The notion of essential predication is connected to what are traditionally called the categories (katêgoriai).
Underlying Aristotle's concept of a definition is the concept of essential predication (katêgoreisthai en tôi ti esti, predication in the what it is).
To speak of essential predication, it is sufficient that the same empirical reality is both the real subject and the predicate, even though the formal principle connoted by the predicate term differs from that connoted by the subject term.
For in every possible world in which God exists, these essential predications (or the propositions they express) are true.
Bucephalus is a horse, and a horse is an animal; so, "Bucephalus is a horse" and "Bucephalus is an animal" are essential predications.
Now consider the essential predication, 'God is omniscient.' Given that a truthmaker of a truth t is an entity whose existence broadly logically necessitates the truth of t, God himself is plausibly viewed as the truthmaker of 'God is omniscient' and like essential predications.
So given that God and Socrates are the truthmakers of the respective essential predications, the nominalizations can be taken to refer, not to properties, but to these very same truthmakers.
At the same time, however, Auriol wants to preserve the universality of universal concepts and their use in essential predications and necessary, scientific knowledge, and he thinks that his theory of concepts does just that.
And since the essence is substance, and the definition is a formula of the essence, for this reason we have discussed definition and essential predication.
It is evident that habitudinal predication does not require any kind of identity between the entity signified by the subject term and the entity signified by the predicate term, but formal predication and essential predication do.
