The Confession (1677/89) states the doctrine of the Trinity as follows:
In this divine and infinite Being there are three subsistences, the Father, the Word or Son, and Holy Spirit, of one substance, power, and eternity, each having the whole divine essence, yet the essence undivided: the Father is of none, neither begotten nor proceeding; the Son is eternally begotten of the Father; the Holy Spirit proceeding from the Father and the Son; all infinite, without beginning, therefore but one God, who is not to be divided in nature and being, but distinguished by several peculiar relative properties and personal relations; which doctrine of the Trinity is the foundation of all our communion with God, and comfortable dependence on him. (2.3)
With a great deal of intention, the Confession employs the term “subsistence,” a noticeable change from the language used by the Westminster Confession, which instead reads, “In the unity of the Godhead there be three Persons of one substance…” (2.3, Emphasis added) Explaining this significant change in language, Dr. James Renihan states:
More significantly, when introducing Trinitarian terminology, the text changes the WCF/Savoy language from persons to subsistences. Richard Muller has composed a lengthy article on the Latin term persona and its perceived liabilities in the history of Trinitarian discussion, asserting that subsistentia came to be a preferred term by some theologians, such as John Calvin.
The term subsistence tends to avoid the confusion caused by the word person which, in addition to its historical obscurities, has of late taken on a unique psychological connotation binding the term to human features, e.g. reason, will, conscience, etc. As a result, modern social trinitarianism and tritheism tend to distinguish the persons along the lines of distinct centers of consciousness or distinct wills.
Kyle Claunch notes this in relation to the subordinationism of Bruce Ware and Wayne Grudem. He writes, “they are making a conscious and informed choice to conceive of will as a property of person rather than essence. This model of a three-willed Trinity then provides the basis for the conviction that structures of authority and submission actually serve as one of the means of differentiating the divine persons.” It appears the modernist assumptions behind the term person have led to a conception of trinitarian relations as distinct intellectual beings—since they each consists of substantially different things, e.g. minds, wills, consciousness, etc.
Conversely, Cornelius Van Til arrives at the awkward language of, to paraphrase, “God the one person in three persons.” He writes, “Over against all other beings, that is, over against created beings, we must therefore hold that God’s being presents an absolute numerical identity.” This is true as far as it goes. But Van Til misses out on some important language and distinctions, concluding, “[God] is one person.” He goes on to correctly note, “When we say that we believe in a personal God, we do not merely mean that we believe in a God to whom the adjective ‘personality’ may be attached. God is not an essence that has personality; he is absolute personality.”
Van Til obscures the manner of distinction between essence and subsistences by identifying essence and subsistences as a numerically single person. He is correct to say that “personality” is not something that God has, but something that God just is. However, he is incorrect to imply the elimination of personal properties by declaring the numerical singularity of personality in God. That God is one essence subsisting in three distinct modes or relations seems to be a consideration lost on Van Til, though seemingly implied in other areas of his work. While the essence and subsistences are substantially identical, there are yet personal properties distinguishing each Person one from another. Such a consideration would prevent the Van Tillian from collapsing the three Persons into one persona.
Renihan helpfully provides the missing piece in much of these contemporary discussions when he writes, “In his Marrow of Sacred Divinity, William Ames uses [subsistence] in these two ways. Prefixed to the front of the book is a brief glossary of terms. It defines subsistence as ‘the manner of being.’” (Emphasis added) Francis Turretin likewise states:
Thus the singular numerical essence is communicated to the three persons not as a species to individuals or a second substance to the first (because it is singular and undivided), nor as a whole to its parts (since it is infinite and impartible); but as a singular nature to its own act of being (suppositis) in which it takes on various modes of subsisting. Hence it is evident: (1) that the divine essence is principally distinguished from the persons in having communicability, while the persons are distinguished by an incommunicable property; (2) that it differs from other singular natures in this—that while they can be communicated to only one self-existent being (supposito) and are terminated on only one subsistence (because they are finite), the former (because infinite) can admit of more than one. (Emphasis added)
Hence, the language of the Confession, “In this divine and infinite Being there are three subsistences, the Father, the Word or Son, and Holy Spirit, of one substance, power, and eternity, each having the whole divine essence, yet the essence undivided…” (2.3) In other words, Father, Son, and Spirit just are the one divine essence. As the Athanasian Creed points out, “Thus the Father is God, the Son is God, the Holy Spirit is God. Yet there are not three gods; there is but one God.” The one and undivided essence subsists in three ways distinguished by personal properties—Father, Son, and Holy Spirit.
Each of these relations are explained by way of origination: the Father is unbegotten, the Son is begotten of the Father, and the Spirit proceeds from both Father and Son. As the Confession likewise states, “the Father is of none, neither begotten nor proceeding; the Son is eternally begotten of the Father; the Holy Spirit proceeding from the Father and the Son…”
The Athanasian Creed states, “The Father was neither made nor created nor begotten from anyone. The Son was neither made nor created; he was begotten from the Father alone. The Holy Spirit was neither made nor created nor begotten; he proceeds from the Father and the Son.” Further, the Nicene Creed also says of the Son, “We believe… in one Lord Jesus Christ, the only Son of God, begotten from the Father before all ages, God from God, Light from Light, true God from true God, begotten, not made…” And regarding the Spirit, the same creed says, “He proceeds from the Father and the Son…”
 James Renihan, To the Judicious and Impartial Reader: Baptist Symbolics, Vol. II, (Cape Coral, FL: Founders Press, 2022), Kindle Edition, Loc. 2260-2265.
 Kyle Claunch, “God Is the Head of Christ,” in One God in Three Persons, ed. Bruce A. Ware; John Starke, (Grand Rapids, MI: Crossway. Kindle Edition), 88-89.
 Cornelius Van Til, Introduction to Systematic Theology, (Phillipsburg, NJ: P & R Publishing, 2007), 364.
 Renihan, To the Judicious and Impartial Reader, Loc. 2259.
 Francis Turretin, Institutes of Elenctic Theology, vol. I, (Phillipsburg, NJ: P & R Publishing, 1992), 282.