P5) Only The Father has the essential property of being Identical to the Father.
My friend @riir52520747 made a Argument against The Trinity, Here goes:
P1) God is triune. (Assumption for Reductio)
P2) The Son, The Father, and Holy Spirit are not identical to each other. (From, "Trinity")
P3) The Son, The Father, The Holy Spirit are each God (From, Trinity)
P5) Only The Father has the essential property of being Identical to the Father.
C1) Therefore, each member of the trinity are identical in quiddity, but still differs haeccetistically. (From 3, 4, 5, 6.)
C3) Therefore, there are 3 distinct entities which each have the property of "Being God"
C4) Therefore, There are 3 Gods.
C5) The Trinity affirms there is only one God.
C7) Therefore, God cannot be triune.
Justification for 4, 5 and 6:
Now clearly, each member of the trinity is going to be essentially identical to *themselves*. And such a property, is strictly going to be identical to what we would call a "Haecceity."
Then, if all these persons differ in this manner, and each are identical to God, then we have that there are 3 Gods. Blatant Polytheism. And clearly, a Contradiction.