In the first and second parts of this series of posts, we discussed the infallibility of the Church as a whole, and then the infallibility of an ecumenical council.
We concluded the last post with the question, Is the infallibility of an ecumenical council enough? In other words, in order to preserve the unity of the Church, and to transmit the faith with certitude to the common believer, is it enough that ecumenical councils alone be infallible?
I believe the answer is, No, the infallibility of ecumenical councils is not enough for the good of the Church.
Why? Because the councils themselves sometimes need clarification.
No doubt the ecumenical councils have done much good for the Church. They have authoritatively interpreted Scripture, resolved disputes, and articulated the Church’s faith.
However, when one reads the histories of the councils, one quickly sees that it was (and is) not a clean business.
The councils resolve controversies but also create some others. Not the least of the controversies created by councils is the very question, Which councils are truly ecumenical and therefore infallible? There were false councils that have claimed ecumenicity. History has witnessed groups of bishops gathering together and claiming to speak for the infallible Church, when they were not authorized to do so and did not truly represent the Church.
How does one discern a true ecumenical council from counterfeits?
The Catholic answer has been simple: those confirmed by the Successor of Peter are truly ecumenical. This principle is based on a concept that has its roots in the worldview of the Gospels: the gathered apostles do not make a quorum without Peter, their leader.
Before I became a Catholic, I did not think the example of the Apostles in the Gospels and Acts provided an enduring model for the government of the Church. The Apostolic age, I thought, was entirely unique. That was for then, this is now. Our Protestant model of Church government was based on other archetypes, like modern Western democracy.
Obviously, the Catholic reading of the New Testament is different. In the Catholic view, we are still living in the New Testament world. The dynamics among the Apostles are still lived out in their successors, the bishops. In fact, the ministry of the Apostles continues in the ministry of their successors. In particular, the ministry of Peter as head of the Apostles continues in the bishop of Rome.
This way of understanding the continuity between the early Church and the later Church can be found in the acts of the ecumenical councils themselves.
After Nicaea, the Council of Chalcedon is probably the most revered of the ecumenical councils. Most Christians would identify themselves with “Chalcedonian orthodoxy”—that is, with the consensus on the natures and personhood of Christ that this Council achieved.
Yet it should be remembered that the Chalcedonian consensus was achieved when Pope Leo I’s “tome” (letter) was read before the council, and the assembled bishops—mostly from the East—responded in affirmation: “Peter has spoken through Leo!” 
Many Christians not in communion with the Bishop of Rome nonetheless would identify themselves with the councils, particularly Chalcedon. Yet the Fathers that gave us Chalcedonian orthodoxy themselves presumed the Petrine succession of the Bishop of Rome, and affirmed that the Petrine ministry continued in Peter’s successor.
To reiterate, the Catholic principle to discern the truly ecumenical (infallible) councils is: Confirmation by the Successor of Peter.
I believe—with the rest of the Catholic Church—that this principle has biblical, historical, and theological support. Obviously, however, the biblical, historical, and theological validity of this principle can be challenged and is challenged by most Christians who are not in communion with the successor of Peter.
However, what principle is proposed to put in its place? There cannot be no principle of discretion, because there clearly have been non-ecumenical councils that have claimed ecumenicity (infallibility). I suggest that the other non-Catholic criteria that are proposed to distinguish authentic Councils are more vulnerable to critique on biblical, historical, and theological grounds than the criterion they propose to replace: Petrine (papal) confirmation.
The voice of Peter, through his successor, is the final voice of the assembled apostles (bishops) which guarantees that the apostolic quorum is met and the assembly is ecumenical (infallible).  One can see, then, that Petrine/papal infallibility is an aspect of the infallibility of the Church:
The Church is infallible.
The Church speaks through an ecumenical council.
An ecumenical council is distinguished by the affirmation of the Pope, the successor of Peter.
Therefore the Pope participates in the infallibility of the Church: unless his affirmation is infallible, we lack an objective and reliable way to distinguish the authentic councils.
An Unending Chain of Infallibility?
Our discussion to this point may seem to have gotten overly complex, the chain of infallibility overly long. Someone may ask: “So many infallible things: Scripture, Church, councils, Pope—what good does it do? Does adding the Pope do anything but add another layer of infallibility to an already cumbersome system?”
It is helpful, then, to step back and observe that the chain of infallibility is not interminable. It is not even very long. In principle, the situation is relatively simple: The Scriptures are infallible, and the Church interprets them infallibly. Who speaks for the Church? Only two voices: her universal (ecumenical) council or her universal pastor (the Pope). Put in biblical terms: the assembled Apostles, or Peter himself.
What Good Does Papal Infallibility Do?
One might ask, what good does it do to “add” the Pope to the chain of infallibility? What does his infallibility do that the infallibility of the Scriptures or the Councils don’t already do?
It is a fair question, but one that has a good answer. The difference lies in this: unlike the Scriptures or the Councils, the Papacy is a living voice that actively resists the misinterpretation of its words.
When I say that the Papacy is a “living voice,” please understand: I am not denying that there is a true sense in which we can say that the Scriptures are a “living voice” and even the testimony of the Councils is a “living voice.”
And yet, there is also a true sense in which the authors of Scripture and the Fathers of the Councils have walked off the stage of history and we cannot bring them back to interrogate them about the intent and meaning of their words. “Does Paul really mean what he seems to be saying here?” “If the Council Fathers were assembled today, would they still insist on this certain discipline in our contemporary context?” These are questions we cannot ask of the sacred authors and the once-assembled bishops.
The papal ministry, however, is different. The canon is closed. Nicaea has concluded and can never be called back in session. But the Pope is always with us.
After someone has left the room, those who remain at the party can talk behind his back. “What he really meant to say was ....”
But the Pope never leaves the party. It is difficult to talk behind his back, and eventually he overhears. He is always able to clarify: “That is not what I meant to say—what I meant was this: ... !” In fact, just such a ministry of clarification against continuing attempts to misconstrue Church teaching is quite visible in the series of encyclicals touching precisely on the doctrine of Scripture: Providentissimus Deus, Spiritus Paraclitus, Divino Afflante Spiritu, Humani Generis.
Papal infallibility means, among other things, that God has provided us a reliable and continuing voice able, when necessary, to clarify the truths of the Scriptures for the contemporary Church.
To summarize what we have been saying: for the sake of the salvation of mankind, God has to transmit to us the saving truth free from error (that is, infallibly). The unerring Truth is primarily found in the Scriptures, but God also needs to ensure that the Truth of the Scriptures is interpreted without error (infallibly). For this reason, he provides the Church. If the voice of the Church is unclear, the universal pastor can clarify. God protects the universal pastor from error in his teaching (infallibility). Since the universal pastor is always present with us and can always clarify his own meaning, the faithful transmission of the truth to humanity is ensured.
Of course, there is much, much more that can be said. For example, we have primarily considered papal infallibility in relationship to conciliar infallibility. Yet the Petrine ministry is much more than simply to confirm councils. I may follow up with another post.