Lecture 8 — The Opinion of Pythagoras

Some philosophers seem to think that, generally speaking, justice is reciprocation, as the Pythagoreans held; in this way, they defined justice without qualification. [965]

However, reciprocation does not belong to distributive justice. [966]

Likewise, it is not suited to the justice that regulates all transactions, although Rhadamantus wished to say that it was, holding that if a man suffers what he himself did to another, justice is attained. [967]

Such justice is at variance with true justice in many situations; for example, if a prince strikes another, it is not required that the prince be struck, but if another strikes a prince, such a man should not only be struck but also punished in addition. [968]

Moreover, it makes a great deal of difference whether the offender acts voluntarily or involuntarily. [970]

But, in dealings of exchange, justice is such that it includes reciprocation according to proportionality but not according to equality. [971]

By reason of proportional reciprocation the state continues to exist, for either the citizens seek to return evil (for evil)—if not, a kind of servitude seems to be present when revenge may not be taken—or they seek to return good (for good) and if not, proper recompense will not be made. It is by return of favors that men live together. Because of this, they promptly express gratitude as if it were a sacred duty to make repayment—a thing characteristic of gratitude. It is fitting that a man should be of service to one who has done him a favor, and in return, begin to do a greater favor. [973]

A conjunction by means of a diagonal shows how to make that compensation that is according to proportionality. Let A be a builder, B a shoemaker, G a house, and D a sandal. It is necessary that a builder should take from the shoemaker his product and in return give what he himself makes. If first an equality according to proportionality be found and then reciprocation be made, it will be as we have said. But if not, there will not be an equality—and the state will not continue to exist—because nothing hinders the work of one craftsman from being of more value than the work of another. Therefore, these things must be equated. [975]

This is to be observed also in the other arts, for they would be destroyed if a workman did not receive according to the quantity and quality of what he produced. Between two doctors, an exchange does not take place, but between a doctor and a farmer who are altogether different and unequal. These then must be equated. [977]

965. Some philosophers seem to think. After the Philosopher has shown how the mean should be understood in both kinds of justice, now he rejects a false opinion about the understanding of the mean of justice.

He discusses this point under three headings.

First, he states the erroneous opinion.

Second, at however, reciprocation (1132b23; [966]), he rejects it.

Third, at but, in dealings (1132b31; [971]), he shows where and how the truth may be found.

He says first that it seems to some that, generally speaking, justice is nothing other than reciprocation, that a man should suffer according to what he has done. This was the opinion of the Pythagoreans, who decided that justice is the same as reciprocation.

966. Then, at however, reciprocation (1132b23), he rejects this opinion on two accounts; and first in regard to distributive justice, he says that reciprocation does not correspond to what is just distributively. The reason for this is evident. The just thing in distributions is not judged according to what one of two who must be equated by justice does against the other or suffers from the other. This is necessary for the nature of reciprocation; but in distribution, a share of the common goods is given to each by an equality of proportion.

967. Next, at likewise, it is not (1132b24), he rejects the preceding error in the case of commutative justice. First, he proposes what he intends to do with commutative justice. He says that reciprocation does not coincide with all the processes in justice that regulate transactions, although the philosophers who expressed the foregoing opinion meant that, in transactions, justice is the same as reciprocation. This is clear from the fact that a legislator named Rhadamantus maintained that this justice is of such a nature that if a man suffers those very things he inflicted on others, justice is vindicated.

968. Then, at such justice (1132b28), he rejects this view for two reasons. In regard to the first, he says that, in many situations, vengeance of this kind is found to be at variance with true justice. For instance, if a ruler strikes a private person, justice does not require that the ruler be struck. But if a person strikes a ruler, it is necessary that such a person not only be struck but be more gravely punished.

969. This seems to contradict what the Philosopher said before [951], that in commutative justice, the different rank of persons is not taken into account—all being equal under the law. But it should be noted that what the Philosopher had said was this: in commutative justice, the law considers only the nature of the damage. It is clear that, when damage is considered in the taking of an external thing—money, for instance—the amount of damage does not vary according to a person’s rank. Still, when the injury is personal, the extent of the injury necessarily changes according to the rank of the person. Obviously, worse damage is done when someone strikes a ruler, by reason of the fact that injury is done not only to the person of the ruler, but also the whole commonweal. Therefore, reciprocation simply taken is not suitable for justice in matters of this kind.

970. At moreover, it makes (1132b30), he gives the second reason. He says that, in the matter of imposing punishment, it makes a great deal of difference whether the offender inflicted the injury voluntarily or involuntarily, that is, because of ignorance or violence or fear. The man who sinned voluntarily ought to be punished more severely than the man who sinned involuntarily, for two reasons. First because, in regard to punishments, consideration is given to the restoration of equality of justice not only by a person restoring what he has taken but also by his being punished for the crime. For this reason some are punished by law even for sins causing no injury or damage to another. Likewise, not only is a thief compelled to restore what he took—by which the equality of justice is reestablished—but beyond that, he is punished for the offense perpetrated. But the offense is increased or diminished by the fact that a man sins voluntarily or involuntarily. Hence, the voluntary offender is punished more severely than the involuntary offender. The second reason is that the injury of the deliberate transgressor is greater, for internal contempt is added to the external damage.

