The words of Matthew 16:18–19 (and Matthew 18:18) have often been the cause of debate and argument, but the passage is straightforward. The promise, “I will give you the keys of the kingdom of heaven, and whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven,” must be understood in the Jewish context. When scribes were admitted to their office, they received a symbolic key of knowledge (see Luke 11:52). The duty of the scribes was to interpret and apply the law of God to particular cases. When the scribes bound a man, they placed him under the obligation of the Law, and when they loosed him they released him from the obligation.
Similarly, the Lord had been training His disciples to be stewards of His teachings. In this promise in Matthew 16:19, He referred to their future writing and preaching as scribes of the New Testament and promised divine help to His disciples in those tasks. In John 14:26 He gave His disciples two promises: a divinely aided understanding and a divinely aided memory. “But the Helper [Counselor], the Holy Spirit, whom the Father will send in My name, He will teach you all things, and bring to your remembrance all things that I said to you.” John 16:13 adds to this a divinely aided knowledge: “He will tell you things to come.”
In order that the disciples might recall accurately all that Christ had said and done, instruct the Christian church in the way of truth, and write of things still in the future, Christ promised the help of the Holy Spirit. The apostles would be writing with no less authority than the Old Testament prophets.
And something else interesting from further down in the article:
Although the Jewish rabbis and Greek and Roman philosophers preferred oral teaching, we know that students of both kept notes of the instruction they received. Notice the “writing tablet” in Luke 1:63. It was also common for civil servants and others (like Matthew, Zacchaeus, and the man in Luke 16:6) to use a “notebook” for their work. This was an early form of book made of parchment sheets fastened together with a primitive spiral bind. The Greek language borrowed the Latin name for it, which is membranae. This is exactly the word translated “the books” in 2 Timothy 4:13. Paul used a notebook.
The Gospels record 21 Aramaic words used by Jesus, and we may therefore assume that Jesus generally taught in Aramaic. Professor Alan Millard comments, “The simplest explanation for the presence of these foreign terms in the Greek text is accurate reporting.” In Galilee, where Hebrew was little used, Jesus may have taught in Greek. A leading Jewish authority on the rabbis of this time concludes, “We would naturally expect the logia [teaching] of Jesus to be originally copied in codices.”
We are not suggesting that all the Gospels were written “on the hoof” as the disciples accompanied Jesus, but it would be natural to expect some listeners to write down His teaching and parables. This would be fully in keeping with what we know of the literacy and note-taking of first century Palestine. There is no reason the Gospel writers would not have had access to written records.
The idea that the Gospels and epistles were not written down until two or three centuries after the death of Jesus is yesterday’s “scholarship.” Ignatius, who was martyred around the year AD 115, wrote of the apostles’ letters and the Gospels as the “New Testament.” This was typical of all the early church leaders who acknowledged only the four Gospels for the life and teaching of Jesus. By AD 150 the Muratorian Canon listed the books accepted by the “universal church,” and it includes the four Gospels and all thirteen letters of Paul.
In 1972 a liberal scholar, John A. T. Robinson, published a detailed study of each of the books of the New Testament and concluded that every one must have been completed before the year AD 70. In addition he condemned the “sheer scholarly laziness” of those who assume a late date for the New Testament and added, “It is sobering too to discover how little basis there is for many of the dates confidently assigned by modern experts to the New Testament documents.”