It has been rightly argued by some that we can distill these claims from the Athanasian creed:It seems to me that these conundrums can be dealt with in many ways by adding additional biblically informed propositions to the incomplete ones. Simply replace some of the abbreviated premises with premises that contain more biblical truth and paradox disappears, yet without being able to uncover the mysteries of the Trinity. (i.e. The solution is rational but ought not to be considered rationalistic.)
1. The Father is God.
3. The Spirit is God.
4. The Father is not the Son.
5. The Father is not the Spirit.
6. The Son is not the Spirit.
7. There is only one God.
An apparent contradiction in view is:
A. f = g (premise)
B. s = g (premise)
C. f ≠ s (premise)
D. f = s (from 1, 2, by transitivity of identity)
Contradiction or Paradox?
Equivocal terms lead to unreliable conclusions:
It should be noted up front that there is a semantic difference between is and =, for x is y does not imply y is x; yet x = y is equivalent to y = x. (Please don't read on without digesting that.) The leap from what x is (found in 1-7) to what x equals (the complaint in the "apparent contradiction" i.e., A-D) is fallacious, which I trust will become apparent.
Points 1-7 (which utilize "is") imply that three distinct persons all share in the one divine nature and occupy what can be called "the same divine space". So far, so good. Points A-D that follow (which utilize "=" instead of "is") leads to confusion (and supposed paradox). Points 1-7 and A-D must be nuanced, for 1-7 does not imply the conclusion of A-D, which is not only an apparent contradictory but rather a real contradictory.
First, with respect to the confusing four points (A-D), the only way Jesus equals God is if Jesus and God are numerically identical - exactly the same without remainder. Yet God can mean Trinity, which Jesus is not. God can also mean the person of the Holy Spirit, which Jesus is not. Finally, God can mean the person of the Father, which Jesus is not. Accordingly, to say that "Jesus equals God" and the "Father equals God" is equivocal at best and if taken literally leads to modalism because identity is transitive, which would mean that Jesus and the Father are the same person.
With respect to points 1-7, indeed, we should rightly say that Jesus is God because Jesus shares the divine essence: he is very God of very God, but that is not what is implied in points A-D when things such as "Jesus = God" are stated. In other words, if what is meant by "Jesus is God" is that that Jesus equals God, then of course that would be incorrect. But that is not what is typically meant by "Jesus is God", which makes reference to his divine nature, one in being with the Father.
Jesus is a specific person. Accordingly, if Jesus equals God, then God must equal Jesus and, therefore, must be a specific person (the same as Jesus), which would preclude any other person from sharing in the divine nature such as the Father, which in turn would undermine the doctrine of the Trinity. So yes, Jesus is God because Jesus is divine, but Jesus and God are not synonymous terms - for if they were synonymous terms, then "Jesus is God" could be equated to "God is Jesus". (In simple terms of analogy, Jim is human does not imply Jim = human.)
Jesus does not equal God, for the Father and the Holy Spirit are also God yet are different persons than Jesus. There is more than one God-person in the Godhead, all of whom mutually indwell the other two. There is only one triune-God, that in three persons and oneness of being lives in perfect harmony.
More on the equally ultimate, unity and diversity:
The Father is God just as the Son is God, but an essential property of the Father’s *person* (not to be confused with the ontological essence), which merely is to say it can only be predicated to the person of the Father, is his relationship to the Son and the Holy Spirit. Being distinct persons, there are differences between the members of the Holy Trinity. The Father is not God apart from his intra-Trinitarian relationships. That to say, the Father is not God apart from being a member of the Trinity. These Trinitarian relationships are essential properties of personhood, not essence (lest Father is Son). If we cannot distinguish properties in this way, we cannot distinguish persons. Accordingly, f does not equal s because neither f nor s have the same intra-Trinitarian relationship with the other two divine persons in the Godhead. So, as we fill in what it means for f and s to be g, we do so not in a vacuum but with other biblical propositions in view, informing us of g as it pertains f and s. Indeed, it is true that f is g and s is g, and if that was the end of the story we might be in trouble. Without further elaboration, f is g plus s is g is consistent with modalism, so we needn’t be surprised that such constructs, though true, must be interpreted through a biblical lens in order to avoid heresy.
Although I don’t deny the prima facie intuitive notions surrounding 1-7 that can lead to a conundrum, it can be maintained on the consistency of God and his desire to communicate to his people that those intuitive notions that appear logically problematic can disappear when we presuppose additional revelation, which is not to say that mysteries can be solved. Logic cannot solve true mysteries, but biblically informed logical pursuit can demonstrate that certain doctrines are not actually seemingly-contradictory. It’s when we think intuitively, which is to say apart from Scripture, we can get in trouble. As I've noted elsewhere, that's an insight of Van Til's apologetic but not one that I think he carried into this thinking on paradox. (For instance, when we use only experience unaided by revelation we can think one essence necessarily implies one person; when we presuppose Scripture we can know that proposition is false.)
Finally, the original formulation if it is interpreted as allowing for f=s, (which is prior to the intra-Trinitarian elaboration that forbids such an interpretation), ends up implying that the sending of the Son was arbitrary, which means the Son could have sent the Father. The arbitrariness is not demanded by the original construct (1-7), rather it comes as a result of an interpretation of the original construct that does not consider other biblical truths, such as each divine person in his intra-Trinitarian relationship with the other two divine persons. In other words, without, for instance, an elaboration of how the Son relates to the Father, 1-7 might be wrongly inferred as implying an apparent contradiction, leaving it open that the Son could have sent the Father. In the final analyses, the original construct of 1-7 is true and it is fine as far as it goes; I believe it is most suitable for a creed, but it is not a full blown theology of the Trinity, which a creed ought not to be.
Finally, regarding the arbitrariness noted above (an idea I gleaned from Robert Letham's writings), there is good reason to believe that there is an actual appropriateness that the Son was sent in the incarnation and not the Holy Spirit, but the first construct is void of such implication.We may learn of the ontological relationship through the economic activity, as Dr. Letham rightly pointed out in his review of Dr. Robert Reymond’s Systematic Theology. So for example (and as Dr. Letham has written here) the submission to Father by the Son reveals something of who the Son is prior to his incarnation, which is consistent with the turning over of the kingdom to the Father by the Son in the eschatological consummation.