Well wasn't it PAUL who taught such things?
Chronology. When were Jesus' statements, and when were Paul's?
Paul taught faith and not works, right?
Many works are mentioned in Paul's Epistles. Paul himself was a Worker! Look at his indefatigable travel in declaring the Gospel. The abuses he was submitted to. The martyrdom that crowned the end of his life. Paul had nothing negative to say about the idea of human effort or good works, and said many positive things about both.
On that day many will say to me, 'Lord, Lord, did we not prophesy in your name, and cast out demons in your name, and do many deeds of power in your name?
Part of the Pauline churches practices, right?
The question suggests exclusivity when in fact there was none. In Acts, we see the other Apostles doing the same great things in the name of Jesus. Exorcisms, healings, prophecy, etc. Even when Jesus was on earth, we see the disciples casting out demons in Jesus' name in the Gospels.
The apparent clash between Paul's teachings and the Gospel teachings and warnings
Apparent is the key word in your sentence. However, there was a definite tension between Gentile and Jewish Christians. However, Paul wrote:
I appeal to you, brothers, in the name of our Lord Jesus Christ, that all of you agree with one another so that there may be no divisions among you and that you may be perfectly united in mind and thought. My brothers, some from Chloe's household have informed me that there are quarrels among you. What I mean is this: One of you says, "I follow Paul"; another, "I follow Apollos"; another, "I follow Cephas(Peter)"; still another, "I follow Christ."
Is Christ divided? Was Paul crucified for you? Were you baptized into the name of Paul? I am thankful that I did not baptize any of you except Crispus and Gaius, so no one can say that you were baptized into my name. (Yes, I also baptized the household of Stephanas; beyond that, I don't remember if I baptized anyone else.) For Christ did not send me to baptize, but to preach the gospel — not with words of human wisdom, lest the cross of Christ be emptied of its power.
We don't see Peter refute Paul. We see Peter refute incorrect interpretations of Paul. The Marcionites come to mind. Peter wrote:
So then, dear friends, since you are looking forward to this, make every effort to be found spotless, blameless and at peace with him. Bear in mind that our Lord's patience means salvation, just as our dear brother Paul also wrote you with the wisdom that God gave him. He writes the same way in all his letters, speaking in them of these matters. His letters contain some things that are hard to understand, which ignorant and unstable people distort, as they do the other Scriptures, to their own destruction. Therefore, dear friends, since you already know this, be on your guard so that you may not be carried away by the error of lawless men and fall from your secure position.
Peter baptized the first Gentile, Cornelius. And Acts 10 records Peter's vision:
About noon the following day as they were on their journey and approaching the city, Peter went up on the roof to pray. He became hungry and wanted something to eat, and while the meal was being prepared, he fell into a trance. He saw heaven opened and something like a large sheet being let down to earth by its four corners. It contained all kinds of four-footed animals, as well as reptiles of the earth and birds of the air. Then a voice told him, "Get up, Peter. Kill and eat."
"Surely not, Lord!" Peter replied. "I have never eaten anything impure or unclean."
The voice spoke to him a second time, "Do not call anything impure that God has made clean."
This happened three times, and immediately the sheet was taken back to heaven.
While Peter was wondering about the meaning of the vision, the men sent by Cornelius found out where Simon's house was and stopped at the gate. They called out, asking if Simon who was known as Peter was staying there.
While Peter was still thinking about the vision, the Spirit said to him, "Simon, three men are looking for you. So get up and go downstairs. Do not hesitate to go with them, for I have sent them."
Peter went down and said to the men, "I'm the one you're looking for. Why have you come?"
The men replied, "We have come from Cornelius the centurion. He is a righteous and God-fearing man, who is respected by all the Jewish people. A holy angel told him to have you come to his house so that he could hear what you have to say." Then Peter invited the men into the house to be his guests.
We also note that Paul submitted the issue of the Law to the rest of the Apostles later on in Jerusalem in Acts 15. Their collective ruling was authoritative, and the pronouncement of the decision was made by the most observant Jew in the group, James the Just. We have no record of Paul gainsaying the decision.
What real clashes occurred, occurred between heterodox, breakaway sects, not apostolic Christianity. On the one hand, you had the Marcionites, which said Paul was the only true apostle and renounced anything to do with the Old Testament. On the other you had the Ebionites, who were judaizers, and said Paul was an apostate.
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