“Could the individual named Gaius, whom John wrote 3 John to, be the same Gaius that Paul baptized in 1 Corinthians 1?”
While this question on the surface might seem of little consequence, in reality, there are those who have used such situations to suggest that the Apostle Paul and the 12 Apostles had the same audience, which is not the case (cf. Rom. 11:13; Gal. 1:16; 2:7-9).
Furthermore, it does not seem likely that the Gaius that John mentioned in 3 John was the same Gaius that Paul baptized since John suggests in verse 4 that his Gaius was one of his “children,” meaning he was led to the Lord by John. We would expect that the Gaius Paul baptized (1 Cor. 1:14) would have been led to the Lord by Paul when he visited Corinth.
Gaius was one of the more popular names of the time. In fact, Paul likely worked with at least two different men named Gaius. One from Macedonia (Greece cf. Acts 19:29) and another from Derbe, which is in Asia Minor – modern-day Turkey (cf. Acts 20:4).
Interestingly, Paul wrote Romans while being hosted by a Gaius (cf. Rom. 16:23), and this almost certainly was the Gaius of Corinth, for in the same verse that he mentions Gaius, he also sends greetings to the Romans from another man named Erastus, who, according to 2 Timothy 4:20, lived in Corinth.
Another detail that suggests that Paul wrote Romans from Corinth is in Romans 15:26, where he said he had a contribution from those in Macedonia and Achaia (regions very close to Corinth) to take to Jerusalem.
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