On the other hand in commutations something is paid to an individual on account of something of his that has been received, as may be seen chiefly in selling and buying, where the notion of commutation is found primarily. Hence it is necessary to equalize thing with thing, so that the one person should pay back to the other just so much as he has become richer out of that which belonged to the other. The result of this will be equality according to the "arithmetical mean" which is gauged according to equal excess in quantity. Thus 5 is the mean between 6 and 4, since it exceeds the latter and is exceeded by the former, by 1. Accordingly if, at the start, both persons have 5, and one of them receives 1 out of the other's belongings, the one that is the receiver, will have 6, and the other will be left with 4: and so there will be justice if both be brought back to the mean, 1 being taken from him that has 6, and given to him that has 4, for then both will have 5 which is the mean.
Reply Obj. 1: In the other moral virtues the rational, not the real mean, is to be followed: but justice follows the real mean; wherefore the mean, in justice, depends on the diversity of things.
Reply Obj. 2: Equality is the general form of justice, wherein distributive and commutative justice agree: but in one we find equality of geometrical proportion, whereas in the other we find equality of arithmetical proportion.
Reply Obj. 3: In actions and passions a person's station affects the quantity of a thing: for it is a greater injury to strike a prince than a private person. Hence in distributive justice a person's station is considered in itself, whereas in commutative justice it is considered in so far as it causes a diversity of things. _______________________
THIRD ARTICLE [II-II, Q. 61, Art. 3]
Whether There Is a Different Matter for Both Kinds of Justice?
Objection 1: It would seem that there is not a different matter for both kinds of justice. Diversity of matter causes diversity of virtue, as in the case of fortitude and temperance. Therefore, if distributive and commutative justice have different matters, it would seem that they are not comprised under the same virtue, viz. justice.
Obj. 2: Further, the distribution that has to do with distributive justice is one of "wealth or of honors, or of whatever can be distributed among the members of the community" (Ethic. v, 2), which very things are the subject matter of commutations between one person and another, and this belongs to commutative justice. Therefore the matters of distributive and commutative justice are not distinct.
Obj. 3: Further, if the matter of distributive justice differs from that of commutative justice, for the reason that they differ specifically, where there is no specific difference, there ought to be no diversity of matter. Now the Philosopher (Ethic. v, 2) reckons commutative justice as one species, and yet this has many kinds of matter. Therefore the matter of these species of justice is, seemingly, not of many kinds.
On the contrary, It is stated in Ethic. v, 2 that "one kind of justice directs distributions, and another commutations."