Cursus Philosophicus Thomisticus, Prima Pars Artis Logicae

In a proposition, the subject has the character of matter, as it were partial matter, with respect to the predicate, because the predicate is said of the subject and is, as it were, received in it. Again, the subject and predicate are said to be, as it were, the matter of the copula, because according to the relation and agreement of the predicate with the subject, the union itself between predicate and subject is made or not made in the proper way. This relation of the terms, from which the proposition is, as it were, composed as from matter, is called the matter of propositions absolutely.

It is threefold: natural, contingent, and remote. Natural matter is that in which one term belongs to the essence of the other; thus it either grounds an essential relation, as when you say “Man is an animal,” or a necessary relation of a proper attribute, as “Man is capable of laughter.” Contingent matter is that in which the predicate belongs accidentally to the subject and can be present or absent without corruption of the subject, as “Peter is just.” Remote matter is that in which the predicate is incompatible with the subject, as “Man is a stone.” Natural incompatibility is enough: for supernaturally, what was in remote matter—namely, God and man—came to be in natural matter after the Word became man.

Predication is either identical or formal, and likewise either direct or indirect. Identical predication is that in which the same is predicated of itself, or a synonym of a synonym, as “Man is man.” Formal predication is that in which a form, or something like a form, is predicated of something, as “Man is just,” “Man is an animal.” Direct predication is that in which what has the character of form is predicated of what has the character of subject, whether the form is essential—as a definition or part of a definition predicated of the thing defined, or a superior predicated of an inferior—or an accidental form predicated of a subject. Hence direct predication is either essential or accidental. Indirect predication is that in which, conversely, the subject is said of the form, or the thing defined of the definition, as “The colored thing is a man,” “Rational animal is a man.” Properly speaking, this is neither essential nor accidental predication. We shall treat these matters more fully in Logic, question 5, article 2.