Does not the above contradict...
Which specifically deals with how God is in His nature? This is what cannot be explained... How the persons of the Godhead have their unity together. I have seen certain explanations of the Catholic version of the trinity which state that none of the members can be separated from the others, because all are composite of the one God. This however creates a conundrum... How did the Son of God die on Calvary and be separated from the Father as a result of the burden of sin laid upon Him?
Saying that something is and comprehending what it is are two different things, so it is not a contradiction. It's like (I am not good with examples so hopefully you get it) if you hear something moving in the woods, you know
that it is without yet knowing
what it is in itself. So there is a distinction.
As for how they have their unity the explanation is simple as well, and St. Gregory of Nyssa's classic work "
Not Three Gods" goes into this explicitly (it is a letter worth reading) so I'll quote from him here: "
The Father is God: the Son is God: and yet by the same proclamation God is One, because no difference either of nature or of operation is contemplated in the Godhead."
No difference of nature is simple, and an analogy can be drawn: there is one human nature but many persons who possess it. A nature is nothing more than "what it is," and a person is the particular individual. So you are a person and I am a person but we both have the same nature. So the Trinity is one nature but three Persons. Note also that the words in Greek underlying "nature" and "substance" here are ousia and hypostasis, so I quote St. Basil (Letter 236 paragraph 6) on this: "
The distinction between 'ousia' and 'hypostasis' is the same as that between the general and the particular; as, for instance, between the animal and the particular man. Wherefore, in the case of the Godhead, we confess one essence or substance so as not to give a variant definition of existence, but we confess a particular hypostasis, in order that our conception of Father, Son and Holy Spirit may be without confusion and clear."
As for the rest of St. Gregory's statement, "no difference of operation," this is what he means: they all do or have the same acts in the divine nature (I saw in the divine nature specifically because the Person of Jesus Christ assumed a human nature and has in it acts that the Father and the Spirit do not have, but that did not change His divine nature so they still do in fact have the same acts in the divine nature, God is immutable) and we receive one act and not many acts. To show this point I will use his own example:
Human persons (let's say there are only three human persons, Adam, Eve, and Cain, which as stated above have one nature) do acts. God does acts as well and there are Three Persons. With human persons the acts are not called one but with God they are called one, why is this? Say Adam and the gang are farming while in general they are all doing the same act the particulars of the act are all individual different: one plants, the other digs, another plows. When God acts the act is the same and we receive it as one and not distinguished by the number of Persons, so when God creates (which is an act/operation) you can not say "the Father made my head, the Son my arms, the Spirit my legs" but "God made my body," for the acts are all one and received as one. As St. Gregory himself says and I quote from the same linked above: "
whatever comes to pass, in reference either to the acts of His providence for us, or to the government and constitution of the universe, comes to pass by the action of the Three, yet what does come to pass is not three things."
So this is why it is right to say there is no difference of either nature or operation. Obviously there are many Scriptural proofs of this, "whatever the Father does the Son does," the Father searching the hearts of men, Jesus doing the same, the Spirit doing the same in Acts, or of the Incarnation in Luke all three Persons bring about the act, the creation of the world all three Persons bring about the act, and so on.
Now as for death: the divine nature is immutable, and the Person of the Son can not be separated from the Father. Death is simply the separation of the body and the soul not the cessation of existence which He experienced through the human nature He assumed, so I do not see why it would divide the indivisible Godhead.