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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—
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—
1 i.e., the party that has too much.
2 The mss. here insert the sentence that appears again at 5.9 init.
3 Literally ‘where the law gives immunity,’ that is, does not give redress for inequality resulting from the contract. Should inequality result from a breach of the contract, this would of course be a case for the intervention of Corrective Justice in Voluntary Transactions (chap. 2 fin.).
4 That is, retaliation: A shall have done to him what he has done to B.
5 Literally ‘whether the act was voluntary or involuntary’; see first note on 2.13.