In the last chapter, we went over the distributive kind of justice. Distributive justice is about taking what people have in common (e.g. profits from a business) and dividing it up into fair shares. That fairness is a kind of equality, which you can see when you look at the shares in proportion. For example, take a case with a 75%/25% split of profits of $100; the first person gets $75, and the other gets $25, you can see that 75%/$75 = 25%/$25. This is just and fair, even though they end up with different, unequal dollar amounts, and there is equality between the ratios. Things are in geometric proportion.

Now, let us go over the kind of justice that is called 'rectificatory'. Rectificatory justice is not about what people have in common. Rather, this kind of justice is about when each person already has what is their own, and then they have a dealing of some kind with each other. These dealings can be either voluntary (e.g. loaning money) or involuntary (e.g. stealing money).

If you think about what a society is and why it exists, you might reflect that a lot of it is based on the dealings that people have with each other. An unjust society will not last long, because people will not want to deal with each other and would rather avoid one another. But yet we need society in order to live full lives and enjoy all the good that comes with civilization. Man is a social animal. So it is important for us to understand rectificatory justice, both so that we can deal justly with others (and so avoid ending up in court) and we need to know when we are being unjustly dealt with (and that we should seek justice).

Rectificatory justice is different from the distributive kind of justice we were talking about before. In the distributive kind, everything has to be in a geometrical proportion for there to be justice (e.g. if you put up half the money for the business, you get half the profits). But for the rectificatory kind, it is not geometrical proportion, but rather it is an arithmetical proportion that things must be in, if there is to be justice.

But what is arithmetical proportion? In short, if I gain then that means you gain exactly the same amount; that makes us be equal, and there is justice. If I lose, then that means you lose exactly the same amount; again, we are equal, and there is justice. If we were equal before, then we must be equal after; and, when that is so, we are in arithmetical proportion.

Let us go through a quick example. We will show that arithmetical proportion means each person gets just what they paid for, no more and no less. Say we have two people (A and B) doing a trade. One person sells a horse to another for, say, 10 gold coins. Suppose that is a fair price. Normally, we would set up a proportion like this:

Person A having 1 horse = Person B having 10 gold coins

then after the trade is done we have

Person A having 10 gold coins = Person B having 1 horse

This is called an arithmetical proportion because everything, the gain and loss on both sides, adds up. Person A lost 1 horse, but got 10 gold coins. Further, that is how much the horse was really worth. So 10 - 10 = 0 (Person A got just what they paid for, everything evened out). Likewise, Person B lost a horse (which was worth 10 gold) but then they gained back the 10 gold again. And we have again, 10 - 10 = 0 (B got just what they paid for). It all evens out on both sides. One more time:

10 - 10 (change in how much Person A has) = 0 = 10 - 10 (change in how much Person B has)

It is only when one person gains more than what is right, which means that the other person now has to lose, that the transaction is out of arithmetical proportion, and is unjust.

A quick extreme example is when one person robs another. Neither person gets what they paid for, because one of them paid nothing and the other person got nothing. That is totally unjust.

But let's go back to our original example. Let's say it turns out that the coin has been debased (i.e. it is like it has been watered down) and, while there are 10 coins, the amount of gold in them is really only worth 5 gold coins. Now what do we have?

Person A having 5 gold coins = Person B having 1 horse (worth 10 gold)

5 is not equal to 10. Things are out-of-proportion. The first person (A) has lost 5 gold coins on what was supposed to be a fair deal. The second person (B) has gained 5 gold worth on the deal.

5 - 10 = -5 (Loss for Person A) is not equal to 10 - 5 = 5 (Gain for Person B)

You can tell that it is unfair because Person B could keep doing the same deal over and over again, and become rich off of the people that are cheated. It is not good for any society to have people doing good, hard work and then get cheated out of what they are ought to get.

Unfair deals are an injustice, and there are laws set up to handle such cases. It does not matter how people stand in relation to one another (like it did with distributive justice, where one person is worth more than another). The law treats both parties as equal and then looks to figure out what is the injury that was done to one side, and how much that cost them, and then it takes away from the other side enough cover the loss. For instance, in the case of selling the horse for debased coin, the judge would, at the very least, either order the unjust person to pay the 5 gold coin he owes or give back the horse. (The judge may, of course, in addition, fine the wrongdoer or make them pay for the lawyer of the injured party, etc.)

So, we start out with things being unjust when the case comes into court. And this means that things are unequal between the two sides, in some way. That is because one person does not have what they ought to have, and the other person has what they ought not. By the time the case is settled, the judge should have made things equal by taking something away from the one that did the unjust action.

OK, now think about it like this: before the unjust thing happened, both sides were equal. Now, even though the terms "gain" and "loss" do not exactly work out for every case (e.g. in cases of assault or illegal gambling), we are still going to say that the one who does the unjust act gets a "gain" of some amount and the one that suffers takes a "loss". (In the case of assault, the attacker does not really have a gain, and in the case of illegal gambling, it may be argued, that there are no real victims that suffer a loss. However, these are the exceptions, and it makes sense, overall, for us to use the terms "gain" and "loss", generally speaking, whenever the court imposes a penalty or assesses damages.) The gain and the loss make the two sides become unequal. But once the court figures out what is the measure of that "gain" and "loss" (i.e. how much money it is), the court will put a penalty on whoever did the unjust act, so that both the sides will again be equal.

Now, the judge could make the penalty be too light or too heavy. And if either of those were to happen, then there would not be equality, and justice would not be done. It is only when the judge makes the penalty be just right (i.e. equal to the amount of gain and loss) that there will then be equality, and justice would be done. So here we see, once again, that justice is a mean that lies between two extremes (viz. too light and too heavy a penalty).

At this point, let us stop and think about the meaning of the words "judge" and "just", "mediator" and "mean". (And after we tie them all together, it will easier to remember what we have been going over.) It is the judge that says what is just (viz. makes the ruling in a case). A just ruling will be at a mean (not too harsh and not too lenient). A mean is an intermediate point between two things. A mediator is someone who sets the mean, and so it is also another name for judge. And to mediate is to divide, at the point of the mean, and make the two sides be equal. So, the mediator (the judge) is someone that brings the two parties to the mean.

You can visualize it like this: imagine that there is a line that is cut into two pieces, but it is not cut straight down the middle, but somewhere else (off-center) instead, so that one side is bigger than the other. What the judge does is chop part off from the bigger side, move it over to the smaller side, and then the two are equal.

Now the terms "gain" and "loss" are also used in voluntary transactions. Here I mean the kind of transactions where the law allows there to be winners and losers. Think of markets where everyone has to decide for themselves what something is worth, and people disagree. It is normal there for it to turn out that one person loses and another gains. For example, gold is always changing price. It could go up or down. Whichever way it goes, either the buyer or the seller of the gold is going to lose, and the other person will gain. That is just how it goes. But in other transactions, they are supposed to be fair when each side gets fair value for what they gave. No one is supposed to gain or lose in these transactions. (And think here, perhaps, of moneychanging.) So the just, or what is fair, is an intermediate on both sides between getting too little for what they gave or getting too much.