Thank you for the question on “Did St. Paul use the Greek translation of scripture because this is the one his target audience was most familiar?”
The Apostle spoke and quoted the Hebrew, Aramaic or Greek language and Scriptures according to the targeted audience. Since the Apostle Paul’s mission was to Greeks, he would have spoken Greek and cited the Septuagint Scriptures to them.
Galatians 2 says this, “7 On the contrary, they recognized that I had been entrusted with the task of preaching the gospel to the uncircumcised, just as Peter had been to the circumcised. 8 For God, who was at work in Peter as an apostle to the circumcised, was also at work in me as an apostle to the Gentiles. 9 James, Cephas and John, those esteemed as pillars, gave me and Barnabas the right hand of fellowship when they recognized the grace given to me. They agreed that we should go to the Gentiles, and they to the circumcised” (NIV).
Ephesians 3 says this, “Surely you have heard about the administration of God’s grace that was given to me for you, 3 that is, the mystery made known to me by revelation, as I have already written briefly…6 This mystery is that through the gospel the Gentiles are heirs together with Israel, members together of one body, and sharers together in the promise in Christ Jesus” (NIV).
The Apostle Paul used the language and the text to capture the attention of his audience. In Acts 22, Paul spoke most likely Aramaic to the Jews in Jerusalem, “When they heard him speak to them in Aramaic, they became very quiet…”(vs. 2). In Acts 17, Paul spoke most likely Greek and quoted the Septuagint to the attendees at Berea and Athenians. To the Bereans, “As soon as it was night, the believers sent Paul and Silas away to Berea. On arriving there, they went to the Jewish synagogue. 11 Now the Berean Jews were of more noble character than those in Thessalonica, for they received the message with great eagerness and examined the Scriptures every day to see if what Paul said was true. 12 As a result, many of them believed, as did also a number of prominent Greek women and many Greek men” (NIV). To the Athenians, he spoke Greek in his debate and presentation of the resurrected Jesus to them. “So he reasoned in the synagogue with both Jews and God-fearing Greeks, as well as in the marketplace day by day with those who happened to be there. 18 A group of Epicurean and Stoic philosophers began to debate with him. Some of them asked, “What is this babbler trying to say?” Others remarked, “He seems to be advocating foreign gods.” They said this because Paul was preaching the good news about Jesus and the resurrection. 19 Then they took him and brought him to a meeting of the Areopagus, where they said to him, “May we know what this new teaching is that you are presenting? 20 You are bringing some strange ideas to our ears, and we would like to know what they mean.” 21 (All the Athenians and the foreigners who lived there spent their time doing nothing but talking about and listening to the latest ideas” (NIV).
Since the Apostle Paul traveled to Macedonia, Achaia, and to Italy, the people in those lands spoke predominately Greek. It would be reasonable to assume that Paul spoke Greek to them and cited the Septuagint. Citing the Hebrew or Aramaic Scriptures would be irrelevant as they would need a translator. Paul was trained in Hebrew and Greek under Gamaliel.
SUMMARY: The Apostle Paul spoke Greek and cited the Septuagint in addressing the Greek hearers of the Greek-Roman Empire.
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