From divine energeia (vestigia & oikonomia), effects proper to no other known causes, we can indeed refer (via semantical univocity, ontological analogy & apophatic predication) to the divine esse naturale/intentionale
a) determinatively, denotatively & indexically, in 1 existential, 2 numeric, 3 quantitative & 4 locative senses,
i.e. 1 THAT 2 One 3 Infinite 4 Eternal cause did create & incarnate, as well as
b) denominatively, connotatively & iconically, in 1 qualitative, 2 implicitly metaphorical & theopoetic, & 3 explicitly analogical & theological senses,
i.e. WHO & HOW of idiomata & propria.
But we cannot describe, in
c) denotative-connotative pragmatic sense, either 1 generically or 2 contextually,
1 WHAT (naturale) created & incarnated or 2 WHY (intentionale).
We can know the creation & incarnation are nonarbitrary, denominatively & connotatively, because of WHO gifted the divine vestigia & oikonomia and HOW it all donatively presents in such a profound aesthetic harmony, but not because we know WHAT or WHY, generically or determinatively.
WHY did we come home to a locked house? I don’t know the reason but my Father always has loving purposes, so He locked it lovingly. Perhaps he had set off a poisonous pesticide bomb? Was that necessary? No, for he’s obscenely wealthy. We could’ve just moved to another house with no roaches. Or any number of other choices available on a Pareto Frontier of otherwise equal optimalities.
We could say we know THAT an act was purposeful & nonarbitrary because we know WHO authored it and HOW they always act (a defense), even as we insist we don’t know WHY (a theodicy).
While we don’t eschew vague answers (defenses) to the logical problem of evil, we resist specific answers (theodicies) to evidential problems of evil.
Deeper into the logic:
For determinate syllogistics, think 3 modes of being: essential, personal & formal; 1 of identity: formal.
For semantics of this modal ontology, think possibilities, actualities & probabilities, where, respectively: NC folds, EM holds; NC/EM hold; NC holds, EM folds.
Actualities/Persons in potency to Possibilities/Essences; Efficient in potency to Material for actualities; Formal in potency to Final for probabilities. Respectively, Acts of Being (naturale) & Willing/Becoming (intentionale).
For divine syllogistics, think 3 modes of identity: essential, personal & formal, as w/o modal ontology or potency, but w/immanent universal, i.e. pure act of being, self-subsisting esse naturale, essentially – like a primary substance & personally – an exemplification, semantically referenced, respectively, by propria & idiomata.
How would we analogically differentiate, though, divine from determinate esse intentionale?
For determinate rational beings, willing (intentionale) always entails becoming, either more or less, what the divine will intends them to be (naturale), as we freely (willingly) participate or not (willfully) in acts of being & willing per potencies or limitations as divinely willed.
Human persons are thus adequately but not fully determined, free to become or not, in degrees, only who we were intended, to participate or not, per divinely willed limitations or potencies, in being. We are free to be & to will to become walking self-contradictions.
For divine being, intrinsically, noncontradiction obtains essentially, personally & formally for esse naturale, as nondeterminate being.
For kenotic divine being, when self-determinate in extrinsic relations to determinate being via divine esse intentionale, excluded middle folds in that (noncoercive) space, where rational determinate beings participate or not in gratuitous divine acts, whether of creation or of grace.
What’s the difference between so called weak (Scotist) vs strong (Thomist) conceptions of DDS?
The “weak” DDS employs univocity with a formal distinction, semantically.
The “strong” DDS employs apophasis with analogia, ontologically.
The weak version chastens radical apophaticism, the strong – radical kataphaticism.
There are distinctions between the divine essence, energy & operations, the nature & will, formally & semantically, that gift a modicum of intelligibility, denominatively & connotatively, via revelation.
Ontologically, though, we predicate the DDS apophatically & analogically, gaining a modicum of intelligibility, determinatively & denotatively, i.e. locatively eternal, quantitatively infinite, numerically One & existentially necessary, although nothing can be known generically (what?).
Taken together, these versions aren’t in opposition but, indeed, emulate different steps in Dionysian logic:
God is | x | is true kataphatically & trans-analogically; as a simile, whether analogically & literally or metaphorically & nonliterally;
God is | not x | is true apophatically & literally; and
God is neither | x | nor | not x | is true relationally & really.
Those who affirm these types of distinctions will be able to reconcile Thomist, Scotist & Palamite approaches, Latin & Byzantine logics.
Some refer to extrinsic denominations & Cambridge properties in the context of categorial discourse, as they make connotative & denominative semantic claims about realities that are signified in terms of their relation to other realities, such as in a analogies of attribution, e.g. First Cause or Creator.
Even when considered semantically, such extrinsic denominations of contingent relations would still have metaphysical implications, for, as long as one hasn’t otherwise reduced any such reference to metaphor, as analogies, they’re predicated literally of their subjects.
Such predicates don’t describe a subject’s real properties, but are appropriate, i.e. make their subject intelligible, by virtue of the real properties of any realities to which the subject’s in relation.
As such, the extrinsic denominations & Cambridge properties of God discourse ad extra, e.g. creation, redemption & theosis, naming God’s contingent relations (gratuities of creation & grace), don’t compromise DDS or Actus Purus.