gods. Yet, the gods "love men who possess good sense and self-control." Hence, justice is not simply having superior power, as Thrasymachus in the Republic had argued (justice being the "will or interest of the stronger").
In slaughtering the cattle (and the men who guarded the cattle), Ajax has offended not only his fellow Greeks, but also the gods, since he has demonstrated a lack of "good sense and self-control." No man is stronger than the gods, and no man can disobey or insult them without offending justice.
The truth of the matter is that justice is a concept which applies mainly to human society. Between Zeus and all other gods, there is no justice; there is only a kind of grudging respect based on a fear of punishment, or as Thrasymachus put it, "the will of the stronger." There is no justice among gods, but there is a hierarchy of order and respect. Between gods and men, however, there are expectations of obedience based on sacrifice and proper forms of worship.
Finally, in human society, justice implies a regard for lawful conduct. If laws are broken, punishment is deemed appropriate or just. Notice that gods are never held accountable for their behavior towards men. If they break their word, they are not punished. Thus, we infer that justice has meaning only to beings holding similar moral convictions. Since gods do not "justify" themselves to men, their actions are, in a sense, "beyond the pale of law."
Of course, Socrates would add that justice must be harmonious with truth and the Good. Otherwise, justice would not be worth pursuing. Was Ajax cheated out of the honor that was due him? If so, was he entitled to exact his own measure of justice by slaughtering those who offended him? It doesn't appear so. Sophocles suggests that only gods can slaughter humans with impunity because justice is the province of immortality. In the end, Ajax receives the dignity of a proper burial and this might be the only justice to which men can aspire.