Jacob … Israel (camp. Isaiah 40:27; Isaiah 41:8, Isaiah 41:14; Isaiah 43:1, Isaiah 43:22; Isaiah 44:1, etc.). "Jacob" is the natural and secular designation; "Israel" is a spiritual or covenant name (Cheyne).
Both terms being appropriate to the ten tribes no less than to the two, and the present address being intended especially for the Jewish captives, a further designation is appended—which are come forth out of the waters of Judah.
Which swear by the Name of the Lord. Swearing "by the Name of the Lord" is an evidence of true religion, to a certain extent (Deuteronomy 6:13; Deuteronomy 10:20). It indicates that there has been, at any rate, no open apostasy.
Still, it does not necessarily prove more than this; and, in the present case, it scarcely showed anything beyond mere outward formal conformity. The bulk of the captives "swore by the Name of Jehovah, and made mention of the God of Israel" (camp.
Joshua 23:7), but did so not in truth, nor in righteousness; i.e. "without their state of mind or mode of action corresponding to their confession, so as to prove that it was sincerely and seriously meant" (Delitzsch).
The condition of the majority of the exiles was that expressed in the words, "This people honoureth me with their lips, but in their hearts are far from me" (Matthew 15:8).