Introduction: The question pertains to what has been called "the Pauline Privilege." The verse reads, "But if the unbelieving depart, let him depart. A brother or a sister is not under bondage in such cases: but God hath called us to peace" (I Cor. 7: 15).
I. The common explanation of I Corinthians 7: 15.
A. Many religionists tell us that there are two allowable cases for divorce and remarriage when there is a living mate. Adultery and desertion, they explain based on Matthew 5: 32, 19: 9, and I Corinthians 7: 15.
B. Is Paul actually introducing a second reason?
II. Exegesis of I Corinthians 7: 15.
A. Paul is addressing the situation of a believer and unbeliever being married (vs. 12-16). Hence, there is immediate restriction and limit regarding an application of "not under bondage."
B. Also, remarriage is not even being discussed in the passage.
C. "Not under bondage" is from the Greek dedoulotai. The grammar posture of dedoulotai is "3 person, singular, perfect tense, indicative mood, and passive voice" (Analytical Greek Lexicon, pg. 85). The perfect tense is, "…the tense is thus double; it implies a past action and affirms an existing result" (Moods and Tenses in New Testament Greek, by Ernest Burton, pg. 37).
D. If "bondage" means marriage, as some insist, Paul is saying the believer is not and has not ever been in bondage (married?). Paul has argued that the believer is bound (marriage bond) to the unbeliever (vs. 12, 13).
a. Deo, the word for the marriage bond, is used 44 times in the Greek New Testament (see Rom. 7: 2, I Cor. 7: 27, 39). However, deo is not used in verse 15.
b. "Depart" is chorizetai and is present tense (ibid., pg. 440).
Conclusion: Paul is not allowing a second reason for divorce and remarriage, but is saying that the believer has not been reduced to slavery (meaning of dedoulotai, Thayer' Greek-English Lexicon, pg. 158, see vs. 23). The pagan's process of leaving was an effort to cause the believer to renounce Christianity. Such must not be allowed.