How is the Trinity not tritheism?

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A. J. Pollock lays out the problem with precision. The word "person," when applied to human beings, naturally implies separate existence, separate will, and separate characteristics. If that human meaning is imported uncritically into the doctrine of the Trinity, the result is tritheism rather than true Trinitarian faith: In human language when we speak of a person, we think of separate entity, separate existence, separate will, different characteristics, thoughts and plans peculiar to each person, not shared with any others. Carry that human thought into the subject before us, and the truth of the Trinity is entirely perverted and lost. Instead of the Trinity — Father, Son and Spirit, ONE God — we should have three Gods, an absolute impossibility, for there can only be one God, unique and incomprehensible. A. J. Pollock Pollock is careful to affirm that the language of "three Persons" is rightly used — it represents real truth — but must be understood in a way that transcends human analogy: There is abundance of teaching in the Holy Scriptures that God reveals Himself as Father, Son and Holy Spirit, not three Gods, but a Triune God, though Scripture teaches that the Father is God, the Son is God, the Holy Spirit is God, yet one God indivisible. Titles of Relationship, Not Names of Separate Beings R. A. Elliott quotes an extended passage that crystallises the distinction. Tritheism pictures three independent divine beings who happen to share the same attributes; the Trinity reveals three who are incapable of existence apart from one another: The threefold personality of God does not contradict His unity in any way: it shows the manner or condition of it. There are not three independent units side by side, on a level with each other, each almighty, each eternal, each finding in Himself the source of His own life. The unity of the three blessed Persons is not a similarity of character and qualities and powers … three Beings each of Whom is a God. … It is true though inexpressible, unity of Three Persons … incapable of existence apart from one another. The life of all three is one and the same life, and it has but one source, not three. The very titles by which They are known to us, imply this. They are not proper names, like those of heathen divinities, but titles of relationship, which involve each other, and would be meaningless alone. Fatherhood is impossible without sonship, and sonship without fatherhood. R. A. Elliott This is a crucial point. "Father" and "Son" are not arbitrary labels attached to two independent deities — they are relational names that imply one another and can only exist together. A "father" with no son is no father at all. The names themselves testify to the unity. One Life, Not Three Independent Lives In a second paper, Elliott sharpens the point further, drawing on a quotation from J. N. Darby: The truth as to the Deity is not that there are Gods — three supreme and omnipotent Beings, each having His own life and acting from Himself — but three in one — Father, Son and Holy Spirit — One God; and though for the sake of accommodation we use the word Person, and speak of three Persons in the Godhead, yet there are not three Persons as we understand persons. Such as Abraham, Isaac, and Jacob were three persons; each having his own separate life. And Darby himself is quoted: "He was not like an independent being with equal rights; another God Who acted on His own account, which, moreover, is impossible. There cannot be two supreme and omnipotent Beings." Community of Thought and Oneness of Action Pollock traces what the unity of the Godhead means practically — not just that Father, Son, and Spirit exist together, but that their thought and will are perfectly one: Such is the unity of the Godhead that there cannot be one thought in the Father's mind that is not altogether shared and approved by the Son and the Spirit — not one intention or purpose in the mind of One of the Persons in the Godhead but what is fully shared and endorsed by the other Two Persons in the Godhead, for God is One. He illustrates this from the Lord's own words in John 5:19 — "The Son can do nothing of Himself, but what He sees the Father do" — and from John 16:13, where the Spirit "shall not speak of Himself" but speaks what He hears. This is not the language of three independent beings cooperating; it is the expression of one divine life shared in perfect unity. Functional Differences Without Separation William Hoste adds an important dimension. The error of tritheism arises when the functional differences between the Persons are denied — when each is described as identical in every respect, with no order or subordination of operation: The result is "tritheism," as has already been pointed out; and a Unitarian might object — "Why should three Divine Persons, all infinite, eternal, omnipotent, be needed, and One not suffice?" This would be sound reasoning were the Persons such as these teachers depict them. William Hoste Hoste insists that it is precisely the distinct functions — the Father as originator, the Son as executor, the Spirit as the power by which divine purposes are fulfilled — that guard against both tritheism and unitarianism. The Father sends; the Son is sent; the Spirit applies. This is not the language of three interchangeable gods, but of one God whose life is expressed through three Persons in an eternal order of love. The Word "Person" Itself J. N. Darby, in an earlier work, engages with the theological use of the Latin word persona. He quotes Dr. Wallis, who argued that "person" in its original and theological sense does not mean what it means in ordinary modern English: The word person (persona) is originally a Latin word, and doth not properly signify a man (so that another person must needs imply another man); for then the word homo would have served … but rather one so circumstantiated. And the same man, if considered in other circumstances (considerably different), is reputed another person. J. N. Darby The theological use of "person" never meant to imply the kind of separate, independent existence that the modern English word suggests. A Story That Captures It A. Snell, writing on the Deity of the Son, tells a memorable story of a young man who came to faith precisely through encountering this truth: In the pew where he was sitting he espied an old book, and on taking it up he read, "The Father is God, the Son is God, the Holy Ghost is God, yet not three Gods but one God." Light immediately flashed in on his soul. A. Snell Synthesis The distinction between the Trinity and tritheism turns on the nature of the divine unity. Tritheism imagines three separate divine beings who merely share the same attributes — like three kings ruling three separate kingdoms but with identical power. The Trinity, as Scripture reveals it, is something altogether different: one divine life, one will, one purpose, expressed in three Persons who are incapable of existence apart from one another. The very names — Father, Son, and Spirit — are not labels for independent beings but titles of eternal relationship that imply and require each other. The Father is not the Father apart from the Son; the Son is not the Son apart from the Father. Their unity is not cooperation between equals who could theoretically go separate ways; it is an absolute oneness of life, thought, and action — so total that what the Son does, the Father does, and what the Spirit speaks, He receives from the Father and the Son. The word "person," as used of the Trinity, must not carry the modern human meaning of a separate individual with a separate existence. It points rather to real, eternal distinctions within the one God — distinctions of relationship and function, not of being or life.

三位一体为何不是三神论？