C2) Therefore, the Son exists a se (From 1, 4)
C3) Therefore, the Son is exists both a se and ab alio (From C1 and C3)
C4) Therefore, "The Son" Is self-contradictory
C5) Therefore, The Trinity is self-contradictory
By a se we are just referring to God's aseity (i.e, the term a se means "through itself"). Aseity refers to God's uncaused, independant, unconditioned, necessary, etc. Existence.
We are simply exemplifying how God's existence is independant from and unaffected by anything outside of him. It's important to note that "Aseity" doesn't just mean "metaphysical necessity" / "existence in every possible world", since we could have Ab Alio necessities as well.
Ab Alio simply meaning, "Through another." In contrast with A se.
The second Premise might seem a bit weird. Someone might argue that the relation between the Father and the Son isn't "causal" in any sense. But this is just heretical.
This is recognized by several Church Historians such as (Kevin Giles, Michel Barnes, Steven Holmes, Christopher Beeley).
It's even acknowledged by several Christian Theologians such as (Richard Cross, Paul Helm, William Hasker, Ryan Mullins, William Lane Craig, J.T Pash, Chad McIntosh.) We can even look at the Nicene Creed, and see the usage of the word "Begotten" be defined as "That which has a…
…cause or source outside itself" (From Alastair Heron, a early church historian).
So now that 2 has been established, we can easily get 3. The Son doesn't exist through himself, but rather by being Begotten.
It's important to note that this causal relation doesn't have to be Asymmetrical. We can agree with St. Gregory of Nyssea and claim that this relation is purely symmetrical, but again, we still have causal dependance.
So the Son cannot exist "A se" (through himself), but rather, "Ab Alio" (through another.)
But, clearly, Christians believe the Son is God. and if God necessarily exists A se (which not a single Christian would even think of denying), then the Son can't be God.
As, nothing can exist both Ab Alio and A se. Therefore, The Trinity is self-contradictory.
All of these doctrines are affirmed by every single major Church Historian, Church Figure and Theologian (I don't think this is literally the case but I haven't been finding a single church figure disagreeing with this.)
The strength of this specific argument is that we no longer have to deal with poor defenses such as "Relative Identity" or anything of that sort. We aren't arguing for Polytheism, but rather a flat-out Contradiction inherent within the Trinity.
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