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@Deadlycause attempted to respond to my thread by using the mereological model below.

Here, he interpreted it as follows:
"H" = humanity
"M" = Mark
"P" = Paul
"T" = Tim
Using this, he attempted to portray the rational behind the incoherence of the Trinity.

Here, he shows that each human is fully human by sharing the essence of "H" while also being district

In this sense, he mimics the view of social trinitarianism (Model A)
The problem follows:

-If "H" represents the Godhead, then the lines leading from "H" must represent proper part relationships. Thus, M,P, and T are all proper parts of the "H"

-Worse though is that M,P, and T each have further proper parts within them (2 circles under)
This suggests that neither M,P, or T are fully human, but rather that the totality of M,P, and T is fully human, since each distinct part has other non-identical distinct parts.

Besides, the obvious problem here is that his model shows 3 humans, and hence, 3 Gods
The misconception he makes is that merelogical models only show essences and not proper parts

To correct his model for him, he would first need to get rid of the additional proper parts

This yields the following model

This model also fails to show each member as a fully God
on this model,no person of the Trinity has all the same proper parts as the Godhead (that Father is a part of the Godhead, but not a part of the Son),since each member is a proper part themselves.Therefore, each of the members lack compositional level below that of the individual
One way to fix this problem is to turn it onto its head. As i said in my original thread, this allows for axiom 1.2 and 1.3, but the obvious contention here is that this would entail modalism, but more seriously, tritheism.
What ever way one decides to look at it, the concept of the trinity can not be rationally depicted. Even if one were to demonstrate an the trinity based on such mereological models, they would still run into the problem of christ's body
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