Is it a common understanding among the Orthodox that Catholic ecclesiology is a "universal-type" ecclesiology, based on the idea that the Church is composed of local parts (or "churches") within a larger, universal Church? Schmemann explains "universal" ecclesiology:
"The Church is the sum of all local churches, which all together constitute the Body of Christ. The Church is thus conceived in terms of whole and parts. Each community, each local church is but a part, a member of this universal organism; and it participates in the Church only through its belonging to the "whole." In the words of one of its best exponents, Roman theology seeks a definition of the Church in which "parts would receive within the whole, conceived really as a whole, that status of genuine parts." (Footnote 15)
The important point here is for us to see that in the light of this doctrine the need for and the reality of a universal head, i.e., the Bishop of Rome, can no longer be termed an exaggeration. It becomes not only acceptable but necessary. If the Church is a universal organism, she must have at her head a universal bishop as the focus of her unity and the organ of supreme power. The idea, popular in Orthodox apologetics, that the Church can have no visible head, because Christ is her invisible head, is theological nonsense."
From: Alexander Schmemann. "The Idea of Primacy in Orthodox Ecclesiology". 145-171. In The Primacy of Peter: Essays in Ecclesiology and the Early Church. Edited by John Meyendorff. Crestwood, NY: St. Vladimir's Seminary Press. 150-151.
Footnote 15: J. Congar. Chretiens Desunis. (Paris, 1937), 241.
In contrast, Schmemann continues, Orthodoxy has a "eucharistic-type" ecclesiology, based on the idea that each local church is indeed the whole Church:
"Through the eucharist, we have the whole Christ and not a "part" of him; and therefore the Church which is "actualized" in the eucharist is not a "part" of "member" of a whole, but the Church of God in her wholeness. For it is precisely the function of the eucharist to manifest the whole Church, her "catholicity." Where there is the eucharist, there is the Church; and, conversely, only where the whole Church is (i.e., the people of God united in the bishop, the head, the shepherd), there is the eucharist...The local church as a sacramental organism, as the gift of God in Christ, is not part or member of a wider universal organism. She is the Church....
The essential corollary of this "eucharistic" ecclesiology is that it excludes the idea of a supreme power, understood as power over the local church and her bishop. The ministry of power, as all ministries and charisms, has its source in and is performed within the organic unity of the Church. It is rooted in the sacraments, whose aim is to fulfill the Church as the Body of Christ. This ministry of power belongs to the bishop and there is no ministry of any higher power. A supreme power would mean power over Christ himself. The bishop is vested with power, yet the root of this power is in the Church, in the eucharistic gathering, at which he presides as priest, pastor and teacher....
Does all this mean that Orthodox ecclesiology simply rejects the very notion of primacy? No. But it rejects the fatal error of universal ecclesiology which identifies primacy with power, transforming the latter from a ministry in the Church into power over the Church."