CLAIM: Caleb said, “The one who attacks Kiriath-sepher and captures it, I will give him Achsah my daughter as a wife” (Josh. 15:16). But then his brother Othniel volunteers to do capture Kiriath-sepher and succeeds. Thus we read, “Othniel the son of Kenaz, the brother of Caleb, captured it; so he gave him Achsah his daughter as a wife” (Josh. 15:17). Why does Caleb allow for incest of this magnitude?
RESPONSE: The Bible doesn’t condone everything that it contains. Even if an incestuous marriage did take place because of Caleb, this doesn’t necessarily mean that God approved of it. In fact, the Levitical law disapproves of incestuous relationships (Lev. 18:6-7; 1 Cor. 5:1).
However, it seems likely that Othniel and Caleb were not blood brothers. Othniel is called “the son of Kenaz” (Josh. 15:17; Judg. 1:13; 3:9), while Caleb is called “the son of Jephunneh” (Josh. 14:6, 13-14, 15:13; 21:12). Madvig writes, “‘Caleb’s brother’ may have been his blood brother or a member of the same clan or tribe. The Hebrew word ʾāḥ can mean ‘brother,’ ‘relative,’ or ‘ally.’”
 Madvig notes that Judges 1:13 calls Othniel Caleb’s “younger brother” (c.f. Judg. 3:9), but given that their father’s names were explicitly mentioned, this most likely refers to a younger relative. Madvig, Donald. Joshua. In F. E. Gaebelein (Ed.), The Expositor’s Bible Commentary, Volume 3: Deuteronomy, Joshua, Judges, Ruth, 1 & 2 Samuel (F. E. Gaebelein, Ed.). Grand Rapids, MI: Zondervan Publishing House. 199(2) 328.