Synonymns?

Something has been on my mind lately, although I ignored it this past weekend for personal reasons. Now it's back again.

It's related to the words: fair, justice, equality, peace.

I know fair and just have been used interchangeably, probably a lot. And you've probably noticed that too, but is the fair thing also a just thing?

 Are equality, justice, and fairness the same? I don't think they are, but I'm not exactly sure why. That's probably why this has been on my mind.

Also, peace is somehow related to fairness, equality, and justice. I've heard some people say that what is just does not always give peace, but I've also heard of an example of peace without justice. The example in question was the peaceful living in the South while slavery existed. That was not fair, it was not just, and there was definitely a lack of equality.

If the four words are related, then how do they work together to keep our society afloat?

Here are the definitions, from http://oxforddictionaries.com/  :
Fair: 1.treating people equally without favouritism or discrimination

Just: based on or behaving according to what is morally right and fair

Justice: just behaviour or treatment

Equal: 1. being the same in quantity, size, degree, or value: 

•  (of people) having the same status, rights, or opportunities
• uniform in application or effect; without discrimination on any grounds

Equality: the state of being equal, especially in status, rights, or opportunities  

Peace: 1.freedom from disturbance; tranquillity


What do you think? I'm still trying to figure it out. Maybe I'll get an answer someday.
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Added June 7, 2012

I've decided on something in regards to this topic.

What is just will give an equal opportunity, but not necessarily equal results. Equal results is equality, but not necessarily just. Fairness may result from equal opportunity, but not always. Peace comes from justice, which is not exactly fair.