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One popular argument against the Bible is that the Gospels are not reliable because they were written late enough that myth and exaggeration could easily have crept in. For example, the article, "40 Problems with Christianity," Michael Runyan says this:
The accounts of Jesus’ life in the gospels were written well after the events allegedly occurred. The crucifixion of Jesus is believed to have occurred around 30 AD. The best estimates date the gospels as follows:
Mark: AD 68-73
Matthew: AD 70-100
Luke: AD 80-100
John: AD 90-110
The time lag between the events and the documentation was long enough for exaggeration and myths to contaminate the historical account. It would be similar if a person today wrote a biography of Dr. Martin Luther King, Jr. just by talking to people who heard something about him from their now-deceased ancestors.
Runyan's argument here is absolutely absurd. Martin Luther King, Jr. died in 1968. It is now 2019, and King's daughter, Bernice King, is still alive.
The gap between King's death and today is 51 years, and the gap between Jesus' death and AD 90 is 57 years. Even assuming the dates Runyan provides (and we will argue later for earlier dates for the gospels), writing a biography of King or Jesus would simply involve talking to people who were eyewitnesses of their lives, which would provide very accurate and reliable accounts of their lives.
Furthermore, Runyan's statement, "The best estimates date the gospels as follows," is also a complete lie. There are very strong arguments for earlier dates for the gospels.
We are starting with the dating of Acts and Luke because they are arguably the easiest to date, and they will help us date the rest of the gospels.
There is no doubt, due to tradition and internal evidence, that Luke and Acts were written by Luke, the companion of Paul.
Acts 28 ends abruptly with Paul arriving at Rome and awaiting his trial before Caesar in about AD 62. At the end of Acts, Paul had spent about two years imprisoned in Caesarea, from about AD 59–61. Acts does not mention any events subsequent to this, such as:
The most natural conclusion is that Luke simply recorded everything that had happened up until the point of his writing.
We know that the gospel of Luke was written before Acts because of the opening verses of each book. Both books are addressed to "Theophilus," and in Acts, Luke references his "first book."
Because of this, we can conclude that Luke was written before AD 62.