Aristotle, Nicomachean Ethics
H. Rackham, Ed.

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 greatest¹ 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.² [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;³ [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. 5.

The view is also held by some that simple Reciprocity is Justice. This was the doctrine of the Pythagoreans, who defined the just simply as ‘suffering reciprocally with another.’⁴ [2]

Reciprocity however does not coincide either with Distributive or with Corrective Justice [3] （although people mean to identify it with the latter when they quote the rule of Rhadamanthys— “ An a man suffer even that which he did,
Right justice will be done）.

” [4] For in many cases Reciprocity is at variance with Justice: for example, if an officer strikes a man, it is wrong for the man to strike him back; and if a man strikes an officer, it is not enough for the officer to strike him, but he ought to be punished as well. [5] Again, it makes a great difference whether an act was done with or without the consent of the other party.⁵ [6] But in the interchange of services Justice in the form of Reciprocity is the bond that maintains the association: reciprocity, that is, on the basis of proportion, not on the basis of equality. The very existence of the state depends on proportionate reciprocity; for men demand that they shall be able to requite evil with evil—