In Brian J. Wright's excellent book "Communial Reading in the Time of Jesus" he mentions an account found in Acts 19:11-20 that is set in Ephesus (p. 150-151). As many can recall, Paul was ministering in Ephesus, preaching the Gospel and performing many miracles and casting out demons. After a local group of Jewish excorists failed to excise a demon they were attacked and the excorcists fled (Acts 19:16). This sparked a huge revival as the populace began to denounce their magical practices and instead beleive in the Gospel message Paul was preaching. As a result of their coversion, Luke tells us,
"And a number of those who had practiced magic arts brought their books together and burned them in the sight of all. And they counted the value of them and found it came to fifty thousand pieces of silver. So the word of the Lord continued to increase and prevail mightily." (Acts 19:19-20; ESV)
In this account, Wright teases out some interesting conclusions. He draws attention to the book burning event, that a significant number of books were burned (worth 50,000 silver coins), and that the burning of these magical texts was set in counter distinction with the the Gospel message in verse 20: "the word of the Lord continued to increase and prevail mightily" (ESV). Because of the book burning event recounted in v 19, Wright proposes that, "[t]he 'word of the Lord' here probably refers to written texts and not merely to oral proclamation, in light of this explicit comparison" (p. 151).
If Wright's interpretation of this text is correct, it would imply that not just Old Testament texts are in view here, but more specifically written texts that include some type of Gospel proclamation. In light of the timing of the composition of Paul's epistles in the Acts narrative, if Wright is correct here, then Luke might include the idea of the circulation of some of Paul's epistles when he wrote that "the word of the Lord continued to increase" (19:20). To be clear, Wright is not specific as to what texts may be in circulation. Because the "word of the Lord" here is referring to the Gospel being spread as a result of Paul's ministry, I wonder if this verse might include the concept of some of Paul's epistles. According to the more common accepted timeline of the composition of Paul's epistles, at this time in the narrative, 1st and 2nd Thessalonians would likely have been written and dispatched, and possibly 1st Corinthians as well while Paul was at Ephesus. Paul at the very least may have begun the process of writing Romans during his three year stay in Ephesus (Acts 19:10; 20:31). The letter to the Galatians may have been written by this time in Acts as well. Therefore, since epistolary writing was a integral part of Paul's ministry, and this reference in Acts 19:20 is speaking specifically about the results of Paul's ministry, it may include the idea of widespread circulation of at least some of the Pauline epistles that had been written at this time and to their reading out to the Church communities as a means by which "the word of the Lord" increased. Especially considering the epistles would have been read out in the Churches as is mentioned in 1 Thess 5:27 (which was written before this time in Acts 19). Edit: I re-wrote the last segment to hopefully better express what ideas I am adding to Wright's proposal and to be more nuanced as to what "the word of the Lord" might be referring to more specifically.
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Brian J. Wright, Communal Reading in the Time of Jesus: A Window into Early Christian Reading Practices (Minneapolis: Fortress Press, 2017).