What is the Oriental Orthodox tradition? In Ephesus 1, Saint Cyril of Alexandria had no problem with the idea of a council excommunicating Nestorius of Constantinople.
Well, no, of course he didn't; we didn't and don't, either.
Yet, OO have historically rejected the 4th and 5th councils. Can someone help me understand how ecclesiologically you would understand the schism question?
Schism is not really understood any differently than you have already put it, in the sense that those who refuse the first three councils are definitely in schism, but I suppose if there is a difference it is that the OO have a much less mechanical way of looking at the councils. You will note, I hope, that Chalcedon is rejected for what we take to be its reversal on the settled matters
already dealt with in the third council, which means that by virtue of what it accepted (in the Tome of Leo's sloppy wording which seems to make the natures themselves separate loci of experience within Christ, thereby running afoul of the anathemas of St. Cyril), the Chalcedonian council is itself not in agreement with what had already been accepted by the entire Church in the third ecumenical council. I am aware already that the Chalcedonians will stress that Chalcedon itself proceeds from the acceptance of St. Cyril's theology and the anathemas, so I don't mean to reopen that discussion again, and yet this is precisely how it can be that we have rejected the Council: because our ultimate allegiance is to the faith itself, not the workability of councils themselves as a thing considered in the abstract (this "Orthodoxy = 7, not 3" business; I have never heard "Orthodoxy = 3" from any OO person, and nor would I say such a thing myself). Hence if there are problems with the faith that is accepted by them (and, to OO, there are such problems with Chalcedon, or to be more specific, with the Tome that was accepted there), they are to be rejected on that account.
I should note here, just for clarity's sake, that the flip-side of this approach is to be found in the acceptance of confessions such as was accepted by our common father HH St. Cyril in his dealings with John of Antioch. And we both like that, right? I know my church does. But that John of Antioch did not confess miaphysitism and was
still accepted (even as St. Cyril himself never budged an inch on that confession himself, as there was no need to, for it is Orthodox) should tell us something of the "Oriental" mindset vis-a-vis that of the Chalcedonians, as this is the same mechanism by which Eutyches was (wrongly, we both know
now) readmitted to communion at Ephesus II (that is, on the basis of his confession read before the assembled bishops), and is the same mindset expressed in the words of our father HH St. Timothy II (r. 457-477), the Pope who succeeded HH St. Dioscorus, who wrote about the communing of the simple layperson who was at that time caught in the midst of the debates between the two larger warring parties:
“If, therefore, an ordinary, simple person comes to you, confessing the holy faith of the consubstantial Trinity, and desirous of being in communion with you who acknowledge our Lord’s fleshly consubstantiality with us – I entreat you, not to constrain those who hold such views as these at all with other words, nor require from them additional verbal subtleties, but leave such people to praise God and bless the Lord in the simplicity and innocence of their hearts….Anyone who does not abuse the saints touching this declaration: ‘I confess that our Lord is our brother and that he was of the same fleshly stock as us for the sake of our salvation’, accept such an one in our Lord.”
(source: Ebied, RY and Wickham LR "A Collection of Unpublished Syriac Letters of Timothy Aelurus" in
The Journal of Theological Studies, Volume XXI, Issue 2, 321-369)
All of this is to say that, on the whole, we are less concerned with worries about "This is an ecumenical council, so we have to agree with it or else we're in schism!" as a method of determining who believes what, who is in schism from whom, and how this all works in comparison to how things work for the Greco-Roman Chalcedonian churches. Such a thought has honestly never even entered my mind with regard to Chalcedon (neither about us who dissent from it nor about you who accept it), because from where I am sitting -- with my fathers HH St. Cyril, HH St. Dioscorus, and HH St. Timothy II in mind -- the councils were made for the Church, not the Church for the councils.
