Biblical Answer

The implications of a 'non-essentialist' understanding of the Trinity on the doctrine of the persons is a matter of significant concern. If the full deity of the Son and the Holy Spirit is not essential, it would undermine the very heart of the doctrine of the Trinity. The unity of God as one undivided being would collapse into simply person A, person A, and person A, with no basis for differentiating the persons from one another. This would lead to a tritheistic view of the Trinity, where the distinct personhood of the Father, the Son, and the Holy Spirit is recognized, but the unity of God is lost.

A non-essentialist understanding of the Trinity would also have significant implications for the person of Christ. If the full deity of the Son is not essential, it would undermine the biblical teaching that the Second Person of the Trinity took on human nature. This would mean that the nature of Christ would be seen as a mixture of human and divine, rather than fully divine. This would also undermine the significance of Christ's work of redemption, as it would not be the work of a fully divine person.

The implications of a non-essentialist understanding of the Trinity would be far-reaching and would undermine the very foundation of the doctrine of the Trinity. It would lead to a tritheistic view of the Trinity, undermine the person of Christ, and undermine the significance of Christ's work of redemption. Therefore, it is essential to hold to the full deity of the Son and the Holy Spirit, as this teaching has significant implications for the heart of the doctrine of the Trinity. This is not a matter of philosophical principles, but rather a matter of biblical teaching and the nature of God. We must be careful not to redefine the doctrine of the Trinity in a way that undermines its core teaching.