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The Catholic Chuch uses from Scripture Matthew 16:18 as one of the supports for the Papacy: (And so I say to you, you are Peter, and upon this rock I will build my church, and the gates of the netherworld shall not prevail against it.)
The modern widespread majority Protestant view on the Matthew verse agrees with the Roman Catholic view, and disagreements about primacy stem from doctrinal sources, and disagreements such as disagreements over the identification of Simon Peter with the Pope. However, a minority of Protestants still assert the following that was popular when the Protestant Reformation began, based on nuances of the use of Peter's name and the use of "rock" in Matthew 16:18:
Jesus gives Simon the new name πητρος. However he refers to the "rock" as πητρα. The inspired New Testament Scriptures were written in Greek, not Aramaic. What Jesus might have said in Aramaic is conjecture. In Greek, there is a distinction between the two words, πητρα being a "rock" but πητρος being a "small stone" or "pebble". (James G. Mc Carthy translates the two as "mass of rock" and "boulder or detached stone", respectively.) Jesus is not referring to Peter when talking about "this rock", but is in fact referring to Peter's confession of faith in the preceding verses. Jesus thus does not declare the primacy of Peter, but rather declares that his church will be built upon the foundation of the revelation of and confession of faith of Jesus as the Christ.
Verse in context
There are several things happening in this verse:
Peter confesses the identity of Jesus.
The Lord does the same for Peter.
He gives Peter the gift of the keys to the kingdom, representing his authority.
The word Petra is the Greek word for rock, not boulder. The masculine form was not used typically in Greek. When Christ changed the name of Peter, he changed his name to Rock. When Jesus first met Simon, a year before Matthew 16:18, in John 1:41, Andrew introduces Simon, Jesus looked at him and said you will be called Cephas, which is translated Peter. That comes from Saint John. He took a word in Hebrew and translated into Greek. In the second line, the Aramaic, he translates it for them. Cephas means Rock. There is no distrinction in size.
When we translate it, it must be done in masculine form because you cannot give a man a woman's name. Petra is feminine in Greek wheras Petros is masculine.
Protestant Scholarship supporting the Catholic position
Protestant scholar Oscar Cullman, writing in the Theological Dictionary of the New Testament, writes,
The Aramaic original of the saying enables us to assert with confidence the formal and material identity between p tra petra and P tros; P tros = p tra. . . . The idea of the Reformers that He is referring to the faith of Peter is quite inconceivable . . . for there is no reference here to the faith of Peter. Rather, the parallelism of "thou art Rock" and "on this rock I will build" shows that the second rock can only be the same as the first . It is thus evident that Jesus is referring to Peter, to whom he has given the name Rock. . . . To this extent Roman Catholic exegesis is right and all Protestant attempts to evade this interpretation are to be rejected. (Oscar Cullman, Theological Dictionary of the New Testament, ed. by Gerhard Kittel and Gerhard Friedrich, (Grand Rapids, MI: Wm. B. Eerdmans, 1968), 6:98, 108.)
Protestant scholar D.A. Carson writes,
Although it is true that petros and petra can mean "stone" and "rock" respectively in earlier Greek, the distinction is largely confined to poetry. Moreover the underlying Aramaic is in this case unquestionable; and most probably kepha was used in both clauses (“you are kepha” and "on this kepha"), since the word was used both for a name and for a "rock." The Peshitta (written in Syriac, a language cognate with Aramaic) makes no distinction between the words in the two clauses. The Greek makes the distinction between petros and petra simply because it is trying to preserve the pun, and in Greek the feminine petra could not very well serve as a masculine name. . . Had Matthew wanted to say no more than that Peter was a stone in contrast with Jesus the Rock, the more common word would have been lithos ("stone" of almost any size). (D.A. Carson, The Expositor’s Bible Commentary, Volume 8 (Matthew, Mark, Luke), ed. Frank E. Gaebelein, (Grand Rapids, MI: Zondervan, 1984), 368.)
Protestant Greek scholar Marvin Vincent wrote,
The word refers neither to Christ as a rock, distinguished from Simon, a stone, nor to Peter's confession, but to Peter himself, ... The reference of petra to Christ is forced and unnatural. The obvious reference of the word is to Peter. The emphatic this naturally refers to the nearest antecedent; and besides, the metaphor is thus weakened, since Christ appears here, not as the foundation, but as the architect: "On this rock will I build." Again, Christ is the great foundation, the chief cornerstone, but the New Testament writers recognize no impropriety in applying to the members of Christ’s church certain terms which are applied to him. For instance, Peter himself (1 Peter 2:4), calls Christ a living stone, and in ver. 5, addresses the church as living stones. (Marvin R. Vincent, Word Studies in the New Testament, (Grand Rapids, MI: Eerdmans, 1946 (orig. 1887)), 4 vols., vol. 1, 91-92.)
Protestant scholar W.F. Albright wrote,
This is not a name, but an appellation and a play on words. There is no evidence of Peter or Kephas as a name before Christian times. . . . Peter as Rock will be the foundation of the future community. Jesus, not quoting the Old Testament, here uses Aramaic, not Hebrew, and so uses the only Aramaic word which would serve his purpose. In view of the background of vs. 19, one must dismiss as confessional interpretation any attempt to see this rock as meaning the faith, or the Messianic confession, of Peter. To deny the pre-eminent position of Peter among the disciples or in the early Christian community is a denial of the evidence. The interest in Peter’s failures and vacillations does not detract from this pre-eminence; rather, it emphasizes it. Had Peter been a lesser figure his behavior would have been of far less consequence (cp. Gal 2:11 ff.). (W. F. Albright and C. S. Mann, Matthew (Garden City, NY: Doubleday & Co., 1971), 195.)
David Hill, a Presbyterian minister at the University of Sheffield wrote,
It is on Peter himself, the confessor of his Messiahship, that Jesus will build the Church. . . . Attempts to interpret the ‘rock’ as something other than Peter in person (e.g. his faith, the truth revealed to him) are due to Protestant bias, and introduce to the statement a degree of subtlety which is highly unlikely. (David Hill, The Gospel of Matthew (Grand Rapids, MI: Eerdmans, 1972), 261.)
You are Peter, and upon this rock I will build my church: the Aramaic word kepa - meaning rock and transliterated into Greek as Kephas is the name by which Peter is called in the Pauline letters (1 Cor 1:12; 3:22; 9:5; 15:4; Gal 1:18; 2:9, 11, 14) except in Gal 2:7-8 ("Peter"). It is translated as Petros ("Peter") in John 1:42. The presumed original Aramaic of Jesus' statement would have been, in English, "You are the Rock (Kepa) and upon this rock (kepa) I will build my church." The Greek text probably means the same, for the difference in gender between the masculine noun petros, the disciple's new name, and the feminine noun petra (rock) may be due simply to the unsuitability of using a feminine noun as the proper name of a male. Although the two words were generally used with slightly different nuances, they were also used interchangeably with the same meaning, "rock."