Jamieson, Fausset and Brown on Hosea 4:15

15. Though Israel's ten tribes indulge in spiritual harlotry, at least thou, Judah, who hast the legal priesthood, and the temple rites, and Jerusalem, do not follow her bad example.

Gilgal--situated between Jordan and Jericho on the confines of Samaria; once a holy place to Jehovah (Jos 5:10-15; 1Sa 10:8; 15:21); afterwards desecrated by idol-worship (Ho 9:15; 12:11; Am 4:4; 5:5; compare Jud 3:19, Margin).

Beth-aven--that is, "house of vanity" or idols: a name substituted in contempt for Beth-el, "the house of God"; once sacred to Jehovah (Ge 28:17, 19; 35:7), but made by Jeroboam the seat of the worship of the calves (1Ki 12:28-33; 13:1; Jr 48:13; Am 3:14; 7:13). "Go up" refers to the fact that Beth-el was on a hill (Jos 16:1).

nor swear, The Lord liveth--This formula of oath was appointed by God Himself (De 6:13; 10:20; Jr 4:2). It is therefore here forbidden not absolutely, but in conjunction with idolatry and falsehood (Is 48:1; Eze 20:39; Zep 1:5).