Below are some scriptures I found regarding some of the matters discussed above:
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Divorce
"For this cause shall a man leave father and mother, and shall cleave to his wife: and they twain shall be one flesh, Wherefore they are no more twain, but one flesh. What therefore God hath joined together, let not man put asunder." (Matthew 19:4-6)
"Unto the married I command, yet not I, but the Lord, Let not the wife depart from her husband: But and if she depart, let her remain unmarried or be reconciled to her husband: and let not the husband put away his wife." (1 Corinthians 7:10-11)
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Adulterous 2nd Marriages
"Whosoever shall put away his wife, except it be for fornication, and shall marry another, committeth adultery: and whoso marrieth her which is put away doth commit adultery." (Matthew 19:8-9)
"Whosoever putteth away his wife, and marrieth another, committeth adultery: and whosoever marrieth her that is put away from her husband committeth adultery." (Luke 16:18)
"If a woman shall put away her husband, and be married to another, she committeth adultery." (Mark 10:12)
I believe an invalid 2nd marriage isn't just a one-time sin that we can tell Jesus we're sorry about and then continue in it, for it ordinarily involves continued sexual relations between two people one or both of whom may actually still be married in God's eyes to somebody else, making the 2nd marriage an ongoing adulterous affair.
The reason I believe it's so important to determine whether a 2nd marriage is adultery or not is because adultery, as every other sin, cannot be continued in if we are going to be saved (Galatians 5:19-21, Hebrews 10:26-27), no matter how much peace we may have about continuing in it (Proverbs 14:12), no matter how many good works we also do (Matthew 7:21-23), and no matter our opinion of scriptures which may appear to us to be too harsh (Mark 8:38).
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Abusive Situations
I believe a woman can physically separate herself from an abusive husband to avoid harm, but that she can't divorce or remarry without her 2nd marriage being an adulterous affair (Mark 10:12).
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Is Celibacy Possible?
When Jesus told his disciples the truth regarding divorce and remarriage in Matthew 19:9, their reaction in Matthew 19:10 may be our own. I believe that anyone stuck in a difficult marriage situation where they can neither continue in an adulterous 2nd marriage nor be at this time reconciled to their 1st valid spouse, can live through it by praying and asking for celibacy (Matthew 19:11-12), remembering that "ye have not, because ye ask not" (James 4:2b) and "everyone that asketh receiveth" (Matthew 7:7-8) and "ask, and ye shall receive" (John 16:24) and "all things, whatsoever ye shall ask in prayer, believing, ye shall receive" (Matthew 21:22).
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Reconciliation
I believe if a woman has had a valid marriage at one time, but is now in an invalid 2nd marriage, repentance from adultery would require she divorce the invalid 2nd husband, and be reconciled to her valid husband or remain single (1 Corinthians 7:11).
Some argue that breaking the 2nd marriage "is like trying to make two wrongs equal a right," but if the 1st marriage was valid, and the 2nd invalid, then breaking the 2nd is right, for it's an adulterous affair. This is true even if there were children by the 2nd marriage, as people can have children even by adulterous affairs.
Some say Deuteronomy 24:1-4 forbids a woman in a 2nd marriage to return to her 1st husband, but Jesus' commands regarding marriage are different than the Mosaic law. "The law was given by Moses, but grace and truth came by Jesus Christ" (John 1:17). "Moses because of the hardness of your hearts suffered you to put away your wives: but from the beginning it was not so. And I say unto you, Whosoever shall put away his wife, except it be for fornication, and shall marry another, committeth adultery: and whoso marrieth her which is put away doth commit adultery" (Matthew 19:8-9, compare 1 Corinthians 7:11, Matthew 5:31-32).
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Adulterous 1st Marriages
If a man has married a 1st wife that was already divorced from a valid husband, I believe his marriage to her is an adulterous affair (Matthew 19:9, Luke 16:18). Therefore I believe he would be free to divorce and remarry validly for the 1st time.
If a woman has married a 1st husband that was already divorced from a valid wife, I believe that unless he divorced his 1st wife on account of fornication, her marriage to him is an adulterous affair (Matthew 19:9). Therefore I believe she would be free to divorce him and remarry validly for the 1st time.
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Sued For Divorce By An Unbeliever
I believe 1 Corinthians 7:15 is saying that if an unbelieving spouse sues a believing spouse for divorce, the believing spouse shouldn't fight it. In this case the divorce itself would not be a sin for the believer because they aren't the one who initiated it (contrast 1 Corinthians 7:10-11). But I don't believe this means the wife can then remarry without her and her 2nd husband committing adultery (Matthew 19:9, Luke 16:18).
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