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It is true that in the Jewish Talmud and other Jewish documents we find statements such as “When a child experiences the taste of wheat (i.e., when it is weaned), it learns to say ’abbā and ’immā” (Berakot 40a in the Babylonian Talmud) (= our “dada” and “mama”).
However, even if the term abba began as a childish babbling sound (and this is far from clear), at the time of Jesus it was a regular adult word meaning “Father” or “my Father” (as terms of address) or “the Father” or “my Father” (as terms of reference).
That is, abba was not a childish term of the nursery comparable to “Daddy.” It was a polite and serious term, yet also colloquial and familiar, regularly used by adult sons and daughters when addressing their father. Ideas of simplicity, intimacy, security and affection attach to this household word of childlike trust and obedience. So to bring out the sense of warm and trusting intimacy that belongs to the word, we could appropriately paraphrase it as “dear father.”