The Trinity/ bi-conditional or conditional relation?

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I agree that I think it is (mono)conditional, but I just want to know for sure the orthodoxy of that before I go spouting it to some debates/dialogues with non-Catholics/Christians:D. If it is not orthodox, I would like to discuss how it could even be remotely possible to bypass the contradiction.

However, the reasons are different for why I think it is not bi-conditional. I think one could say (not assuming the Trinity) that God is Father, and still leave room for more description, just like one could say *John is tired *and John is tall. The contradiction arrises, assuming Trinity and bi-conditional relations from Persons to God, when one says God is Father, Son is God, yet also say Son is not Father, since you can derive Son is Father just from those two premises (G is F, S is G) by hypothetical syllogism.
 
You can go quite deep in studying the Trinity, and in fact to do so can be quite profitable spiritually. There are some differences in terminology as used by West and East that are especially illuminating. The main thing I want to add to this thread is that the verb “is” as used in “Jesus is God” and similar constructions is being used as a copula, and not as a formal equality sign. It’s not adequately orthodox to write “Jesus = God” instead of “Jesus is God”.

I’ll borrow some text from Pharsea, which unfortunately doesn’t survive reformatting by this forum very well:
Code:
The Western account of the matter roughly went as follows.

    * God is, first of all, One Being: ousia, esse, substance.
    * In this Single Being are three activities, agents, understandings or knowings: hypostases, personae.
    * These are distinct from each other,
          o but equally possess the Single Divine Being (substance).
          o They are consubstantial.
    * The personae form a community or network of mutual relationships of love.
          o The Father immediately gives rise to the Son
                + by self-knowing or "generation";
          o and the Son and Father jointly give rise to Holy Spirit,
                + by "procession", as their mutual love.

The Eastern account of the same reality roughly went as follows.

    * There are three existences or foundations (hypostases)
          o which each fully uphold, under-stand and together constitute
          o the One Divine Being: ousia, esse.
    * They each fully possess the self-same identical single being:  "homo-ousion",
          o not three exactly similar beings: "homoi-ousion"
           (yes, that nice distinction amounts to an "iota" in the Greek, an un-dotted "i"!), 
          o however, they do so in different ways.
    * The Father's way of being God, is primary,
          o while the ways in which the Son and Spirit are God are secondary.
    * There is the suggestion that the hypostasis of the Father
          o actually gives rise to the Being of God,
          o which He then fully passes on to and shares with
          o the hypostases of His Son and Spirit.
 
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