Well, the unjust man we have said is unequal, and the abstract “Unjust”
unequal: further, it is plain that there is some mean of the unequal,
that is to say, the equal or exact half (because in whatever action
there is the greater and the less there is also the equal, i.e. the
exact half). If then the Unjust is unequal the Just is equal, which all
must allow without further proof: and as the equal is a mean the Just
must be also a mean. Now the equal implies two terms at least: it
follows then that the Just is both a mean and equal, and these to
certain persons; and, in so far as it is a mean, between certain things
(that is, the greater and the less), and, so far as it is equal,
between two, and in so far as it is just it is so to certain persons.
The Just then must imply four terms at least, for those[9] to which it
is just are two, and the terms representing the things are two.
And there will be the same equality between the terms representing the
persons, as between those representing the things: because as the
latter are to one another so are the former: for if the persons are not
equal they must not have equal shares; in fact this is the very source
of all the quarrelling and wrangling in the world, when either they who
are equal have and get awarded to them things not equal, or being not
equal those things which are equal. Again, the necessity of this
equality of ratios is shown by the common phrase “according to rate,”
for all agree that the Just in distributions ought to be according to
some rate: but what that rate is to be, all do not agree; the democrats
are for freedom, oligarchs for wealth, others for nobleness of birth,
and the aristocratic party for virtue.
The Just, then, is a certain proportionable thing. For proportion does
not apply merely to number in the abstract,[10] but to number
generally, since it is equality of ratios, and implies four terms at
least (that this is the case in what may be called discrete proportion
is plain and obvious, but it is true also in continual proportion, for
this uses the one term as two, and mentions it twice; thus A:B:C may be
expressed A:B::B:C. In the first, B is named twice; and so, if, as in
the second, B is actually written twice, the proportionals will be
four): and the Just likewise implies four terms at the least, and the
ratio between the two pair of terms is the same, because the persons
and the things are divided similarly. It will stand then thus,
A:B::C:D, and then permutando A:C::B:D, and then (supposing C and D to
represent the things) A+C:B+D::A:B. The distribution in fact consisting
in putting together these terms thus: and if they are put together so
as to preserve this same ratio, the distribution puts them together
justly.[11] So then the joining together of the first and third and
second and fourth proportionals is the Just in the distribution, and
this Just is the mean relatively to that which violates the
proportionate, for the proportionate is a mean and the Just is
proportionate. Now mathematicians call this kind of proportion
geometrical: for in geometrical proportion the whole is to the whole as
each part to each part. Furthermore this proportion is not continual,
because the person and thing do not make up one term.
The Just then is this proportionate, and the Unjust that which violates
the proportionate; and so there comes to be the greater and the less:
which in fact is the case in actual transactions, because he who acts
unjustly has the greater share and he who is treated unjustly has the
less of what is good: but in the case of what is bad this is reversed:
for the less evil compared with the greater comes to be reckoned for
good, because the less evil is more choice-worthy than the greater, and
what is choice-worthy is good, and the more so the greater good.
This then is the one species of the Just.