What are the implications if this Cephas IS the Peter whom Paul rebuked and IS only one of three named pillars and only second in the list: James, Cephas, and John?
None whatsoever for the objective reader.
On Peter, Paul and Hypocrisy
In their effort to deny the primacy of Peter and the doctrine of papal infallibility, many non-Catholics point to Paul’s rebuke of Peter over the issue of eating with Gentiles as recorded in the Paul’s Letter to the Galatians.****
Galatians 2:11-14
11When Peter came to Antioch, I opposed him to his face, because he was clearly in the wrong. 12Before certain men came from James, he used to eat with the Gentiles. But when they arrived, he began to draw back and separate himself from the Gentiles because he was afraid of those who belonged to the circumcision group. 13The other Jews joined him in his hypocrisy, so that by their hypocrisy even Barnabas was led astray. 14When I saw that they were not acting in line with the truth of the gospel, I said to Peter in front of them all, "You are a Jew, yet you live like a Gentile and not like a Jew. How is it, then, that you force Gentiles to follow Jewish customs?
In this passage, we see that Paul opposed Peter for not practicing what he preached. Although Peter may have been wrong to draw back from eating with the Gentile believers, we must note that is apparently James, and not Peter, who was the leader of the “circumcision group” in Jerusalem. Thus, those who assert that it was James, and not Peter, who was the real leader of the Church must answer for this error. However, Peter’s actions do not constitute formal teaching, and the doctrine of infallibility does not apply to Peter’s private opinions or behavior. Therefore, this passage does nothing to disprove either Peter’s primacy or the doctrine of papal infallibility. Peter, like his successors, was not above reproach nor impeccable.
However, it must also be noted that Paul was not above taking prudent measures out of fear of those who held to the tradition of circumcision, either. One such measure is found in the following passage:
Acts 16:1-3
1He came to Derbe and then to Lystra, where a disciple named Timothy lived, whose mother was a Jewess and a believer, but whose father was a Greek.
2The brothers at Lystra and Iconium spoke well of him.
3Paul wanted to take him along on the journey, so he circumcised him because of the Jews who lived in that area, for they all knew that his father was a Greek.
Paul wrote that “circumcision means nothing” (1 Corinthians 7:19, Galatians 6:15). Moreover, in the same letter in which Paul accused Peter of hypocrisy and boasted of having opposed Peter to his face, he writes the following:
Galatians 5:2-3
2Mark my words! I, Paul, tell you that if you let yourselves be circumcised, Christ will be of no value to you at all.
3Again I declare to every man who lets himself be circumcised that he is obligated to obey the whole law.
Imagine how Timothy must have felt when he first heard these words. He had let himself be circumcised by the very man who condemned the practice. Was Christ of no value to Timothy at all as a result of being circumcised?
This was not the only time that Paul had acted out of fear of the Jews. Later in the book of Acts, we find the following:
Acts 21:17-26
17When we arrived at Jerusalem, the brothers received us warmly.
18The next day Paul and the rest of us went to see James, and all the elders were present.
19Paul greeted them and reported in detail what God had done among the Gentiles through his ministry.
20When they heard this, they praised God. Then they said to Paul: “You see, brother, how many thousands of Jews have believed, and all of them are zealous for the law.
21They have been informed that you teach all the Jews who live among the Gentiles to turn away from Moses, telling them not to circumcise their children or live according to our customs.
22What shall we do? They will certainly hear that you have come,
23so do what we tell you. There are four men with us who have made a vow.
24Take these men, join in their purification rites and pay their expenses, so that they can have their heads shaved. Then everybody will know there is no truth in these reports about you, but that you yourself are living in obedience to the law.
25As for the Gentile believers, we have written to them our decision that they should abstain from food sacrificed to idols, from blood, from the meat of strangled animals and from sexual immorality.”
26The next day Paul took the men and purified himself along with them. Then he went to the temple to give notice of the date when the days of purification would end and the offering would be made for each of them.
Clearly, the brothers in Jerusalem were concerned that some harm might come to Paul from those who knew that Paul taught against circumcision. Paul agreed to purify himself according to Jewish customs and to pay the expenses of those who were purified along with him rather than openly admit that circumcision was of no value. Was this a wise course of action? Assuredly as subsequent events indicate.
However, it cannot be denied that Paul was preaching one thing (at least in private to Gentile Christians) while practicing another—the very thing he accused Peter of doing.
Whatever was going on - specifically identifying in the words you want: “Peter is Leader and Peter’s Successors will be the future Leaders (Popes).” was not the Will of God. What is necessary, is that you look at all of the other organizaitons - especially those that have sprung up since the 16th Century - and continued to spring up ever since - and appreciate the chaos, disorganization and fragmentation give to the Body of Christ. When Christ prayed to His Father that all could be one - He was aware of what was going to happen - hence, the prayer.
We are not the doubting Thomas’s. These were not mystic visions by James, Cephas, and John. They were visions about them.