My friend @riir52520747 made a Argument against The Trinity…

P4) Only The Son has the essential property of being identical to the "Son." (From the definition of "Essential Property", and Haecceity.)
P5) Only The Father has the essential property of being Identical to the Father.

P6) Only the Holy Spirit has the essential property of being identical to the Holy Spirit.
C1) Therefore, each member of the trinity are identical in quiddity, but still differs haeccetistically. (From 3, 4, 5, 6.)

C2) Therefore, each member of the trinity is essentially non-identical. (From, "Haecceity")
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.

C6) Therefore, the Trinity is contradictory.
C7) Therefore, God cannot be triune.

Justification for 4, 5 and 6:

An essential property, is simply going to: be A property P is essential to an individual x iff it is not possible that x exist and fail to bear property P. We do not mean essential property in the medieval sense, and even if we did we can still derive this notion of essential…

…identity/haecceity very easily.

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."

Now that each member differs haeccetistically, they're going to be essentially non-identical. As X and Y are going to be distinct iff there is some property they don't share given the identity of indiscernibles + the indiscernibility of Identicals.

Now that we've established that each person of the trinity differs in such a manner, they're going to be distinct in such a way that we no longer have some "3 in 1" notion we can work off, as we just introduced a principle of individuation, namely their haecceities, which…

…treats them as wholly seperate.

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.

This argument is specifically strong, because trinitarians can no longer appeal to Relative Identity, or adopt say, a thomistic account of the Trinity.

They're going to need to introduce a completely different definition of essential property, and explain why some individual X's haecceity cannot be easily derived from such a definition.

Note that this definition was pioneered by Alvin Plantinga, and is generally accepted among philosophers. So it's going to be very hard to see how someone would attempt doing that.

END