Aristotle, Nicomachean Ethics
H. Rackham, Ed.

The remaining kind is Corrective Justice, which operates in private transactions, both voluntary and involuntary. [2] This justice is of a different sort from the preceding. For justice in distributing common property always conforms with the proportion we have described （since when a distribution is made from the common stock, it will follow the same ratio as that between the amounts which the several persons have contributed to the common stock）; and the injustice opposed to justice of this a kind is a violation of this proportion. [3] But the just in private transactions, although it is the equal in a sense （and the unjust the unequal）, is not the equal according to geometrical but according to arithmetical proportion.¹ For it makes no difference² whether a good man has defrauded a bad man or a bad one a good one, nor whether it is a good or a bad man that has committed adultery; the law looks only at the nature of damage, treating the parties as equal, and merely asking whether one has done and the other suffered injustice, whether one inflicted and the other has sustained damage. [4] Hence the unjust being here the unequal, the judge endeavors to equalize it: inasmuch as when one man has received and the other has inflicted a blow, or one has killed and the other been killed, the line³ representing the suffering and doing of the deed is divided into unequal parts, but the judge endeavors to make them equal by the penalty or loss⁴ he imposes, taking away the gain. [5] （For the term ‘gain’ is used in a general way to apply to such cases, even though it is not strictly appropriate to some of them, for example to a person who strikes another, nor is ‘loss’ appropriate to the victim in this case; [6] but at all events the results are called ‘loss’ and ‘gain’ respectively when the amount of the damage sustained comes to be estimated.） Thus, while the equal is a mean between more and less, gain and loss are at once both more and less in contrary ways, more good and less evil being gain and more evil and less good loss; and as the equal, which we pronounce to be just, is, as we said, a mean between them, it follows that Justice in Rectification⁵ will be the mean between loss and gain. [7]

This is why when disputes occur men have recourse to a judge. To go to a judge is to go to justice, for the ideal judge is so to speak justice personified. Also, men require a judge to be a middle term or medium—indeed in some places judges are called mediators—, for they think that if they get the mean they will get what is just. Thus the just is a sort of mean, inasmuch as the judge is a medium between the litigants. [8]

Now the judge restores equality: if we represent the matter by a line divided into two unequal parts, he takes away from the greater segment that portion by which it exceeds one-half of the whole line, and adds it to the lesser segment. When the whole has been divided into two halves, people then say that they ‘have their own,’ having got what is equal. [9]

⁶This is indeed the origin of the word dikaion （just）: it means dicha （in half）, as if one were to pronounce it dichaion; and a dikast （judge） is a dichast （halver）. The equal is a mean by way of arithmetical proportion between the greater and the less. [10] For when of two equals⁷ a part is taken from the one and added to the other, the latter will exceed the former by twice that part, since if it had been taken from the one but not added to the other, the latter would exceed the former by once the part in question only. Therefore the latter will exceed the mean by once the part, and the mean will exceed the former, from which the part was taken, by once that part. [11] This process then will enable us to ascertain what we ought to take away from the party that has too much and what to add to the one that has too little: we must add to the one that has too little the amount whereby the mean between them exceeds him, and take away from the greatest⁸ of the three the amount by which the mean is exceeded by him. [12] Let the lines AA, BB, CC be equal to one another; let the segment AE be taken away from the line AA, and let the segment CD be added to the line CC, so that the whole line DCC exceeds the line EA by CD+CF; then DCC will exceed BB by CD.⁹ [13]

The terms ‘loss’ and ‘gain’ in these cases are borrowed from the operations of voluntary exchange. There, to have more than one's own is called gaining, and to have less than one had at the outset is called losing, as for instance in buying and selling, and all other transactions sanctioned by law;¹⁰ [14] while if the result of the transaction is neither an increase nor a decrease, but exactly what the parties had of themselves, they say they ‘have their own’ and have neither lost nor gained. Hence Justice in Involuntary Transactions is a mean between gain and loss in a sense: it is to have after the transaction an amount equal to the amount one had before it.