Relation between the four terms of the proportion in Distributive

Justice.

Justice, then, (as a due proportion in the distribution of honours) involves four terms at least, and the ratio between the members of the two pairs of terms will be the same, since the persons interested and the things at stake are divided. similarly. The proportion will then be—A : B :: CD (or, alternando, A: C: B : D); and hence the whole AC (which the distribution unites together) is proportionate to the whole B + D; and if they be united in the manner indicated, the distribution unites them in conformity with justice.

The joining together, therefore, of the term A to the term C, and of the term B to the term D, is what is just in the distribution of honours; and this kind of justice is a mean point between whatever violates a due proportion; what is proportionate being a mean and what is just being proportionate.

Arithmetical and geometrical pro

Mathematicians call this kind of proportion geometrical' (as opposed to arithmetical' proportion) because in geometrical proportion the whole is related to the whole precisely as each term is to each. [This proportion is of course not continuous, since the person interested and the object at stake cannot be one in number.] Justice of this kind, therefore, is 'proportionate.'

portion.

Injustice the violation of proportion.

On the other hand what is unjust' is what violates a due proportion; and such a disproportionateness is found in the forms of the more' and 'the less.' Such is the effect found in actual experience. The man who commits injustice has 'more' than is due to him of what is good; and the man who is injured has less than he should have of the good. Conversely in the case of what is 'evil:' the lesser evil becomes an item in the account of what is good,' compared, that is, with the greater evil, since a lesser evil is more desirable than a greater one, that which is desirable being a good, and that which is more desirable being a greater good.

This, then, is one aspect or form of Justice.

What is just,' therefore, is what is a mean,' and what is equal,' and what is proportionate; and Justice is the principle which produces a true mean and equality' and proportionateness in civil life. What is just is a mean because it is midway between what is too much and what is too little,' between what is above the right proportion and what is below it; in that respect being like all the other virtues, since the law of the mean is applicable to all the forms of moral excellence. But its equality is a characteristic peculiar to Justice: it renders to each man what is appropriate and fitting for him to receive: and what it gives is equal relatively to the recipient (ie. things which are appropriate are things which are fair and equal, and what is fitting is in a sense what is appropriate). Moreover, since Injustice is inequality and what is unjust is what is unequal, it will only be natural that Justice should be an equality and that what is just should be equal, as being a mean between what is too much and what is

'too little.' In any course of action in which the more' and 'the less' find a place, it is a consequence that there should be room for what is 'equal.' In fact without any argument of ours, that is the view which is universally approvedthat what is just is (what is) equal.

Justice is also proportionate' because it makes what has to be divided proportionate to the recipients according to a standard of distribution. The things which are given bear the same proportion to one another that the recipients do to each other. If Achilles is, let us say, worth double of Ajax in respect of bravery, the honour which must be paid by the just man to Achilles, will be twice as great as that which he will pay to Ajax.

In so far as Justice is a mean,' it is a mean between many extremes, since the things which lie outside the mean' are many, being distant therefrom in varying degrees of nearness or remoteness. In so far, again, as Justice is an equality,' it is an equality between two specific things-the recipient of the gift and the gift itself. (Equality' is a term of relation and always implies some two objects between which there must be an equal relationship.) In so far, again, as Justice is proportionate, it implies, at the least, four terms. Proportion must of course always lie between four objects, being as it is an equality between two ratios, each ratio consisting of two terms; and so any proportion must imply four objects. Suppose, for instance, that the ratio is twofold or threefold: there is then a scheme of relation between two quantities, one of them being double, and the other half, the other-as 20 is related to 10. Hence there must be two terms in every single ratio. If we take this same ratio in two other terms, i.e. between 12 and 6, we can then form a proportion, and we shall have as 20: 10 :: 12: 6; and so proportion will always consist in four terms at the least, though of course it may consist of more.

[If it happens that we have taken three terms and constructed a proportion out of them, e.g. as 20: 10 :: 10: 5, then, as we take the 10 twice over, there are thus found to be four terms. This kind of proportion is called 'continuous," whilst that which consists of four distinct terms, is called discrete.' Both kinds alike are distinguished by Mathematicians as 'Geometrical Proportion,' on account of there being yet another kind of Proportion which is called Arithmetical Proportion,' which is of this nature: A exceeds B, by as much as C exceeds D.'] But distributive Justice is proportionate according to the standard of geometrical proportion-for reasons which we will now state.

