Lecture 5 — Proportionality

Therefore, the just thing is something belonging to proportion, for the proportional is proper not only to abstract number, but to all enumerations. Proportionality is an equality of ratios. [938]

Proportionality consists of four parts at least. It is clear that discrete proportionality has four terms, but so does continuous proportionality, for we use one term in two different aspects and state it twice: for example, A is in proportion to B as B is to G. So B has been stated twice. Therefore, if B is used twice, there will be four proportioned terms. [940]

Like proportionality, what is just is also found in four terms at least, for both the things and persons are divided according to a similar proportion. Therefore, as the term A will be to B, so G will be to D. Hence, alternating, as A is to G, B will be to D. Therefore, the whole will be related to the whole, and this is what distribution conjoins. If adjustment be made in this way, it will be justly done. Therefore, the union of term A with G and of B with D will be the just thing and the mean guiding distribution. But the unjust thing is outside of what belongs to proportion, for the proportional is a mean and the just thing belongs to proportion. [941]

Mathematicians call this proportionality geometrical, for in geometry, it happens that the whole is compared to the whole as part to part. [944]

But this proportionality is not continuous, for there is no numerically common term for the person and the thing. [945]

This just thing, then, is proportional. But the unjust thing is outside the proportional either by excess or by defect. This occurs in distributions in which a man acts unjustly when he accepts too much and a man suffers unjustly when he has too little of good. The reverse is true in regard to evil. By comparison with a greater evil, a lesser evil has the aspect of good, for a lesser evil is preferable to a greater one. Good is preferable, and a greater good is more to be preferred. This, then, is one kind of the just thing. [946]

938. Therefore, the just thing is something. After the Philosopher has shown that the mean of distributive justice is taken according to proportionality, he now shows according to what proportionality and in what way it is understood.

He considers this point in a twofold manner.

First, he explains in what way the just thing should be taken according to a certain proportionality.

Second, at this just thing (1131b16; [946]), he shows how the unjust thing is outside that proportionality.

He discusses the initial point under three aspects.

First, he presents in advance some general comments about proportionality.

Second, at like proportionality (1131b3; [941]), he explains how the just thing consists in a certain proportionality.

Third, at mathematicians call (1131b12; [944]), he shows the nature of the proportionality by which a thing is judged just in distributive justice.

On the first point, he premises two comments.

The first is that the just thing is fittingly said to be according to proportionality, for not only is proportionality found in the enumeration of units (which is number simply taken and here called abstract number), but the quality of being proportionate is met with wherever number is found.

939. This is so because proportionality is simply geometrical equality: “this to this and that to that” contains the proportion of equality. Proportion is only a relation of one quantity to another. But quantity has the nature of a measure. It is found in numerical unity and is transferred from there to every kind of quantity, as Metaphysics 10 indicates. (Metaphysics 10.1.1052b20.; see Aquinas, In X metaph., lec. 2, n. 1938.) Therefore, number is found primarily in the enumeration of units, and after that is attributed to every genus of quantity that is measured according to the idea of number.

940. He makes the second comment at proportionality consists (1131a31), saying that every proportionality consists of four parts at least. It has a twofold division, one of which is a disjunctive proportionality, and the other a continuous proportionality. The disjunctive proportionality is an equality of two proportions not alike in any term. Therefore, when any proportion exists between the two, it is evident that the disjunctive proportionality consists of four terms, as when I say, “six is to three as ten is to five,” and there is a double proportion on both sides. The continuous proportionality is an equality of two proportions alike in one term, for instance, if I say, “as eight is to four, so four is to two,” and there is a double proportion on both sides. Therefore, in this continuous proportionality, there are in some measure four terms, inasmuch as we use one term in two different aspects, declaring it twice—namely, in either proportion—as when I say, “the proportion of A to B (or eight to four) is the same as the proportion B to C (or four to two),” and there is a double proportion from both sides. In this way, B is used twice. Hence, although B is one in subject, nevertheless, because it is taken in two different aspects, there will be four proportioned terms.

941. Then, at like proportionality (1131b3), he shows how the mean of distributive justice is taken according to proportionality. He says that, like proportionality, the just thing is found in four terms in which the same proportion is observed, because the things that are distributed and the persons to whom distribution is made are divided according to the same proportion. Therefore, let A be one term, for example, two pounds, and B one pound. But let G be one person, say, Socrates, who has worked two days, and D, Plato, who has worked one day. Therefore, as A is to B so G is to D, because a double proportion is found on the one side and the other. Hence, by alternation, as A is to G, so B is to D. Whatever things are proportionable one to another are proportionable by alternation, as is evident in the preceding example [940]—as ten is to five, so eight is to four. Therefore, by alternation, as ten is to eight, so five is to four, for there is a ratio of five to four on one side and the other. In this way, then, by alternation, it will be true to say that, as A is to G—that is, two pounds to the man who worked two days—so B is to D, that is, one pound to the man who worked a day.

942. In such matters, we must also consider that, in the things proportionable in this way, the ratio of one to the other is the ratio of the whole to the whole. For example, if the ratio ten to eight is the same as five to four, it follows further that the ratio ten to eight and five to four will be the same ratio as ten and five taken together (fifteen) to eight and four taken together (or twelve). The reason is that here we have also the ratio of five to four. How does this happen? Because fifteen contains twelve and its fourth part, namely, three.

943. In the proposition, it follows that, if this thing is to this person as that thing is to that person, then also the whole will be to the whole in the same way—that is, both things taken together will be to both persons taken together. This is as distribution connects them. If in distribution man unites the things to the persons in this way, he acts justly. It is plain, then, that the union of A with G (that is, of a thing doubled with a person doubly more deserving) and of B with D (that is, of a half thing with a person deserving only half) is the just thing in distribution, and that such a just thing is a mean. But the unjust thing is outside this proportionality. The proportional is a mean between excess and defect, because the proportionality is an equality of proportion, as has been remarked [939]. So the just thing is a mean, since it is a certain proportional.

944. At mathematicians call (1131b12), he explains the nature of the proportionality according to which this just thing is understood.

On this point, he does two things.

First, he says that the proportionality mentioned above, which is considered according to the equality of proportion, is called geometrical by mathematicians. In this, it happens that, as the whole is to the whole, so one part is to another, as we have pointed out in previous discussions [939–40]. But this does not take place in arithmetical proportionality, which we will treat later [950].

945. Second, at but this (1131b15), he says that this proportionality observed in distributive justice cannot be continuous, for on one side are the things and on the other the persons. So it is not possible to take for a common term a person to whom distribution is made and the thing that is distributed.

946. Then, at this just thing (1131b16), he considers what is unjust in distributions. He says that, since the just thing is proportionable, it follows that the unjust thing is outside the proportionable. This happens by reason of either more or less than the equality of proportion demands, as is evident in the very operations of just and unjust distribution. That man acts unjustly who accepts for himself too many goods, but he suffers unjustly who has too few. The reverse is true in regard to evils. Since a lesser evil has the aspect of good by comparison with a greater evil, the lesser evil is more to be preferred than the greater evil. Everything is chosen under the aspect of good, and for this reason, the thing that has the aspect of greater good is more to be preferred. So, then, this is one species of justice that has been discussed.