East–West Schism
Ecclesiological structure

There are several different ecclesiologies: "communion ecclesiology", "eucharistic ecclesiology", "baptismal ecclesiology", "trinitarian ecclesiology", "kerygmatic theology". Other ecclesiologies are the "hierarchical-institutional" and the "organic-mystical", and the "congregationalist".

The Eastern Churches maintained the idea that every local city-church with its bishop, presbyters, deacons, and people celebrating the eucharist constituted the whole church. In this view called eucharistic ecclesiology (or more recently holographic ecclesiology), every bishop is Saint Peter 's successor in his church ("the Church"), and the churches form what Eusebius called a common union of churches. This implied that all bishops were ontologically equal, although functionally particular bishops could be granted special privileges by other bishops and serve as metropolitans, archbishops or patriarchs. Within the Roman Empire, from the time of Constantine to the fall of the empire in 1453, universal ecclesiology, rather than eucharistic, became the operative principle.

The view prevailed that, "when the Roman Empire became Christian the perfect world order willed by God had been achieved: one universal empire was sovereign and coterminous with it was the one universal church". Early on, the Roman Church's ecclesiology was universal, with the idea that the Church was a worldwide organism with a divinely (not functionally) appointed center: the Church/Bishop of Rome. These two views are still present in modern Eastern Orthodoxy and Catholicism and can be seen as foundational causes for the schisms and Great Schism between East and West.

The Orthodox Church does not accept the doctrine of Papal authority set forth in the Vatican Council of 1870, and taught today in the Catholic Church. The Orthodox Church has always maintained the original position of collegiality of the bishops resulting in the structure of the church being closer to a confederacy. The Orthodox have synods where the highest authorities in each Church community are brought together, but, unlike the Catholic Church, no central individual or figure has the absolute and infallible last word on church doctrine. In practice, this has sometimes led to divisions among Greek, Russian, Bulgarian and Ukrainian Orthodox churches, as no central authority can serve as an arbitrator for various internal disputes.

Starting from the second half of the 20th century, eucharistic ecclesiology is upheld by Catholic theologians. Henri de Lubac writes: "The Church, like the Eucharist, is a mystery of unity – the same mystery, and one with inexhaustible riches. Both are the body of Christ – the same body." Joseph Ratzinger called eucharistic ecclesiology "the real core of Vatican II's (Second Vatican Council) teaching on the cross". According to Ratzinger, the one church of God exists in no other way than in the various individual local congregations. In these the eucharist is celebrated in union with the Church everywhere. Eucharistic ecclesiology led the council to "affirm the theological significance of the local church. If each celebration of the Eucharist is a matter not only of Christ's sacramental presence on the altar but also of his ecclesial presence in the gathered community, then each local eucharistic church must be more than a subset of the universal church; it must be the body of Christ 'in that place'."

The ecclesiological dimension of the East–West schism revolves around the authority of bishops within their dioceses and the lines of authority between bishops of different dioceses. It is common for Catholics to insist on the primacy of Roman and papal authority based on patristic writings and conciliar documents.
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