Book 5 / Chapter 3
Paragraph 2 - Justice and Proportionality
Explanation - Part By Part
"The just, then, is a species of the proportionate (proportion being not a property only of the kind of number which consists of abstract units, but of number in general)."
In this part, Aristotle is explaining that what is "just" can be understood as a kind of proportional fairness. The idea of proportion is not limited to abstract mathematical numbers or calculations—it applies broadly across relationships and comparisons in general. Essentially, justice involves maintaining a balance or equality that is proportionate to the situation or the people involved. This proportionality is central to his understanding of what is fair and just.
"For proportion is equality of ratios, and involves four terms at least (that discrete proportion involves four terms is plain, but so does continuous proportion, for it uses one term as two and mentions it twice; e.g. 'as the line A is to the line B, so is the line B to the line C'; the line B, then, has been mentioned twice, so that if the line B be assumed twice, the proportional terms will be four); and the just, too, involves at least four terms, and the ratio between one pair is the same as that between the other pair; for there is a similar distinction between the persons and between the things."
In this section, Aristotle is trying to explain justice as a kind of proportional fairness, using the concept of mathematical proportions to describe it. He says that proportion means an equality of ratios and involves at least four elements. Here's how that works:
- In a proportion, you compare two pairs of things and their relationships. For example, in the mathematical proportion "as A is to B, so is B to C," there are four terms involved: A, B, B again (repeated), and C. This makes it clear that a proportion needs at least these four elements when you consider how everything fits together.
- Aristotle connects this idea to justice. Justice, he argues, also involves at least four terms: two people (the ones receiving something) and two things (the things being distributed). The relationship or ratio between the two people should match the relationship or ratio between the two things they are receiving.
In simple terms, Aristotle is saying that justice isn't just about giving everyone the same amount—it’s about proportional fairness. If two people are not equal (say, one works harder than the other), their rewards or shares should not be equal either. Instead, the ratio of what people give or contribute should match the ratio of what they receive.
This mathematical analogy helps Aristotle show how fairness in giving and receiving is about balance and fitting rewards or distributions to the situation—not arbitrary equality.
"As the term A, then, is to B, so will C be to D, and therefore, alternando, as A is to C, B will be to D. Therefore also the whole is in the same ratio to the whole; and this coupling the distribution effects, and, if the terms are so combined, effects justly."
Aristotle is explaining how justice in distribution works by using the concept of proportional relationships, drawing on mathematical ideas of balance and ratios. He’s saying that if you compare two pairs of things—let's say A and B (representing two people) and C and D (representing two goods or rewards)—justice requires that the ratio of one person to their reward (A to C) should match the ratio of the other person to their reward (B to D).
For instance, if Person A contributes or deserves twice as much as Person B, then Person A should receive something twice the size or value of what Person B gets. This proportional match ensures fairness.
Then, Aristotle extends this idea to say that if we add up the terms in each pair (i.e., combine A and B as "all the people" and C and D as "all the things being distributed"), the overall distribution of rewards should reflect the same ratio as the individual pairs. In simpler terms, the balance isn’t just about matching individuals to their rewards but ensuring the whole system of distribution is consistent and fair.
This coupling or matching of people to their rightful shares is what Aristotle defines as "just." If something violates this proportional balance—like if one person gets way more than their fair share or someone else gets much less—then it becomes unjust.
"The conjunction, then, of the term A with C and of B with D is what is just in distribution, and this species of the just is intermediate, and the unjust is what violates the proportion; for the proportional is intermediate, and the just is proportional."
Aristotle is explaining that justice in distribution follows a principle of proportionality. Imagine there are four terms: two are the people involved (A and B), and the other two are the things being distributed (C and D). Justice happens when the distribution maintains a proportional relationship between these terms.
In simpler terms, if Person A is to receive something compared to Person B, their "share" (C and D) should correspond to their respective "merit" or qualifications. If the proportional balance between people and what they receive is preserved, the outcome is just. If this proportion is skewed or violated—say one person gets more than what they deserve compared to another—that’s when we encounter injustice.
He emphasizes that justice is about balancing relationships in a precise way, where fairness acts as an intermediate guide to ensure proportional distribution. It’s not about everyone getting the same amount, but about everyone getting what is proportional to who they are or what they deserve.
"(Mathematicians call this kind of proportion geometrical; for it is in geometrical proportion that it follows that the whole is to the whole as either part is to the corresponding part.)"
Aristotle is explaining here how the concept of justice, particularly in the sense of fairness or equitable distribution, can be thought of as a kind of proportional relationship. Specifically, he likens it to a geometrical proportion.
In geometric proportion, the relationship between parts is consistent, harmonious, and balanced. For example, in mathematics, if you have four terms in a proportion (A, B, C, D), the ratio of A to B must be equal to the ratio of C to D (A/B = C/D). Similarly, justice works in the same way: what one person receives in relation to what another person receives should reflect the equitable and fair relationship between them based on merit or relevance. In other words, fairness aligns with maintaining balance and proportionality between people (or entities) and the things being distributed.
This connection to geometry emphasizes the structured and precise nature of justice—it's not arbitrary but systematic and based on logical principles of proportional equality.
"This proportion is not continuous; for we cannot get a single term standing for a person and a thing."
In this part, Aristotle is emphasizing that the proportional relationship he describes—where the "just" distribution involves a balance between individuals and the things being distributed—cannot be seamlessly condensed into a single unified term that represents both a person and an object. In other words, it isn’t possible to find one term that equally represents and encompasses both the person receiving a share (a subject) and the thing being distributed (an object). The nature of proportional justice requires distinguishing between these two categories because people and things are fundamentally different and occupy distinct roles in this relational framework. Aristotelian justice, therefore, treats them separately while maintaining the proportional equality necessary for fairness.