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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 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, 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 [Sidenote: 1131b] 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. 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 choiceworthy than the greater, and what is choiceworthy is good, and the more so the greater good.
This then is the one species of the Just.
And the remaining one is the Corrective, which arises in voluntary as well as involuntary transactions. Now this just has a different form from the aforementioned; for that which is concerned in distribution of common property is always according to the aforementioned proportion: I mean that, if the division is made out of common property, the shares will bear the same proportion to one another as the original contributions did: and the Unjust which is opposite to this Just is that which violates the proportionate.
But the Just which arises in transactions between men is an equal in a certain sense, and the Unjust an unequal, only not in the way of that proportion but of arithmetical. [Sidenote: 1132a ] Because it makes no difference whether a robbery, for instance, is committed by a good man on a bad or by a bad man on a good, nor whether a good or a bad man has committed adultery: the law looks only to the difference created by the injury and treats the men as previously equal, where the one does and the other suffers injury, or the one has done and the other suffered harm. And so this Unjust, being unequal, the judge endeavours to reduce to equality again, because really when the one party has been wounded and the other has struck him, or the one kills and the other dies, the suffering and the doing are divided into unequal shares; well, the judge tries to restore equality by penalty, thereby taking from the gain.
For these terms gain and loss are applied to these cases, though perhaps the term in some particular instance may not be strictly proper, as gain, for instance, to the man who has given a blow, and loss to him who has received it: still, when the suffering has been estimated, the one is called loss and the other gain.
And so the equal is a mean between the more and the less, which represent gain and loss in contrary ways (I mean, that the more of good and the less of evil is gain, the less of good and the more of evil is loss): between which the equal was stated to be a mean, which equal we say is Just: and so the Corrective Just must be the mean between loss and gain. And this is the reason why, upon a dispute arising, men have recourse to the judge: going to the judge is in fact going to the Just, for the judge is meant to be the personification of the Just. And men seek a judge as one in the mean, which is expressed in a name given by some to judges ([Greek: mesidioi], or middle-men) under the notion that if they can hit on the mean they shall hit on the Just. The Just is then surely a mean since the judge is also.
So it is the office of a judge to make things equal, and the line, as it were, having been unequally divided, he takes from the greater part that by which it exceeds the half, and adds this on to the less. And when the whole is divided into two exactly equal portions then men say they have their own, when they have gotten the equal; and the equal is a mean between the greater and the less according to arithmetical equality.
This, by the way, accounts for the etymology of the term by which we in Greek express the ideas of Just and Judge; ([Greek: dikaion] quasi [Greek: dichaion], that is in two parts, and [Greek: dikastaes] quasi [Greek: dichastaes], he who divides into two parts). For when from one of two equal magnitudes somewhat has been taken and added to the other, this latter exceeds the former by twice that portion: if it had been merely taken from the former and not added to the latter, then the latter would [Sidenote:1132b] have exceeded the former only by that one portion; but in the other case, the greater exceeds the mean by one, and the mean exceeds also by one that magnitude from which the portion was taken. By this illustration, then, we obtain a rule to determine what one ought to take from him who has the greater, and what to add to him who has the less. The excess of the mean over the less must be added to the less, and the excess of the greater over the mean be taken from the greater.
