An early tanna. At the end of the Mishnah Abot (v. 22, 23) two sentences are given concerning the study of the Torah; one by Ben Bag-Bag, the other by Ben Hê-Hê. Both sentences are also ascribed to Hillel (Ab. R. N. xii.); as indeed in their pithy language as well as Aramaic wording they are similar to the well-known Aramaic sentences of Hillel. Tradition reports two exegetical questions, which Ben Hê-Hê asked of Hillel (Ḥag. 9b). Ben Hê-Hê and Ben Bag-Bag may, therefore, be considered disciples of Hillel; or, as is even more likely, both names represent one and the same person.
The peculiarity of these names may be explained by the following anecdote (Shab. 31a): Hillel once convinced a proselyte of the truth of the oral law by proving to him, in a lesson on the Hebrew alphabet, that even a knowledge of the phonetic value and of the order of the letters of the alphabet is not possible without a belief in their oral transmission from age to age. If this proselyte is identical with the disciple of Hillel quoted under the above pseudonyms, then the one name, "Ben Hê-Hê," may have been chosen to indicate that "He" is always pronounced "Hê," as the tradition shows; and the other name, "Ben BG-BG," to show that in the alphabet the sequence bet gimel is fixed by tradition. That Ben Hê-Hê and Ben Bag-Bag are identical is apparently an old tradition, mentioned by Abraham Zacuto in "Yuḥasin."
In Tos. to Ḥag. 9b Ben Bag-Bag and Ben Hê-Hê are also considered to be proselytes, although the symbolic meaning of their names is differently accounted for. Several halakic interpretations of Scriptural passages by Ben Bag-Bag have been transmitted: of Ex. xiii. 13 (Bek. 12a); of Lev. xix. 11 (Sifra, Ḳedoshim, ii. 2; Tosef., B. Ḳ. x. 38; Bab. B. Ḳ. 27b); of Num. xxviii. 2 (Pes. 96a; Men. 49b; 'Ar. 13b; anonymously stated in Sifre, Num. 142, and in the name of 'Akiba in Meg. Ta'anit i.); of Deut. xiv. 26 (Sifre, Deut. 107; 'Er. 27b).
There is another rabbi distinct from this elder Ben Bag-Bag who was never cited with a given name. He is Johanan ben Bag-Bag, possibly the son of the former. Nothing is known about him except that he sent to Nisibis a halakic question to Judah b. Betera, a contemporary of Akiba, who in his reply referred to Ben Bag-Bag as one noted for being "familiar with the chambers of the Law" (Tosef., Ket. v. 1; Yer. Ket. v. 29d; Bab. Ḳid. 10b; Sifre, Num. 117).