"There is nothing more grievous than the sacrilege of schism....there can be no just necessity for destroying the unity of the Church" (St. Augustine, Contra Epistolam Parmeniani, lib. ii., cap. ii., n. 25).
Παρακαλῶ δὲ ὑμᾶς, ἀδελφοί, διὰ τοῦ ὀνόματος τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ, ἵνα τὸ αὐτὸ λέγητε πάντες, καὶ μὴ ᾖ ἐν ὑμῖν σχίσματα, ἦτε δὲ κατηρτισμένοι ἐν τῷ αὐτῷ νοῒ καὶ ἐν τῇ αὐτῇ γνώμῃ. (1 Corinthian 1:10)
"Now I exhort you brothers through the name of our Lord, Jesus Christ, that all of you say/teach the same thing, and there be among you no schisms, but you be made complete/restored/united in the same mind and in the same judgment/purpose/intention." (1 Corinthians 1:10)
"We believe in one, holy, catholic and apostolic non-entity"
I have discussed elsewhere the gnostic roots of the idea that the visible Church is the plurality (or set) of all embodied believers. The major problem with this position is that a "set" or "plurality" is not an actual entity, but only a conceptual entity, i.e. an abstraction of some sort. Imagine the set of all the objects on my desk. The members of that set include books, a printer, some photos, some coins, pens, prayer cards, a toy space shuttle that my daughter gave me, a piece of hard candy, a lamp, a bottle of cologne, etc. I can refer to all the things on my desk by speaking of them with a singular term: "set", when I say, "The set of all the things on my desk." But there is no *single* thing on my desk composed of (or consisting of) the books, the printer, the photos, the coins, pens, etc. on my desk. There is no actual set of things on my desk, even though on my desk there are only actual things that can be referred to collectively as belonging to a set. There are many things on my desk, and I can refer to those many things in a unitive manner, by mentally placing them all into a single set or category, i.e. the set of things on my desk. But there is in fact no set on my desk; on my desk there are only the books, the printer, the photos, the coins, etc. Though the members of the set are actual, the set itself is only a mental construct, not an actual entity.
So when a person claims that the visible Church is the set (or plurality) of all embodied believers, the semantic confusion regarding "set" and "plurality" allows the person to seem as though he affirms the existence of the visible Church. But in fact he has adopted a position in which there is no such thing as the visible Church; there are only embodied believers, just as in actuality there are only objects on my desk, and not, in addition to the objects on my desk, one more item, namely, the set of objects on my desk. Those who claim that the visible Church is the set (or plurality) of all embodied believers have a position in which the visible Church does not exist at all.
The Possibility of Schism as a Test of Ecclesiology
Any conception of the visible Church in which schism is either impossible or cannot decrease the unity of the visible Church must be a false conception of the visible Church. One such conception treats the visible Church as the set of all embodied believers. The disunity of believers against each other, so long as they remain believers, does not detract in any way from the unity of the set of all believers. Why? Because a set is only a conceptual unity, and the category by which the members of this set are conceptually united is 'believer', and has nothing to do with the harmony and communion between believers. Likewise, the plurality of believers cannot be divided by divisions between believers. Likewise, the sum of all believers cannot be divided by divisions between believers. The Westminster Confession of Faith comes very close to this sort of conception of the visible Church when it says: "The visible Church ... consists of all those throughout the world that profess the true religion; and of their children...." (WCF XXV.2) If the visible Church is the plurality of those who profess the true religion, then while the visible Church can be larger or smaller, it can be neither more nor less unified, and thus it is absolutely impervious to schism. Another conception of the visible Church is the set/plurality of assemblies of embodied believers. But the unity of the set of all assemblies of embodied believers is not lessened so long as the assemblies of embodied believers remain, even if the assemblies have no communion with each other. So this conception of the visible Church treats the Church as impervious to schism.
Schism is only possible if the visible Church is both a unity and a plurality. If the visible Church were only a unity and in no way a plurality, then no schism would be possible. What has no parts cannot be divided. Similarly, if the visible Church were only a plurality, then again no schism would be possible, for what has no unity can lose no unity. The notion of the Church as a Body (i.e. a living organism) allows for the possibility of schism, because an organism is both a unified and composite entity.
The Three Modes of Organic Unity
Now an organism is unified fundamentally in three ways, and each of these modes of unity can be seen in the Trinity. First, an organism is unified in its essence. Each of its parts shares the very same essence. All the cells of our body are human cells. All the cells of a sunflower are sunflower cells. Etc. They all have the very same formal nature. So likewise do all three Persons of the divine Trinity share the very same divine essence. And so likewise, as St. Paul says in Ephesians 4:5, in the Church there is "one faith". We all believe the same thing, the one faith of the Church. When we affirm the Creed at our baptism, we are incorporated through baptism into the body of Christ. The Creed has long been called the "symbol of faith". We are formally unified because we all believe the same thing.
Second, an organism is unified in its activity. Each part of an organism is performing some specific task, but each of these specific tasks is part of a larger unified task, the activity of the organism. This same sort of thing can be seen in the divine Trinity. Each Person of the Trinity does an activity, and yet that activity is part of the overall activity of the Godhead. Likewise, in the Church all of our individual activities must be coordinated to the overall activity of the organism which is the Church. We all, like Christ, offer ourselves up to God as living sacrifices. But we do so most fully in the liturgical assembly when we offer ourselves up to the Father in union with Christ's sacrifice, and then feed upon Christ in return. "Since there is one bread, we who are many are one body; for we all partake of the one bread." (1 Cor 10:17) We are dynamically unified because we all are engaged in the very same activity. (This is precisely why those who do not participate in this activity with us are "deprived of a constitutive element of the Church" and "cannot be called "Churches" in the proper sense". See here.)
Third, an organism is unified in its hierarchy. Not every part of the organism is the head. The parts of a body are ordered hierarchically, in systems, organs, tissues, and so on. (Cf. 1 Corinthians 12) The hierarchy is unified because the head is one. If the top of the hierarchy were a plurality, then the hierarchy would not be unified. Again we find the same thing in the Trinity. The Son does only what the Father tells Him; the Spirit seems to be obedient to the Father and the Son. Likewise, in the Church, the Head of the Body is Christ. Before His ascension Christ appointed Peter to feed His sheep until He returned. In this way, the visible Church as organism retains a visible head, and thus retains all three marks of unity. When Christ ascended, the Twelve Apostles would not have been the *Body* of Christ if Christ had not appointed Peter to be the visible head. Unity of faith and unity of activity cannot remain without unity of hierarchical authority.
[These three modes of unity correspond also to Christ's roles as prophet, priest, and king. They are also the three "bonds of unity" in the Church (CCC 815).]
The third bond of unity is violated by schism. Schism is defined as "the refusal of submission to the Roman Pontiff or of communion with the members of the Church subject to him." (CCC 2089) No other definition makes sense, in part because no other definition can distinguish schism from excommunication, and no other definition makes schism always wrong.
The two greatest threats to the Church are internal, not external. They are schism and heresy. But neither 'schism' nor 'heresy' can be objective apart from a unified universal magisterial authority. Apart from the Petrine office, 'schism' merely means "separated" or "separated from me", and 'heresy' means "disagreeing with my interpretation of Scripture". And thus apart from the Petrine office, there is no possibility of schism or heresy. Thus the test of the possibility of schism and heresy confirms the Catholic position.
"Let unity, the greatest good of all goods, be your preoccupation." - St. Ignatius of Antioch (Letter to St. Polycarp)