Simon answered Jesus’ question - “You are the Messiah, the Son of the living God” to which Jesus said: “Blessed are you, Simon son of Jonah, for this was not revealed to you by flesh and blood, but by my Father in heaven". Because of this he renames him rock and proceeds to say: and on this rock (the same rock) I will build my church.
Jesus said to Peter, “Blessed are you. . . . And so I say to you, you are Peter. . . . I will give to you the keys to the kingdom. . . . Whatever you bind on earth shall be bound in heaven.” Jesus uses the word you seven times in just three verses. It doesn’t follow that Jesus would address so much of this passage to Peter, and then say, “But I will build my Church upon me.” The context is clearly one in which Jesus is communicating a unique authority to Peter. Plus, it would be unnecessary for Jesus to claim the obvious which is that He is the Divine rock/cornerstone upon which His church is built. He is also King who holds the divine keys; nevertheless he gave a set of key, metaphorically speaking, gto His steward in His absence, as was the case with the kings in the OT.
Regarding the Petros/Petra dilemma: As everyone knows Matthew was translated into Greek and petra would have been used for rock. However, petra is a feminine noun. It would have been improper to call Peter " petra," and so petros, the masculine form, was employed. Do we at least agree on that?
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