Okay, I think I've come up with a simple and direct (albeit very philosophical) argument: every person in this world is governed by a completely natural and perfect justice that is based upon a universal perception of the physical world: Newton's Third Law.
1.) The most basic question of philosophy: what is real? There are two major schools of thought: idealism (only the mind is real: the physical world is only there because we perceive it) and realism (only the physical world is real).
2.) Society mostly agrees that the physical world is real, and so they base the definition justice as the proper consequence for action. This is because completely private thought is only known to the individual that thinks it. Even a person who is punished for something he said or wrote is not being punished for a thought - he is being punished because he spoke or otherwise let his thoughts be known. Speech and writing both require physical action, which proves that society's idea of justice is based on the physical world. In other words, by accepting that the real world is dominant to thought, the majority of the world agrees that justice is a reflection of the physical world.
3.) If justice is based upon the physical world, then the most natural justice would be physical justice: Newton's Third Law (which has been proven beyond reasonable doubt to be truth and not theory). This law states that for every action, there is an equal and opposite reaction, which means that every action made by every single thing is met with a completely equal response. In effect, the world’s belief in realism ensures the justice of the whole world, since the physical world is governed by a universal law of natural justice.
4.) For those who believe that the physical world is a creation of the mind, the only way that justice can exist is if there is some presence or being that can know the innermost thoughts of every human being. After all, believing that action is only a response to thought (or created from thought and perception) logically implies that only thought can receive justice. In that sense, because the physical world is a perception, and because we perceive a world that is governed by Newton’s Law of natural justice, universal justice exists for these people too.
5.) No matter what strange thoughts a person might think about in regards to justice, the universal belief in either the reality of the physical world or in the world of the mind ensures that there is universal justice. It is a logical conclusion to both realism and idealism…even if some are too stupid to realize that everyone is governed under the independent and perfectly fair justice of Newton’s Third Law.
I would think you can, because the validity of this statement depends on one's philosophy of truth, justice, right and wrong- which is what would determine whether there is a standard. For instance, one might argue that the bible is the standard, because if their philosophy is that the bible is truly the inerrant word of a sovereign creator, then that would make it Truth (with a capital "T"- an absolute truth that is objective and does not change with perspective) and thus it is the ultimate standard, and this could be argued for any basis by which one believes all truth to be measured. On the other hand, if the philosophy is that there is no Truth, but only truth (no capital "T") which is subjective to one's perspective (that is, if the idea is that truth is whatever one believes it to be, with no objective measure or reference), then the statement of justice being in the eye of the one in power would be the acceptable premise. Hope this helps.