The language of Christ has been the subject of much conjecture and discussion among Christian theologians for centuries, and the real answer is, no one knows for certain. However there are some fairly accurate assumptions that can be made by a study of the history of the area, and what was customary for the time,
For the sake of this discussion, let's forsake the theory that as the Son of God, he was capable of speaking in any language, and focus on what can be proven from the historical evidence at hand.
The first fact in this logical exercise is that, of course, Christ was a Jew. As such he was educated in the Temple as a child, and scripture tells us that he studied the Torah and Talmud with the scholars of the day. In order to do so, he would have to speak (and read) ancient Hebrew, which is the language of the texts, and that used by the Rabbis in their daily Temple lives. However, there is little evidence that Hebrew was the language most commonly in use in the Holy Land at the time.
The next fact that must be considered is that the Holy Land was at the time of Christ, a part of the Roman Empire, so one would logically assume that Latin was spoken at least by some. However, Roman historical documents of this period indicate that Latin was only used in the common manner in Rome and its immediate surrounds, and that by edict, it was not used provincially. The use of Latin existed only in internal documents and communications between military and political officials, and primarily in written form, and not as a "spoken language" in what is now known as Israel.
Then there is Aramaic.........Aramaic is a "composite" language, which evolved during the Jews captivity in Babylon, after the destruction of the first Temple, and following the first diaspora. Aramaic is a mixture of ancient Hebrew, and the Babylonian (ancient Persian) languages, including classic Arabic. It was widely used in the Holy Land by the common people, and was further widely dispursed in usage in the entire Middle East. It would be a safe assumption that Christ, being of the "common people" would have been capable of speaking Aramaic, however whether he was capable of writing the language is unknown.
Much of Christ's early years, following his childhood are not spoken of in scripture. We are therefore left with a "gap" that most certainly held a plethora of education, and life experiences that cannot be verified in the texts. It would be a safe assumption that that portion of his life was devoted to working, spending time with his family, friends, and learning the ways of the peoples that surrounded him, as well as continuing his scriptural education as a pious Jew.
Now comes the "fly in the ointment" so to speak, as the languages that we have discussed above were, by no means, the ones most commonly used in the Holy Land, and Middle East during this period. The most widely used language at the time was Koine Greek........Why Greek? Well.........the Greeks were traders, and had developed the most civilized society on the planet prior to Rome. Their merchants and vessels travelled the entire Mediterranean basin for centuries, and wherever they travelled and entered into commerce, they left their language behind. Koine Greek is a blend of several Greek dialects with "Attic', Attic being the form of Greek spoken exclusively by the elite in Athens. Interestingly, Greek was much more commonly spoken in Rome during this period than Latin, however the Romans preferred "Ancient Greek" which they considered a more perfect form of the language. Therefore, if there was such a thing as a "universal language" spoken in the Holy Land at the time of Christ it would be Koine Greek. We know for a fact that his Apostles spoke it, as they preached in that language in the emerging churches throughout the area following the Crucifixion.
Therefore, to accumulate all these assumptions, conclusions, and historical facts, the most plausible theory is that Christ was multilingual.....and likely spoke at least three languages on a conversational basis, Koine Greek, Aramaic, and Hebrew. There is a further theory that he might have also spoke Egyptian, however, critics state that due to the widespread use of Greek in Egypt, this assumption would be a stretch.
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