There are many arguments for the existence of God that use logic. Here I want to use logic to look at the question of infallibility. Moreover, I will look at it through the perspective of an Old Believer. Having read a number of disputes between various strands of the Old Orthodox (as they call themselves) and between Priesthood-accepting as well as Priestless Old Believers and Russian Orthodox missionaries, I came to this argumentative scheme for "personal" (using individual-personal property distinction here) infallibility. This argument presupposes belief in Church infallibility and does not go over its limit: simply demonstrating that personal infallibility exists. I will use the typical Old Believer Q&A mode here.
Does infallibility exist?
Yes, the Church of Christ has it.
What is the Church?
The faithful, their fullness that includes the Church Militant and the Church triumphant.
Can an individual faithful fall astray?
Yes, since the Psalmist says: "Every man is a liar" (116:11).
Can all faithful fall astray?
No, because of Christ's promise in Mt. 16:18.
What is the Church?
The faithful, their fullness that includes the Church Militant and the Church triumphant.
Can an individual faithful fall astray?
Yes, since the Psalmist says: "Every man is a liar" (116:11).
Can all faithful fall astray?
No, because of Christ's promise in Mt. 16:18.
What does it mean to not be prevailed by the gates of hell?
According to the Fathers such as Cassian, it means not to be conquered by "misbelief of heretics" (On Incarnation, III, 14).
What is the minimum number of faithful for the Church to not be conquered by heresy?
Based on Maximus' words: "Were the entire world to embrace the new heresy, I would not" at least one.
How can that person not fall?
God gives that person the power of perseverance against error (his intellect and will cannot succumb to a false doctrine) in order to keep the promise, given in the Gospel of Matthew.
According to the Fathers such as Cassian, it means not to be conquered by "misbelief of heretics" (On Incarnation, III, 14).
What is the minimum number of faithful for the Church to not be conquered by heresy?
Based on Maximus' words: "Were the entire world to embrace the new heresy, I would not" at least one.
How can that person not fall?
God gives that person the power of perseverance against error (his intellect and will cannot succumb to a false doctrine) in order to keep the promise, given in the Gospel of Matthew.
Thus, there must be at least one person, who will persevere against heresy.
This is not an attempt to prove Papal infallibility, but, as I've already said, it is simply an attempt to demonstrate the possibility of an individual infallibility. As you might have noticed, there appears a difficulty at a particular point in this argumentative chain: Priestless Old Believers do not believe that the earthly priesthood must exist until the end of the world and thus, the last standing Christian in the world might be a regular lay person. For some Priest-accepting Old Believers that one person must be a priest, because New Testament priesthood and more importantly, the Eucharist cannot cease to exist. For some, that individual must be the bishop, because a priest cannot do anything without a bishop. There are many difficulties with this position if we only take one mode of interpretation concerning "Thou art Peter", which most Old Believers interpret as talking about the faith of Peter, not Peter himself. ROC missionaries had to abandon this interpretation, which they often used against Catholics, for obvious reasons. The promise was not to Peter but to all of the Apostles and their successors. However, a) no one believes that all bishops are infallible and b) there still is a question of how many people there must be if the only mode of infallibility is "collective". Catholics, of course can easily give the answer, who that last Christian must be.