As is evident, identical predication is extensionally defined, whereas formal predication is intensionally defined, since formal predication entails a relation modally determined between the subject-thing and the predicate-thing.
In fact, formal predication presupposes that there is a necessary connection between the subject-thing and the predicate-thing of the given proposition.
According to him, predication by essence (1) shows a partial identity between the subject-thing and the predicate-thing, which share some metaphysical component parts, and (2.1) does not require (or even (2.2) excludes) that the form connoted by the predicate-term is directly present in the essence signified by the subject-term.
This identity relation is a sort of intellectual composition by which we understands that the thing (res) signified by the subject term and the thing signified by the predicate term of a proposition belong to the same substance(s) (QP, q. 3, p. 250).
An affirmative proposition is true just in case that the thing or things denoted by the subject term are in the class of things denoted by the predicate term; otherwise it is false.
The realist about universals admits that the predicate 'scarlet' applies to a scarlet thing.
Similarly, a negative proposition is true just in case that no thing denoted by the subject term is a member of the class of things denoted by the predicate term.
On the other hand, the monadic predicate "is a thing", the dyadic predicate "is identical with", and the quantifier "everything" do not distinguish between Lucky Feet and the Statue of Liberty.
The predicate "aesthetic" can qualify many different kinds of things: judgments, experiences, concepts, properties, or words.
Apparently both the subject and the predicate adjective, 'The Just' and 'just', refer to the same thing, namely the Form of Justice.
The subject is the person, place, thing or idea we want to express something about; the predicate expresses the action, condition or effect of that subject.
