Nicomachean Ethics

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.