On the formula for trinity of God

Continuing this blog post:

It is clear that the set of all predicates true for God bijectively corresponds to the set of all predicates true for Christ (with some bijection F). (All properties of God “directly correspond” to properties of Christ, in mundane language.)

It could be taken as a formal definition of the “trinity” relations between God’s persons.

But later I notice the simple fact that every two objects X and Y correspond in this way to each other: the set of all predicates true for X bijectively corresponds to the set of all predicates true for Y (take the bijection F which exchanges X and Y values of the arguments of the predicates).

So my “theory” of trinity is found not to have sense.

Well, I believe it should have sense, but we need to restrict the set of allowed bijections F to functions which preserve the essence of properties of God. What is “the essence”? I do not know.

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