The antecedent is what necessitates, and that is the point of our maxim: “When the necessitant exists, the necessitated follows; and when the necessitated is absent, the necessitant is absent.” In every conditional statement, therefore, the condition is the necessitant and the result its necessitated consequence.
Cast in categorical form, this becomes: “This person is praying, and every person who prays is in a state of purification; therefore this person is purified.” Or: “This person is not purified, and whoever is not purified is not praying; therefore he is not praying.” The governing universal propositions are: “Every person who prays is purified,” and “Whoever is not purified is not praying.” Both the affirmative and the negative are universal. This universality, however, is known from the explicit wording of the Law, not from unaided reason; for had it been accessible to pure reason it would have been known through analogical reasoning. Indeed, it can be framed analogically: “This person is praying, so he is purified, like all those who pray”; or “This person is not purified, so he is not praying, like all those who lack purification.” One then shows that the shared element entails the ruling, just as in the first formulation.
The same applies to the disjunctive conditional that expresses division and alternative: when it is said, “This is either even or odd,” it is likewise said, “It must be one or the other, and the two cannot coexist. If it is even, it cannot be odd; or if it is odd, it cannot be even.” This proposition is self-evident, and grasping each instance is clearer than grasping the universal statement. Hence no instance needs to be proved by a general logical syllogism: whenever one knows something to be even, one already knows it is not odd, without appealing to some overarching universal or reasoning by analogy. There is therefore no need to say, “Every even thing is not odd,” or “Every odd thing is not even.”
Accordingly, as noted earlier, the particulars that some seek to establish through universal propositions are known without those propositions and even without analogical reasoning. If one knows that this garment—or anything else—is black, one knows that it is not white, without having to say, “Every black thing is not white.” The universal statement that whatever is black cannot be white is itself known without first knowing the theorem that two contraries cannot coexist; and were one to try to prove the particulars by means of that universal, he would still have to demonstrate that black and white are in fact contraries—something he did not know to begin with.