Jesus likely spoke more than one language and showed at least some ability in Aramaic, Hebrew, and Greek.
What language did Jesus speak?
The Gospels reveal Jesus speaking numerous Aramaic words: 1) talitha koum (little girl, arise) (Mark 5:41), 2) ephphatha (be opened) (Mark 7:34), 3) eloi, eloi, lama sabachthani (My God, my God, why have you forsaken me?) (Matthew 27:46; Mark 15:34), and 4) abba (father/daddy) (Mark 14:36). In addition, historians have established that Aramaic was the common Jewish language spoken during this time period, meaning most of the words spoken by Jesus were in Aramaic.
Jesus clearly read and spoke some Hebrew. He read from a Torah scroll (Luke 4:16-19) in a synagogue early in His public ministry; the scroll would have been written in Hebrew. At the age of twelve Jesus discussed the Hebrew Scriptures with the religious teachers in the temple, impressing them with His wisdom (Luke 2:41-50). Hebrew was not the common spoken language, but was important for Jewish education and religious practice in the synagogue. Jesus could clearly read and discuss Hebrew according to the New Testament accounts.
Jesus also may have known and spoken some Greek. Greek was the primary spoken language of the Roman Empire at the time and was the language in which the New Testament was originally written. During the trials of Jesus with Pilate and Herod, Jesus may have spoken in Greek (or possibly even Latin, though unlikely), yet this is uncertain. Both Pilate and Herod may have known Aramaic or used a translator. Because a translator is not mentioned, however, many suggest Jesus spoke at least some Greek.
In Matthew 8:5-13, Jesus spoke with a Roman centurion. The centurion would have almost certainly spoken in Greek. It appears no translator was used, meaning Jesus spoke in Greek with the centurion, or the centurion spoke in Aramaic with Jesus. The more likely conclusion is that it was Jesus who spoke Greek rather than a centurion with no Jewish background speaking Aramaic.
Further insight regarding Jesus' ability to speak Greek can be found in the language of Scripture itself. Both Matthew and John wrote their Gospels in Greek, indicating a level of Greek language usage among the apostles. Though the Gospel accounts themselves do not directly show Jesus speaking Greek phrases, the common use of Greek as a commercial language indicates He likely had some knowledge of the language.
Certainly, as fully human and fully divine, Jesus could have spoken in any language He desired. The question here is what language or languages did He speak on earth? There is clearly evidence for both Aramaic and Hebrew, with some additional support that Jesus may have spoken Greek on some occasions.
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