Aristotle's Ethics Book V
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(B) The remaining one is the rectificatory, which arises in
connexion with transactions both voluntary and involuntary. This
form of the just has a different specific character from the former.
For the justice which distributes common possessions is always in
accordance with the kind of proportion mentioned above (for in the
case also in which the distribution is made from the common funds of a
partnership it will be according to the same ratio which the funds put
into the business by the partners bear to one another); and the
injustice opposed to this kind of justice is that which violates the
proportion. But the justice in transactions between man and man is a
sort of equality indeed, and the injustice a sort of inequality; not
according to that kind of proportion, however, but according to
arithmetical proportion. For it makes no difference whether a good man
has defrauded a bad man or a bad man a good one, nor whether it is a
good or a bad man that has committed adultery; the law looks only to
the distinctive character of the injury, and treats the parties as
equal, if one is in the wrong and the other is being wronged, and if
one inflicted injury and the other has received it. Therefore, this
kind of injustice being an inequality, the judge tries to equalize it;
for in the case also in which one has received and the other has
inflicted a wound, or one has slain and the other been slain, the
suffering and the action have been unequally distributed; but the
judge tries to equalize by means of the penalty, taking away from
the gain of the assailant. For the term 'gain' is applied generally to
such cases, even if it be not a term appropriate to certain cases,
e.g. to the person who inflicts a woundand 'loss' to the sufferer;
at all events when the suffering has been estimated, the one is called
loss and the other gain. Therefore the equal is intermediate between
the greater and the less, but the gain and the loss are respectively
greater and less in contrary ways; more of the good and less of the
evil are gain, and the contrary is loss; intermediate between them is,
as we saw, equal, which we say is just; therefore corrective justice
will be the intermediate between loss and gain. This is why, when
people dispute, they take refuge in the judge; and to go to the
judge is to go to justice; for the nature of the judge is to be a sort
of animate justice; and they seek the judge as an intermediate, and in
some states they call judges mediators, on the assumption that if they
get what is intermediate they will get what is just. The just, then,
is an intermediate, since the judge is so. Now the judge restores
equality; it is as though there were a line divided into unequal
parts, and he took away that by which the greater segment exceeds
the half, and added it to the smaller segment. And when the whole
has been equally divided, then they say they have 'their own'-i.e.
when they have got what is equal. The equal is intermediate between
the greater and the lesser line according to arithmetical
proportion. It is for this reason also that it is called just
(sikaion), because it is a division into two equal parts (sicha), just
as if one were to call it sichaion; and the judge (sikastes) is one
who bisects (sichastes). For when something is subtracted from one
of two equals and added to the other, the other is in excess by
these two; since if what was taken from the one had not been added
to the other, the latter would have been in excess by one only. It
therefore exceeds the intermediate by one, and the intermediate
exceeds by one that from which something was taken. By this, then,
we shall recognize both what we must subtract from that which has
more, and what we must add to that which has less; we must add to
the latter that by which the intermediate exceeds it, and subtract
from the greatest that by which it exceeds the intermediate. Let the
lines AA', BB', CC' be equal to one another; from the line AA' let the
segment AE have been subtracted, and to the line CC' let the segment
CD have been added, so that the whole line DCC' exceeds the line EA'
by the segment CD and the segment CF; therefore it exceeds the line
BB' by the segment CD. (See diagram.)

  These names, both loss and gain, have come from voluntary
exchange; for to have more than one's own is called gaining, and to
have less than one's original share is called losing, e.g. in buying
and selling and in all other matters in which the law has left
people free to make their own terms; but when they get neither more
nor less but just what belongs to themselves, they say that they
have their own and that they neither lose nor gain.

  Therefore the just is intermediate between a sort of gain and a sort
of loss, viz. those which are involuntary; it consists in having an
equal amount before and after the transaction.