  Supposing that being is a structural kind that functions in two ways, let us consider its operation with categorial and other structural kinds. Take some kind F-ness. F-ness is itself by itself (auto kath’ hauto), if being links F-ness to its own nature, to what F-ness is by (or because of) itself. For instance, change is changing by itself, largeness is large by itself, heat is hot by itself, the one is one by itself. The associated statements are self-predications of the sort Plato’s characters mention in earlier dialogues (“largeness is large,” “justice is just;” for self-predications in the Sophist, see 258b–c). Scholars disagree about how to understand self-predication in Plato. (For a view quite different from that articulated here, see the entry on  Plato: middle period metaphysics and epistemology.)  In self-predications the item specified by the subject-expression and the item specified by the predicate are identical, but the relation between them is participation (cf. Heinaman 1981). F-ness has its own nature by (or because of) itself. One might say that the property F-ness exhausts what F-ness is in its own right.