Let us assume that the thing which is to be distributed is honour, and that the persons among whom the honour is to be conferred are Achilles and Ajax. The honour in the one case ought to bear the same relation to the honour in the other that Achilles does to Ajax; and the honour of Achilles ought to bear the same relation to Achilles that the honour of Ajax does to Ajax; or, combining the terms together, the relation which Achilles honoured bears to Achilles ought to be the relation which Ajax honoured does to Ajax; and, inversely, the relation which Achilles honoured bears to Ajax honoured, ought to be the relation which Achilles bears to Ajax.

Now the whole proportion when it is of this form is suitable to distributive justice, being as it is of the kind which can be discovered not in arithmetical proportion, but solely in geometrical. It is shown by the geometrician that all these forms of proportion are found in geometrical proportion. But that it is impossible for them to be found in arithmetical proportion is clear from the following considerations. Suppose that there are four quantities in arithmetical proportion, 4, 3, 6, 5: then 4 exceeds 3 by as much as 6 exceeds 5. But if you combine the quantities in either ratio there will no longer be a proportion in the arithmetical sense: i.. if 6 and 5 be added together the whole will exceed 5 by 6, whereas if 4 and 3 be added together the whole will exceed 3 by 4. Conse quently these quantities only show an arithmetical proportion while disjoined (ie. there is the same excess of 4 over 3 as there is of 6 over 5). If however these quantities are combined, there is no longer a proportion :-11 exceeds 5 by more than 7 exceeds 3.

For these reasons, then, distributive justice is proportionate, according to the

principles of geometrical proportion, but that not of the continuous but of the discrete kind. The terms implied in it must be four in number, since it is impossible that the thing given and the recipient of the gift should be one in number. Justice of this kind is proportionate so far as it consists of distributions -when, that is, a man receives what is proportionate to his merit, whether honour or money or what else there be that is to be divided. By such principles it is that peace and good order are established in communities; since by different conditions civil strife and feuds and incriminations arise-when, that is, equals do not receive equal treatment, or those who are unequal are dealt with as equals. There is, moreover, this further point which makes it clear that a man who would effect an arrangement of society in accordance with justice aims at what is proportionate. All men consider that to be just which corresponds to each man's individual worth, but as to what the worth is, on account whereof a man is to be honoured, all men do not agree in their views. The lovers of a democracy say that the only condition of merit is personal freedom; the oligarchs say that wealth is the ground of merit, and aristocrats say that it is personal excellence. Since, then, there are these divergent grounds of merit, if any one be desirous of apportioning honour to each man according to his worth, and upon a principle of justice, he will not make the apportionment equal but proportionate. Justice, therefore, is the proportionate, as has been explained.

On the other hand, what is unjust is what is wide of the proportionate relation -when, that is, the distribution is made on a principle of excess or of deficiency compared with the worth of the recipients; and that is a result which is found in the general effects of wrong doing. The man who commits a wrong strives to get more good than the person injured and the person injured has less good in consequence. Conversely in the case of evil, the wrongdoer has less evil and the person injured has greater evil in consequence, since the lesser evil is more choiceworthy than the greater, and is sought for as a greater good.

Such, then, is the distributive form of Justice: we may now treat at once of the other form.

vi. -The Principles of Corrective Justice explained.

There is one remaining form of Justice, Corrective Justice, which finds its sphere in business transactions between man and man whether entered into freely or not.

The sphere in which Remedial Justice is exercised defined.

Corrective Justice has a character quite distinct from Distributive Justice. Distributive Justice, dealing with the apportionment of public goods, proceeds invariably on the principle of geometrical proportion described above:-if distribution be made to the citizens out of the public funds, the various apportionments must bear the same ratio to one another that the respective contributions of the different citizens do. (Conversely the injustice which is the direct opposite of this kind of Justice, is in contravention of this kind of proportion.)

