So I've gathered that you accept that there are distinctions among the Father, Son and Holy Spirit, and there you agree with the Pope. You disagree with the Pope's choice in words to define the distinctions, rejecting hypostasis & person. Correct?
And here you disagree with the Pope in equating the two words hypostasis & person?
OK. (I assume that you mean by "the simplistic definition," the definition given by the Pope.)
So therefore if I read you correctly, you're saying that where the Pope uses hypostasis, he should rather be using substance? Because there is only one substance to the Trinity?
Now I'm lost. If you disagree with him using the word hypostasis to denote the distinctions, but agree with his definition (woefully misrepresented as it may be) of hypostasis, then what are you saying?
And here is where the Pope uses the words substance, essence, and nature, but you would use hypostasis here? Is that correct?
The Pope is irrelevant. I have no regard for that false ecclesial position. But let's look at the doctrine indepth.
Let me try to simplify and clarify with contrast from a tweaked recent post in another thread. But first let me clarify the definition of hypostasis.
Hypo is "under", while stasis is "to stand". That which stands under. The underlying reality of substantial existence. The substance of that which is presented, which is the prosopon (person/face/presence/appearance).
Hypostasis, in a concise expanded linear amplified definition, is foundational underlying absolute assured substantial objective reality of existence. The hypostasis underlies the special (spee-cee-ahl - species) ousia, which is the type of essence (Divinity, humanity, or others). The hypostasis is inward reality that is outwardly presented as/by the prosopon.
Since the prosopon is the apparent tangible reality as the face/person or presence, hypostasis was employed to represent that fundamental substrate FOR the person (since substantia in Latin was already assigned and substance couldn't be utilitzed for translation from the Greek). Hypostasis is the inner for the outer. The foundational existence and true reality, since the flesh is dust and will pass away.
My Monohypostatic Trinity formulation represents the appropriate scriptural procession of the Logos and Pneuma. Since the singular two-fold procession (NO Filioque and dual procession) is exerchomai for the Logos and ekporeuomai for the Pneuma, they MUST be economic as energies, depicting movement rather than static immutable essence as ontology.
Ex- and ek- both indicate motion out of/from. There cannot be "eternal begottenness" as exerchomai for the Logos, and there cannot be "eternally proceeding" as ekporeuomai for the Pneuma. Such are ontological, whereas ex- and ek- absolutely mandate economic movement.
The following should outline it in some sense. It may be difficult to follow, as most don't know their own doctrine beyond a few rote paragraphs of creedal description or general conceptualization.
The Orthodox Multihypostatic Trinity doctrine posits three hypostases underlying the ousia; and the Logos/Pneuma procession being ontological because the quantitative threeness must have such ontology before any economy. This is necessary because essence (ontology) must be pre-existent relative to creation via energies (economy).
The Ortho Trinity also posits multiple inherent attributes for God, including eternity, infinity, aseity, and others. Then a contrast is made of a "second kind of eternity" that has a beginning and is everlasting relative to the third heaven, but is NOT depicted as created or accounted for within the creative act.
Thus there is no economy of God regarding the creative act and being omnipresent within a creation that had an inception. For His multi-omni attributes to have relevance other than their intrinsic existence, there has to be an economy to inhabit creation, or creation is some reflection of God's ontology. That leads to Emanationism and Pantheism; or at least PanENtheism.
According to scripture, I posit God as a singular hypostasis underlying the singular ousia; with the Logos and Pneuma being inherent ontological qualitative distinctions of the singular hypostasis. The Logos is both Nooumenological and Phainomenological, so there is no "coming into existence" at any point. There was never when/that the Logos "was not".
Thus, I don't need an unscriptural ontological procession that isn't representative of economy. The Logos and Pneuma are already ontologically inherent to both the singular hypostasis and the singular ousia.
From this eternal and Self-existent ontology of God as a singular hypostasis underlying a singular ousia, the eternal Logos and Pneuma are spoken/breathed forth. As this economy occured, creation was instantiated into existence from mere Nooumenological potentiality into Phainomenological actuality of existence. (This is what is often referred to as Ex Nihilo, though I don't necessarily prefer that semantic personally. It's appropriate primarily for apophaticism to oppose Ex Deo, even though subsequent forming of instantiated created elements is Ex Materia.)
The Logos and Pneuma are qualitative distinctions of the singular hypostasis underlying the ousia; not quantitative distinctions as multiple hypostases. The MultiHypoTrin doctrine MUST have an ontological procession, though that's contrary the the very terms exerchomai and ekporeuomai. Ex- and ek- specifically demonstrate movement, so the two-fold singular procession MUST be economic with eternal, infinite, immutable ontology already established. The Logos and Pneuma I depict are "more" ontologically Divine than the Multihypostatic Trinity, which has a quandry and paradox because the procession MUST be economic rather than ontological; EXternal rather than INternal.
The inherently ontological Logos and Pneuma economically processed into creation when/as it was instantiated into existence. Thus, ALL things are upheld by the Rhema of His dunamis.
The Logos and Pneuma are the singular (qualitative) two-fold procession of God's singular hypostasis into creation. Multiple (quantitative) ontological hypostases requires a non-biblical ontological procession, and implies some beginning even though the entirety of God's immutable eternality has no beginning (along with His infinity, aseity, etc.).
My formulation of a Monohypostatic Trinity resolves the paradox of "eternal begottenness", among several others; and while retaining every other tenet and sub-tenet of the faith because I didn't just migrate to one of the historical heresies.