Now this is confusing. You say:
the notion of papa or Pope is being used precisely in the manner that Saint Paul speaks of being a Father to the Corinthians.
But in post 412 you seem to suggest there can only be one pope. So now you have a problem. Because if, as you say, the sense of the title is exactly the same, then you cannot be limited to one pope, because you would have Peter being "papa" at the same time as Paul being "papa." Ergo, two popes. But if you say no, no they're not the same, then the sense of the title cannot be the same.
"precisely in the manner" means "
precisely in the manner," not "almost the same except for some raft of unspoken qualifiers."
Bu there are further problems. Let's say I accept your hypothesis that the Papa is the Papa in precisely the manner of Paul being father to the Corinthians. To be true, that would mean the Papa was personally involved in in-person Gospel ministry, and further actually participant in the conversions of everyone who can relate to him as Papa. Because that is Paul's sense, inescapably evident from the text. So are you saying the Papa was really personally involved in the Gospel conversions of every Catholic on earth? But if not, then the sense is different, is it not?
One more thing. None of what Paul said makes go away the command of Jesus to avoid certain ecclesiastical titles. For review:
Mat 23:8-10 But be not ye called Rabbi: for one is your Master, even Christ; and all ye are brethren. (9) And call no man your father upon the earth: for one is your Father, which is in heaven. (10) Neither be ye called masters: for one is your Master, even Christ.
So now we have a new conundrum: How can Paul's statement be reconciled with Christ's command? If Paul is assuming an ecclesiastical title to himself, then He is in violation of the command of Christ, because that is what is forbidden here. It was a practice among the rabbinics of His day to allow themselves to be called "Father Paul," or "Father Jose ben Jochanan," or "Father Chanan," or "Father Chelphetha," to name only a few examples. See Gill on Matthew 23:9.
Those are ecclesiastical titles, tokens of high honor given to the sages. And it is against those ecclesiastical titles that Jesus' command is specifically directed, not the sense of a man as father to his natural son, nor even the sense of an evangelist to those converted under his ministry. Those do not represent an office of universal scope, but a real, and very local, human relationship. So Paul's sense is of personally begetting children in the faith, not an ecclesiastical title worn as a crown of authority over billions of people he never even met, let alone evangelized.
But the command of Christ does not go away. "Papa's" title is a standing rejection of that command.
Peace,
SR