On the other hand the Justice which arises from the transactions dependent on mutual intercourse, though a kind of equality, as Injustice is inequality, yet is not an equality according to the standard of geometrical but of arithmetical, proportion. In this view of Justice (as 'corrective' or 'remedial') it is immaterial

Remedial Justice determined by the principles of arithmetical proportion.

whether the good man has cheated the bad man or whether it be the bad man who has cheated the good man; or, again, whether the man who has committed an adultery be a good or a bad man. The law looks simply to the different degrees of injury in different cases; and where there is one man who has committed a wrong and another who has suffered it, or one man has done a harm and another man been the victim of it, the law treats the persons affected as equal (and deals simply with the inequality caused by the wrong). Wrong being an equality between the author of a wrong and its victim, the judge endeavours to make matters equal between them. When, for instance, one man has been struck and another man has dealt the blow, or when one man has been killed and another man has done the murder, the action of the one and the suffering of the other form a division into two unequal parts; but the Judge endeavours to make the relation equal by the infliction of punishment, thus taking away from the man who has profited a proportionate amount of his 'gain.' [In transactions of this kind the advantage to the aggressor is called his 'gain,' while the result to the victim is called his 'loss'though in some cases the term is inappropriate; yet when the whole circumstance is measured out in its consequences to the different parties, the consequence to the one is gain' and to the other is 'loss.']

The inequalities in contracts may be represented as loss' and 'gain' -too much and too little, which the Judge must equalise.

The equal,' therefore, is a mean point between 'too much and 'too little,' and 'gain' is too much and loss' too little, in inverse ratio to one another-too much of good and too little of evil, or too little of good and too much of evil; the mean point between the two being, as we have shown, the 'equal' which we assert to be the just.' Corrective Justice will, consequently, be a mean Hence when men are at issue themselves to the judge, since

point between 'loss' and 'gain.' between one another, they betake to have recourse to the judge is to have recourse to justice, the very purpose and raison d'être of a Judge being, as it were, to act as a living embodiment of Justice. Men in fact seek in a Judge an ideal of a right; and they sometimes call them 'Mediators,' as feeling that if they can find in them a mean ' or ideal standard of reference, they will be sure to meet with Justice. Justice, therefore, is a kind of mean if the Judge be a mediator.

Now the Judge equalizes the wrong. Just as if a line be divided into two unequal parts, he takes away from the greater section that part by which it exceeds the half, and adds the same to the less. The whole being divided into two equal parts, men

say that they have their own when they receive exactly as much as their rivals. The equal is a mean point between the greater and the less, according to the principles of arithmetical proportion. [This is, indeed, the reason why Justice is called díkalov ('division') because it divides things into equal portions, just as though one were to call Justice an equilibrium and the Judge a balancer.] Suppose, for instance, that two lines being equal a part be taken from the one and added to the other, this other line exceeds the first by twice the amount subtracted from it; whereas if the part subtracted from the one were not added to the other, this other would have only exceeded this first by once this part. Therefore the line which is added to, exceeds the mean by once the part added; and the mean again exceeds the part subtracted from, by once that part.

From these considerations we may learn what we must take away from the term which has more and what we must add to that which has less. We must add to that which has less the amount by which the mean exceeds it, and we must take from the larger term the amount by which the mean is exceeded.

Let the lines A A, B B, C C

be equal to one another. From

A

B

с

E

Ꮓ

A

-B

D

A A take E A. Add C D (equal to E A) to C C. Then the whole C C D exceeds A E by Z D, and also B B by C D.

Application of this principle to the law of supply and demand.

The very terms

This principle applies to the arts generally: they would have been annihilated but for this law of compensation -if, that is, the power of production had not produced just the quantity and the quality required for exchange, or if the consumer had not consumed a corresponding quality and quantity. 'loss' and 'gain' are derived from the associations of voluntary exchange. To have more than one's own is called 'gaining,' and to have less than at the commencement is called 'losing;' for example, in buying and selling and in other transactions generally where the law allows freedom of contract. But when a man has neither more nor less, but the outlay and return are equal, then! men say that they have their own, and neither lose nor gain. Justice, therefore, is a mean point between a kind of gain and loss, in matters outside the sphere of the voluntary, so that men have what is equal' after, as before, such transactions.

The second form of Justice is the Corrective, which has to regulate the transactions between man and man whether voluntary or involuntary, fraudulent or violent. This kind of Justice also proceeds according to a certain scheme of pro