In Acts 19:20 Luke sums up the fifth section of his thesis by saying: “So mightily grew the word of God and prevailed.” It almost seems out of place here before the riot later in the chapter, but it isn’t. Paul’s 3rd recorded missionary journey is not yet complete, but Luke uses what is already said to sum up what turns out to be Paul’s mission to the world in the name of the Kingdom of God as a free man. A glance backward would show us that Luke sums up his entries into his thesis at the conclusion of conflicts—either within the Church (Acts 6:7; 16:5; 19:20) or in respect to the unbelieving community (Acts 9:31; 12:24; 28:30-31).
The significance of Luke’s testimony in verse-20 seems to point to what believers did in Acts 19:18-19. I think that many scholars miss the point here by making the climax of Paul’s ministry in the province of Asia simply a contest between the power of God and magic. I believe Luke wants to bring us deeper than that. When we come to Christ, we bring a lot of baggage with us, whether Jew or gentile. For the Jews it was circumcision; for the gentiles it was certain traditions they were attached to concerning paganism. We see a little of this in verse-12 in reference to Paul’s handkerchiefs and aprons. This wasn’t evil in itself, as Acts 5:15 and Luke 8:44 show, but it testifies to their superstitious heart. Yet, just as Jesus wanted to make sure the woman who touched him knew how she was healed (Luke 8:45-46), so Luke tells us that it is God who did these powerful works through Paul (Acts 19:11). Then he goes on to tell us how this became evident to all.
It must have been apparent to all that the power of God was unusually evident in Paul’s ministry, but does this mean that God would work in and through all gentile traditions? After all, Paul concludes in his letter to the Corinthians that although there are many who are called ‘gods’ by others, for believers, there is but one (1Corinthians 8:5-6). So, is Paul teaching that gentiles could worship God in the same manner they had done in ignorance with those they called ‘gods’? This seems to be a valid argument, because Paul also says in the same epistle that ‘we know the idol is nothing… and there is but one God’ (1Corinthians 8:4). So, would the practice of astrology be blessed by God to predict the future; or could one use pagan forms of calling upon the gods to address the true God; and could one use the names of pagan deities or secret names to induce God to act according to man’s will? I don’t believe Luke’s point has to do with ‘magic v/s the power of God’ as much as it has to do with what is proper for a new believer to do in God’s name.
The Jews had accused Jesus of casting out demons by calling upon the power of the prince of demons (Matthew 12:24). Such a practice was performed regularly by Jewish exorcists as implied by Jesus reply to his accusers in Matthew 12:27 concerning the sons of Jesus’ accusers. The point is, if Paul’s Gospel concerned the Jewish Messiah, and since it seems apparent that gentiles knew of the Jewish practice of exorcism (cp. Acts 19:13-17), then the Jewish practice of using the power of evil to destroy evil must be permitted, if not endorsed, by God, whom the Jews worshiped.
What I find very interesting in all this is that Luke doesn’t show Paul was interested in exorcising every sin new believers were committing or even searching out what one might suspect the new believer may not understand. He doesn’t seem to be all that interested in so-called ‘secret sins’. Luke seems willing to let the Lord bring it all out in the open in his own way, letting the Holy Spirit, dwelling in the believer, do his work in good time. How many of us would do that today? I know I haven’t witnessed this kind of faith in God to do his work in my whole Christian experience!
Anyway, as a result of what occurred to the Jewish exorcists, new believers became aware that all power is not God’s power, and all their traditions are not necessarily acceptable to God. As a result they brought their books before Paul and publicly burned them (verse-19). This was an ancient custom expressing one’s repudiation of the content, and was done to control the spread of unacceptable ideas. The difference we see between what was done by others and what was done by the believers in Acts 19 is that these burned their own books. Paul didn’t command it; it was their own decision and concerned their own property. Thus, “…mightily grew the word of God and prevailed” at Ephesus.
 See Suetonius, Augustus 31; Livy 39.16; 40.29.3-14; Diogenes Laertius, Lives of Eminent Philosophers 9:52; Lucian of Samosata, Alexander the False Prophet 47.