Trinitarianism has historically taught that the Trinity is one being, not more than one being.
The problem for me has always been wrapping my head around what a single "being" means in this context, yet maintain that Father and Son and Holy Spirit are not identical. We can express the orthodox doctrine of the Trinity (three persons in one God) as a set of propositions in this way:
1. There is only one God.
2. The Father is God.
3. The Son is God.
4. The Father is not the Son.
5. The Holy Spirit is God.
6. The Holy Spirit is not the Father.
7. The Holy Spirit is not the Son.
For simplicity’s sake we need consider only 1 through 4 (for 5 through 7 will stand or fall on the same logical analysis we apply to 1 through 4):
1. There is only one God.
2. The Father is God.
3. The Son is God.
4. The Father is not the Son.
The difficulty in understanding the Trinity has always been that these four propositions are, as a group, logically inconsistent when analyzed from the standpoint of the three basic rules of logical equivalence: self-identity (everything is identical to itself, i.e., x = x); symmetry (if two things are equivalent, they are equivalent in any order, i.e., if x = y, then y = x); and transitivity (if one thing is the same as another and that other is the same as a third, then the first is the same as the third, i.e., if x = y and y = z then x = z). The orthodox doctrine of the Trinity fares ill in this analysis.
To make them logically consistent, we would need to sacrifice one of the four tenets. Thus, Arius sacrificed the third one:
1. There is only one God.
2. The Father is God.
4. The Father is not the Son.
3′. Therefore the Son is not God.
and Sabellius sacrificed the fourth one:
1. There is only one God.
2. The Father is God.
3. The Son is God.
4′. Therefore the Father is the Son.
Both Arius’ argument and Sabellius’ argument are logically consistent because, unlike the orthodox doctrine of the Trinity, they satisfy all three of the aforementioned principles of logical consistency. Arius and Sabellius, although approaching the inconsistency from different perspectives, each preferred rationality to irrationality―even if it meant preferring heresy to orthodoxy.
Now, we Trinitarians have two choices. We can simply throw up our hands and declare that God does not have to play by the rules of logical consistency, thereby forever assigning the Trinity to the status of unfathomable mystery. Or, we can allow for identity and equivalence to be relative to their contexts. Thus, “Robert is good” can be consistent with “Robert is not good” as long as a different sense of “good” holds for each proposition (e.g., he is a good theologian; he is not a good golfer.)
To say that “The Father is not the Son” is likewise context-dependent and predicate-specific. One can maintain without contradiction both that “The Father is not the same
person as the Son” and “The Father is the same
God as the Son” by separating out personhood from Godhood.
How to tease them apart is the ultimate challenge of orthodox Trinitarian theology.
