Vine's Expository Dictionary of NT Words
is an Aramaic word, found in Mark 14:36; Romans 8:15 and Galatians 4:6 . In the Gemara (a Rabbinical commentary on the Mishna, the traditional teaching of the Jews) it is stated that slaves were forbidden to address the head of the family by this title. It approximates to a personal name, in contrast to "Father," with which it is always joined in the NT. This is probably due to the fact that, abba having practically become a proper name, Greek-speaking Jews added the Greek word pater, "father," from the language they used. Abba is the word framed by the lips of infants, and betokens unreasoning trust; "father" expresses an intelligent apprehension of the relationship. The two together express the love and intelligent confidence of the child.
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Vines, W. E., M. A. Entry for 'Abba'. Vine's Expository Dictionary of NT Words. https://www.studylight.org/dictionaries/eng/ved/a/abba.html. 1940.