Does the Catholic's Trinity doctrine imply that the Unitarian God Multiplied into Three persons by Generating the other Two?

Question

Does the cause-effect and begotten doctrine of the Eastern and Roman Catholic Church imply a division or multiplication in the nature of God? Unitarian God (Father) begets or caused into effect the second person- Son, who is subordinate to the Father. I am not using Subordinate in the sense of having a lesser divine and different substance/essence than the Father, but when they say "begotten not made", and that the Father alone is uncaused seem to imply that the Father begot the Son like a living creature begets its offspring. The offspring of God is not created from outside substance (like man from dust) but literally derived/generated/caused/begotten from the Father's divine nature, and he is equally divine. The Son is lesser in rank by the virtue of "generation", and the Spirit "proceeds". The words begotten and proceed are used, but seem to imply causation and generation. As though the Monarch, Unitarian God generated the (co-divine persons) Son and the Spirit, transforming into Multipersonal or the Trinity.

The topics on "begotten, not made" and the "Monarchy of the Father" doctrine and the doctrines of "eternal generation", "eternal sonship" and "eternally begotten" generated this question. The language and these phrases in their creeds have resulted in confusion and debate; One might even say that such a literal generation of the divine persons undermines the doctrine of Immutability or the unchangeable nature of God.

Eastern Orthodox - Wiki

According to the Eastern Orthodox view, the Son is derived from the Father who alone is without cause or origin. This is not subordinationism, and the same doctrine is asserted by western theologians such as Augustine. In this view, the Son is co-eternal with the Father or even in terms of the co-equal uncreated nature shared by the Father and Son. However, this view is sometimes misunderstood as a form of subordinationism by Western Christians, who also asserts the same view even when not using the technical term i.e. Monarchy of the Father. Western view is often viewed by the Eastern Church as being close to Modalism.[40]

Catholics
The Catholic Church also believes that the Son is begotten of the Father and the Holy Spirit is proceeding from the Father through / and from the Son. Catholic theologian John Hardon wrote that subordinationism "denies that the second and third persons are consubstantial with the Father. Therefore it denies their true divinity."[42] Arius "made a formal heresy of" subordinationism.[43] The International Theological Commission wrote that "many Christian theologians borrowed from Hellenism the notion of a secondary god (deuteros theos), or of an intermediate god, or even of a demiurge." Subordinationism was "latent in some of the Apologists and in Origen."[43] The Son was, for Arius, in "an intermediate position between the Father and the creatures." Nicaea I "defined that the Son is consubstantial (homoousios) with the Father. In so doing, the Church both repudiated the Arian compromise with Hellenism and deeply altered the shape of Greek, especially Platonist and neo-Platonist, metaphysics. In a manner of speaking, it demythicized Hellenism and effected a Christian purification of it. In the act of dismissing the notion of an intermediate being, the Church recognized only two modes of being: uncreated (nonmade) and created."[43]

Answer 1

Asking about Catholic/Orthodox doctrine suggests a desire to understand the doctrine. If the question seeks an answer that criticizes the doctrine, that is another matter. My answer will be based on the first suggestion. One does not have to agree with the doctrine to understand it.

Catholic doctrine rejects the idea that there was ever a "Unitarian God." The divine "economy" takes place in eternity, outside of time. In this view, to apply temporal categories to the process takes it back inside time. For trinitarians, to speak of multiplying the unitarian God is blasphemous. The word "generation," however, is sometimes discussed. No less an authority that Thomas Aquinas admitted to a type of generation in the Godhead, although he was careful to point out that it was not an "outward" creation, but an inward procession:

It was left to St. Thomas to clarify the exact nature of this generation. In the Summa, he explains two types of procession. One is an outward act of creation, while the other is an “inward procession corresponding to the act remaining within the agent.” This second kind of procession is purely an act of the intellect. If you have a thought, that thought may proceed outwards and become manifested as words or actions, or it may proceed inward as a “conception of the object understood, a conception issuing from our intellectual power and proceeding from our knowledge of that object.” - From Generation and Spiration: The Processions of the Trinity by Thomas L. McDonald

The OP is correct when it says "the language and these phrases in their creeds have resulted in confusion and debate." However, trinitarian Christians would not agree that "One might even say that such a literal generation of the divine persons undermines the doctrine of Immutability or the unchangeable nature of God." For "orthodox" trinitarians, God exists outside of time as an eternal Trinity, which is, in itself, the immutable nature of God. Again, one does not have to agree with the doctrine to understand it.

Answer 2

No, it does not. The Trinity, as taught by both the RCC and by Eastern Orthodoxy, is a divine mystery ultimately incomprehensible to human nature (necessitating Faith for our knowledge of it at all). For the West it is best expressed in the Athanasian Creed, which states

...And the catholic faith is this: that we worship one God in Trinity, and Trinity in Unity; neither confounding the Persons, nor dividing the Essence. For there is one Person of the Father; another of the Son; and another of the Holy Ghost. But the Godhead of the Father, of the Son, and of the Holy Ghost, is all one; the Glory equal, the Majesty coeternal. Such as the Father is; such is the Son; and such is the Holy Ghost. The Father uncreated; the Son uncreated; and the Holy Ghost uncreated. The Father unlimited; the Son unlimited; and the Holy Ghost unlimited. The Father eternal; the Son eternal; and the Holy Ghost eternal. And yet they are not three eternals; but one eternal. As also there are not three uncreated; nor three infinites, but one uncreated; and one infinite. So likewise the Father is Almighty; the Son Almighty; and the Holy Ghost Almighty. And yet they are not three Almighties; but one Almighty. So the Father is God; the Son is God; and the Holy Ghost is God. And yet they are not three Gods; but one God. So likewise the Father is Lord; the Son Lord; and the Holy Ghost Lord. And yet not three Lords; but one Lord. For like as we are compelled by the Christian verity; to acknowledge every Person by himself to be God and Lord; So are we forbidden by the catholic religion; to say, There are three Gods, or three Lords. The Father is made of none; neither created, nor begotten. The Son is of the Father alone; not made, nor created; but begotten. The Holy Ghost is of the Father and of the Son; neither made, nor created, nor begotten; but proceeding. So there is one Father, not three Fathers; one Son, not three Sons; one Holy Ghost, not three Holy Ghosts. And in this Trinity none is before, or after another; none is greater, or less than another. But the whole three Persons are coeternal, and coequal. So that in all things, as aforesaid; the Unity in Trinity, and the Trinity in Unity, is to be worshipped. He therefore that will be saved, let him thus think of the Trinity.

To our human minds the above contains contradiction after contradiction (Trinity in Unity and Unity in Trinity, etc.). So Pseudo-Athanasius explicitly corrects any possible errors that may come in our understanding, e.g. by reminding that there are not three eternals but one eternal. This is faith which is believed requiring the infused virtue of Faith whereby it is believed.

Answer 3

let's look at the original text:

The Lord says, “I am the Lord your God, who led you out of Egypt. You have no God but me. I alone am your savior. Hosea 13:4 GNT

here clearly state there is 'no God' but God of Israel, and 'alone'. i think there is more than 50 verses that contains similar wordings that shows there isnt any other god(s) than God of Abraham, Isaac and Jacob.

Hope God had given the best introduction of HIMSELF to the world to know.