An oath by the LORD, literally “an oath of Yahweh,” means to swear in the name of Yahweh, or “by Yahweh” (New Jerusalem Bible). Shall be between them both is quite literal. It does not necessarily mean that both men shall take the oath. More likely “the man in custody of it [the animal] shall swear an oath” (Translator’s Old Testament). New American Bible has “the custodian shall swear by the LORD.” Good News Translation misses the point of swearing in the personal name of Yahweh. A possible rendering (see verse 8) is “make a strong statement with God as his witness.”
To see whether he has not put his hand to his neighbor’s property is identical to the same phrase in verse 8. And the owner shall accept the oath is literally “and its owner shall take,” without stating what he is to take. This may mean either that “the owner shall accept the loss” (Good News Translation) or that “the owner must accept the oath” (New American Bible). New Jewish Publication Society’s Tanakh has “the owner must acquiesce.” New Jerusalem Bible has “the owner will take what remains,” but this meaning is unlikely. And he shall not make restitution is literally “and he will not pay back.” The he, of course, refers not to the owner but to “the other man” (Good News Translation), or “the man who had custody” (Translator’s Old Testament) of the animal.
An alternative translation model in languages that must use direct speech is:
• If you swear [or, make a strong statement] with me [Yahweh] as your witness, saying, “I did not steal the other man’s animal,” the owner must accept your statement, and you do not have to replace the animal.
Quoted with permission from Osborn, Noel D. and Hatton, Howard A. A Handbook on Exodus. (UBS Helps for Translators). New York: UBS, 1999. For this and other handbooks for translators see here .
