According to Aristotle, there are two kinds of equality, numerical and proportional. A form of treatment of others or as a result of it a distribution is equal numerically when it treats all persons as indistinguishable, thus treating them identically or granting them the same quantity of a good per capita. That is not always just. In contrast, a form of treatment of others or distribution is proportional or relatively equal when it treats all relevant persons in relation to their due. Just numerical equality is a special case of proportional equality. Numerical equality is only just under special circumstances, when persons are equal in the relevant respects so that the relevant proportions are equal. Proportional equality further specifies formal equality.
When factors speak for unequal treatment or distribution, because the persons are unequal in relevant respects, the treatment or distribution proportional to these factors is just. Unequal claims to treatment or distribution must be considered proportionally: that is the prerequisite for persons being considered equally.
Aristotle’s idea of justice as proportional equality contains a fundamental insight. The idea offers a framework for a rational argument between egalitarian and non-egalitarian ideas of justice, its focal point being the question of the basis for an adequate equality. Both sides accept justice as proportional equality. Aristotle’s analysis makes clear that the argument involves the features deciding whether two persons are to be considered equal or unequal in a distributive context.