In the 2008 EFS debate between Bruce Ware and Wayne Grudem versus Tom McCall and Keith Yandell, two interesting lines of thoughts emerged primarily from Yandell's presentations and rebuttals. One line of thought spells trouble for classical theism as currently presented, and the other is a trouble for Yandell's view.
The philosopher Wilhelm Gottfried Leibnitz in his Law of the Identity of Indiscernables assert that for two named objects X and Y, if both of them have the exact same properties, then they are one object (X = Y). Conversely, two objects can only be distinct if and only if they have at least one property different from the other. Intuitively, that seems correct. Identical spheres have different spatial properties therefore they are identical but not the same; they do not occupy the same space at the same time.
Keith Yandell asserted that the persons of the Trinity are essentially the same, and seem to reject any distinguishing marks between the persons. Upon Leibniz's law however, if the three persons of the Godhead are essentially the same with no different properties, then they are basically one thing — one thing that connsists of Person A, Person A, and Person A. That one is called 'Father,' another 'Son,' and another 'Spirit' is mere nominal unless there is something really different: some property that the Father has which the Son does not, and somme property the Son has that the Spirit does not, and so on. At the minimum, claiming that the persons of the Trinity have the same haecceity ("thisness") means that "Father," "Son," and "Spirit" are purely interchangeable, such that the fact that the Son was the one incarnating is purely accidental (i.e. it just happens to be the case that the person called "Son" is incarnated). But even if such were the case, the fact that the person named "Son" became incarnated means that this "Son" has gained the property "being incarnated," and therefore has at least one different property from the other two persons of the Trinity. Needless to say, it is clear that the Father, Son, and Spirit must have different personal properties from each other, even if we have only the incarnation in mind.
The second line of thought poses a problem for classical theism, or at least the Thomistic classical theism that is anti-EFS. As one of the audience questioned during the Questions and Answers section: If it is argued that anything that is necessary from eternity is necessary in all possible worlds and therefore essential (pertaining to the essence of a thing), then it seems that any mark that distinguishes the persons in eternity past would logically lead to ontological differences. For example, if the Father is necessarily unoriginate while the Son is necessarily begotten, then this must be true in all possible worlds. Thus, the Father is essentially unoriginate and the Son is essentially begotten, and therefore the Father is different in essence from the Son. Therefore the Father and the Son have different essences, which is the denial of the homoousious. That is the problem for anti-EFS classical theism in its attempt in eradicating "subordinationism." If any distinguishing mark of a person from eternity is necessary, then the creedal position of the Trinity is subordinationist in nature. The historical rejection of Arianism would be seen as being an affirmaton that Jesus is God, not a rejection of subordinationism per se.
How should we solve this problem? Again, the Scriptures made it clear that there is one God, and there are three distinct persons. Therefore, any personal property of a person even if necessary are not part of the divine essence. In order to remain orthodox, the premise that for a thing, what is necessary is essential, must be rejected. Only then can we not have subordinationism in our doctrine of God.
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