971. Next, but, in dealings (1132b31), he explains in what matter and manner the statement is true that reciprocation is justice.

He discusses this point from three aspects.

First, he shows that there must be reciprocation in exchanges according to proportionality.

Second, at a conjunction by means (1133a5; [975]), he explains the form of this proportionality.

Third, at therefore, all things (1133a19; [978]), he shows how such a form can be observed.

On the initial point, he does two things.

First, he states his intention.

Second, at by reason of proportional (1132b33; [973]), he proves his statement.

He says that, in dealings of exchange, it is true that justice is of such a nature that it includes reciprocation, not according to equality, but according to proportionality.

972. It seems this is contrary to what was said before [950], that in commutative justice, the mean is taken not according to geometrical proportionality, which consists in an equality of proportion, but according to arithmetic proportionality, which consists in a quantitative equality. We must say that, in regard to commutative justice, there should always be an equality of thing to thing, but not of action and passion, which implies corresponding requital. But in this, proportionality must be employed in order to bring about an equality of things, because the work of one craftsman is of more value than the work of another, such as the building of a house compared with the production of a penknife. Hence, if the builder exchanged his work for the work of the cutler, there would not be equality of things given and taken, that is, of house and penknife.

973. Then, at by reason of proportional (1132b33), he proves his statement, saying that justice in exchanges includes reciprocation according to proportionality. This can be shown by the fact that citizens live together amicably because they have proportionate kindliness toward one another. Accordingly, if one does something for another, the other is anxious to do something in proportion in return. Obviously, all citizens desire that reciprocation be done to them proportionately. By reason of this, all men can live together because they do for one another what they themselves seek. Therefore, they never seek in regard to evil that corresponding requital be done to them proportionately. But if they do not seek this in regard to evil, for example, when one man does not take vengeance on another who injures him, a kind of servility seems to result. Indeed, it is servile when a man cannot gain by his own activity something that he does not desire in an evil way.

974. We may even say that not only do men not desire that corresponding requital be done to them proportionately when unjust, but they do not desire that it be done even when just. In this way, if corresponding requital is not done them in a proportionate way, proper retribution will not be effected. But men live together because one makes a return to another for the favors he has received. So it is that virtuous men promptly express gratitude to their benefactors as if it were a sacred duty to make them a return in this way—repaying a favor is characteristic of gratitude. It is fitting that a man should be of service to one who has done him a favor—that is, bestowed a gratuitous kindness—and that he be not content to give only as much as he received, but that, rather, in return, he begins to offer more than he got so that he himself may do a favor.

975. Next, at a conjunction by means (1133a5), he makes known the form of proportionality according to which reciprocation ought to be made. First, he gives an example in the shoemaker and the builder; then, at this is to be observed, he shows that the same is found in other arts. He says first that a conjunction by means of a diagonal shows how to make compensation or reciprocation according to proportionality. To understand this, draw ABGD, then make two diagonals intersecting one another, AD and BD. Let A represent a builder, B a shoemaker, G a house that is the work of the builder, and D a sandal that is the work of a shoemaker. It is necessary at times that the builder should take from the shoemaker his product, a sandal. But the builder himself ought to give his product as a recompense to the shoemaker.

976. Therefore, if first an equality according to proportionality is found such that a certain number of sandals be fixed as equal to one house (for a builder incurs more expense in building one house than a shoemaker in making one sandal), then there will be corresponding reciprocation, so that the builder may receive many sandals equal to one house and the shoemaker receive one house, and there will be recompense made according to proportion by a diagonal conjunction, as was said. The reason is that a proportionate number of sandals are given to the builder, and the house to the shoemaker. But if compensation is not made in this way, there will not be an equality of things exchanged—and so men will not be able to live together—since nothing hinders the work of one craftsman from being worth more than the work of another, a house than a sandal. For this reason, these things must be equated one with the other according to the previously mentioned proportionality, such that a just exchange may take place.

977. Then, at this is to be observed (1133a14; [977]), he shows that the same thing is found in the other arts. He affirms that what was said [975, 976] about the builder and the shoemaker must be observed also in the other arts, such that reciprocation and exchange may take place according to diagonal proportionality. Indeed, the arts would be destroyed if a workman did not receive according to the quantity and quality of what he produced—a thing that must be discovered in the way indicated. It is not common for men practicing one art, for example, two doctors, to communicate their work with one another, but very often men practicing different arts do, such as a doctor and a farmer, who are entirely different from each other and unequal. These must be equated in the preceding way.