I think you posed a question and used available resources ( dictionary ) to answer said question. Now thanks to your post we all know the definition of justice, thanks!
You may now consider the purpose soundly defeated.
DarkBlack, it's a difficult question. Dictionary definitions are a place to start, so we speak a common language. In the abstract, the dictionary helps. But what about in the real world?
How do you define the rightfulness or moral principle for someone who is a victim of a crime? If someone is murdered, should the killer also be killed? That would be the definition in the ancient codes of Babylon, and ancient Hebrew, and other places. In ancient Rome, if a slave killed his master, all other slaves of that master would be executed, because it was a slave's responsibility to defend the master. In one case, that meant 400 men, women, and children, were crucified.
What about the case of mistaken identity, when someone is killed because of the false, but honestly held, belief that the victim was a threat? If the killer made a mistake resulting in someone's death, is it just to deal with the killer in the same way as someone who intentionally committed murder? What of the accident, when by carelessness or distraction, a motorist kills a pedestrian? Is it just for the victim's family' that the killer is not dealt with in the same way as an intentional murder? Their loved one is just as dead either way. I don't know the answers to these.
Then there are past wrongs. A big example, underplayed and under-appreciated, is the history of slavery in the Americas. The slave trade brought tremendous profit to merchants and slave owners, by creating a manufacturing system and distribution system for sugar, rum, tobacco, and cotton. Billions of dollars in profit. That was at the expense of kidnapping somewhere around 12 million people from Africa, and somewhere around 5 million were either murdered outright (thrown off ships when they became ill, to avoid infecting other "merchandise", whipped to death, and other murders), died as a result of the trade, or died in the first year of enslavement in the plantations of the Caribbean, Brazil, and the US. After the abolition of slavery, for another century there was Jim Crow and peonage, which again involved kidnapping by false arrest, hundreds of thousands of the descendents of slaves, holding them in bondage for labor, and often working them to death. With multi-generations, spanning hundreds of years, being affected, is there a place for reparation now? What is the justice? What about families that were enriched by the process, which is just another version of concentration camp based labor? Ill-gotton gains, may be dissipated, or may have passed through many generations, or not. If the past 3 generations or so are not subjected to the same treatment, but many of their lives are still affected by the ripple effect of that treatment, who pays? Who receives? Some punishments in the bible were unto the 7th generation. Should justice in the form of reparation work that way?
To me it's unanswerable, but it is about justice.
Too much here. It's an important concept.
Justice --here is a topic I didn't want to get into too deeply because it might send encourage revile and disgust from people who are subconsciously emotive to the subject. That is because justice means specific things to specific people.
I believe justice is meaningless. Vigilante justice is the only kind of justice. A lot of people are ready to accept that morality is subjective, yet when it comes to justice, there's a knot in their hearts. Because if morality isn't specific enough, justice gets to the heart of the matter: When people do bad things, how do we respond? There's nothing that will illicit response faster than imagining the threat.
However, if, we as atheists need to go forward consistently with our beliefs, then we need to make a decision: If hard atheism and the belief that science and nothing else can be our interface to the natural world, then objective moralism seems to me to be a necessary sacrifice -- and by extension to that, objective justice. And "subjective" justice just seems contradictory, or at least arbitrary.
Objective morality (and justice) is incompatible with scientific atheism because objective morality stipulates that morality exists as a property in nature regardless of agents. If this property is theoretically observable, then it sure hasn't been proven to exist by science. If this property is non-observable, then we could eliminate it by Occam's razor in the same way that we've eliminated God, for a non-observable property does not need to exist. Furthermore, even if we could observe a morality property in nature, that would contradict many definitions of morality, because of the naturalistic fallacy. Just because something "is" in nature doesn't mean it is necessarily "right".
And if it's not observable, nor can we all agree on some basic axioms, or presuppositions (e.g. math requires many assumptions to work, such as the multiplicative axiom ab = ba), then what is it? Just something we invented out of thin air.
I agree, justice does not exist in the natural world. Is it maybe something that needs creating to keep order in society (which we also created)?