In another thread I mentioned the known fact that many Patriarchs (including Pope Honorius) were known to be heretics in the past.
What was the condition of the flocks of their sees? Were they considered heretic as well? How were they reintegrated into the Orthodox communion?
I ask that because that examination can suggest ways of how the Roman see could heal itself from Catapapism just like Eastern Patriarchates healed from other heterodoxies.
Michael, I have proposed elsewhere in this forum, the following expressions: Catameric, catapapic and catabiblic churches, in contrast with "catholic".
The word "catholic" has been claimed to mean "universal". But it comes from "cata holic". This "cata" or "kata" is the same "kata" that we see in "Evangeliou kata Ioannis" (Gospel According to John) and also in the other "accordings" of the remaining three gospels. Therefore, "cata holic" seems to mean "according to the whole", that which agrees with the whole. Just like the Gospel "katas" denote the source of authority of the corresponding Gospel, "kata holic" denotes the source of authority of the Church: the whole, from every part, because the Spirit blows wherever He wants. "Universal" as far as I understand, may have two words in Greek: "kosmic" for the physical universe, and "ecumenic" for the social universe. "Kata holic", therefore, cannot mean any "universal" but only a definition of the source of authority in the Church.
The Church is composed of various elements: lay people, bishops, priests, councils, a primate, etc. etc. The only one who is Infallible is God. God-Holy Spirit manifests the Truth (the Son) in the Church "according to the whole", that is at the same time, everywhere. That is why when we see Church history we can see Truth winning over falsehood through any of the elements of the Church: a lay person, a priest, a monk, a deacon, a bishop, a primate, a council. Many, many times, some of the elements are corrupted and one of the others has to stand alone against all the rest. But because Truth is with him, it eventually wins (sometimes at the cost of the life of the martyr).
The 2nd millenium saw the advent of a new category of heresies, those that deal with this manifestation of the Infallible Holy Spirit. Instead of acknowledging the catholicity of the Church, that is, the true "doxa" and the true doctrine are manifested "cata holic", according to the whole, Western communions stopped accepting this "holism" of the source of Truth, in favour of this manifestation occurring exclusevily in some special pronouncements of the Pope. Later, Protestants would also deny the authority of the "holos" of the Church in all places and in all times, to claim that this infallible or inerrant authority manifests only in the Bible.
Well, the Primate of the Church and the Bible are just elements, parts of the Church. If one denies traditional Catholic source of authority (according to the whole), and exchange it for a source according to one of the elements you can say that in fact that communion ceased to be "cata holic" and believes in a church "according to" an element.
Truely, we have a church that believes that the infallibility of God only manifests in ex cathedra statements of the Pope, to the exclusion of the proper "holos" of the Church. Therefore this church may be called "Catapapic", according to the Pope. Likewise, if the "inerrancy" of the Holy Spirit is now limited to the Bible, those who believe this may properly be called "Catabiblic". If someone choses any single element of the Church as the exclusive source of the Infallibility of the Spirit, they could be described by similar words: Catasynodic, Cataparadosic, Catagerontic, Catamysteric, etc etc. All these are species of the same order, that of denying that the infallibility of the Holy Spirit is manifested "according to the whole" and that it is manifest only "according to a part". "Part" in Greek is "meros", so we can say that there are several kinds of "Catameric" faiths, depending which "meros" is chosen.