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Did Peter take on the trait of infallibility one this "true and proper" jurisdiction was conferred upon him?I don't think there's a teaching on this, so I don't really know for sure, but I'd imagine that Peter was given the charism of infallibility either:
- when the Father revealed to him that Jesus was "the Christ, the Son of the Living God" (Mt 16:16-17),
- when Jesus changed Peter's name and declared that He would build His Church on him (Mt 16:18), or
- when Jesus gave Peter the keys of the kingdom of heaven (Mt 16:19).
It's my understanding that the pope's words are deemed infallible.Well, yes and no. The pope's words are deemed infallible, but only when, as the successor of St. Peter given the task of feeding and tending the sheep, he articulates some point regarding faith or morals meant to be held by all the faithful.
Actually, you mentioned the First Vatican Council in this thread, and that Council addresses when it is that the pope is infallible:
Therefore . . . we teach and define as a divinely revealed dogma that when the Roman pontiff speaks ex cathedra, that is, when, in the exercise of his office as shepherd and teacher of all Christians, in virtue of his supreme apostolic authority, he defines a doctrine concerning faith or morals to be held by the whole church, he possesses, by the divine assistance promised to him in blessed Peter, that infallibility which the divine Redeemer willed his church to enjoy in defining doctrine concerning faith or morals. Therefore, such definitions of the Roman pontiff are of themselves, and not by the consent of the church, irreformable.I hope that answers your question.
Another question: Could an apostle who's been given apostolic primacy be rebuked by a lesser apostle?Yes, and I know what you're referring to: Paul's letter to the Galatians where he talks about rebuking Peter to his face. What you have to keep in mind is that Peter is being rebuked for misbehaving, not for teaching error on matters of faith or morals. Infallibility does not mean that a pope will always live his life in perfect uniformity to what he believes, or that he will never sin. All of the popes of the Church were sinners and there were a few who actually led quite scandalous lives. I don't deny that in the least. Furthermore, no man is above fraternal correction. Even the pope has a confessor.
Infallibility simply means that the Church is protected from teaching in a formal capacity any doctrinal error. Since Peter was not propogating doctrine, Paul's rebuke of him does nothing to reject Peter's primacy or his infallibility.
Would the apostle with primacy be the one to make final declarations, or could that authority be given to another?I have a feeling you're referring to the Council of Jersualem in Acts 15, but I'll wait until you specifically say something about that before I give you my take on it.
Regarding your question, the pope is the final and highest authority in the Church. But that does not mean that he always has to have the final say on everything that happens within the Church. For example, the bishop for each diocese is the one responsible for the liturgy in his diocese. So, if there's a problem in the diocese, the pope doesn't have to be the one to handle it and it is not necessary for the pope to sign off on the legitimate decisions that the bishop makes within the bounds of his authority.
Similarly, the pope signed off on all 16 documents of the Second Vatican Council, but various committees of bishops and expert theologians/liturgists were responsible for the implementation of the documents.
So, there is a hierarchy and a delegation of responsibility within the Catholic Church, but, the pope is always the highest authority.