I really wish I could keep this simple. You commented to Lakis:
This is true if you mean that "Christ has one [Ousia] composed of two [Ousias]" which is not what the non-chalcedonians believe at all.
I would be the odd man out, however I can think that everything has "a" essence, substance, or being, and that therefore Christ has one essence composed of both and thus He is consubstantial with both.
However, neither Chalcedonians nor nonChalcedonians assert this. They both agree that Christ has two essences and one hypostasis, but it looks like many Eastern Orthodox disagree with many Orientals over how many natures he has. However, some EOs and OOs both agree that He has a united nature and also two natures that compose it and yet are not removed.
You are right that:
The two Ousias or Essences were united "WITHOUT CONFUSION, MINGLING, ALTERNATION,..."
The MiaPhysis of the Oriental Orthodox is not MiaOusia as the above quote implies.
The non-chalcedonia/ Oriental Orthodox confess that Christ has all the properties of divinity and all the properties of humanity, including natural will an engergy belonging to humanity in Him
By the English word [Nature] which means "Physis" to some and "Ousia" to others, the Oriental Orthodox mean One concrete reality of the Logos Incarnate is both completely God and completely man at the same time. The Oriental Orthodox do not speak in terms of Ousia, generally, but they mean the same thing as the Chalcedonians.
One [Nature] from [two] means One concrete reality from two realities- Divinity (1) and Humanity (2) and now you have one fully Divine Human Being.
The word essence or substance mean "ousia" and vice verse, as translated in the Nicene Creed in Latin and Greek.
The Orientals use the word physis, because their discourse was in Greek, rather than English. The discussion therefore is over the meaning of physis, which means nature.
Personally, I think Essence (ousia), Nature (physis), and Hypostasis are all different concepts as they are different words with different connotations. At least, this is an easy way for me to understand it.
For me, a nature refers much more to properties, while essence refers much more to something more concrete, like an "ether." For example, we say someone has a good nature, something has a hot nature, the weather can have a windy nature one day and a calm one the other. But is hard to say that something has a windy essence one day and a calm one another day. Essence is much more inherent, internal, and "core" than nature, which means just a collection of properties, I think.
The other idea, which I sometimes hear is that Orientals mean something different than Eastern Orthodox when they say nature, such that Orientals really mean hypostasis. Personally I am doubtful about that two, because again, those are two different words, and I think that they would know the difference. It is strange for me to think that Christ's hypostasis came from two hypostases- divinity and humanity, although I do think that of course He came from the Father and His human mother. And they do not say His hypostasis came from two hypostasis, I think, unless they mean His Father and mother. But actually, I am not even sure it can be said His hypostasis came from His mother, since it seems to me His hypostasis was just the Word, while it was His essences and natures that came from both.
Now, even if they don't mean hypostasis by "nature", but just "concrete reality," this is still tough for me. Unless we are talking about His Father and mother both being the concrete realities, it is hard for me to see in what way those two "concrete realities" came together - without incurring the kinds of objections raised against the idea of a "united nature".
Namely, when I say a nature is simply a character, and Christ's character came from two other collections of properties (characters- divine and human), some object that this means God is not "one", but that I created a new God. (Personally I do not really get that objection, because we already say Christ is God and has two natures and essences). But anyway, if we define Christ as a concrete reality as composed of two concrete realities, which as Cyril says are "preserved", it seems that we would run up against the same kind of objection- and even more so, because now we have proposed not just that Christ's collection of properties are "complex", but also that his concrete reality is complex. Granted, Cyril says Christ's nature is complex. But in any case, I feel like the same kinds of objections made to my idea of a united collection of properties would remain in the case you mentioned.
Now, do I think you are right that they mean a concrete reality different than a collection of properties? Well, first I think they don't mean "essence", like many Eastern Orthodox do, when they say "nature", because they treat the number of both differently.
For them, a nature must be something "united" in a person or anything. Everything to them that is a whole must have "a" nature. Does this mean that they think it is just a collection of properties, or something more fundamental and core? I have seen both- an Armenian writer, Grigor Yan who administrates the Agape Dialogue agreed that a nature is a collection of properties and that everything has one such collection or totality, while Fr. Peter Farrington contrasted essence with nature, and said nature is something much more concrete and inherent. In my view, Grigor is correct and nature just means a collection of properties because that is how we generally use it in speech. Nature does not have to be concrete and inherent, as in a "windy nature" that can vanish the next day. Instead, it is because Orientals focus on Christ's unity that they also say that His Nature is one, and by this they do not realize that something can also have two collections of properties (natures), while still having one "nature."
In fact, I would go as far as to say that if humanity and divinity are "concrete realities", that Christ is still in both of them, and this by definition means He can really be in two concrete realities. He has the fullness of humanity and the fullness of divinity and those has both "realities".
Thus I say that for me much of this is a terminological difference, and the problem becomes stronger when one rejects that the other view (not two natures, not two "concrete realities" - human and divine, not one nature, etc.) is incorrect.