I recently got in to philosophy and started reading The Republic. We find Socrates and others discussing the question "What is justice?"
What is /lit/'s definition of justice?
as for me, my definition would be something like this: Justice protects those who act with good intentions and punish those who act with bad intentions
Your definition sucks because everyone acts thinking they have good intentions. Everyone is the hero of their own story. Even the guy murdering his wife for cheating on him thinks he's justified and doing good.
Justice is socialized power, it goes beyond the needs of the individual in favor of the needs of society.
It doesn't have any metaphysical justification, but exists because a society with Justice has a competitive advantage over a society with Anarchy. There is no "good and evil," there is only reality, and structures that sustain and out compete other structures.
There are good objections, but that is not one. Saying you respond to intentions doesn't mean you take everyone at their word about their intentions or that you don't take an objective stance on what "good and bad intentions" are outside the opinion of the crime-committer.