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Fausset's Bible Dictionary
Deuteronomy 24:1-4 permits the husband to divorce the wife, if he find in her "uncleanness," literally, "matter of nakedness," by giving her "a bill of divorcement," literally, a book of cutting off. Polygamy had violated God's primal law joining in one flesh one man to one woman, who formed the other half or converse side of the male. Moses' law does not sanction this abnormal state of things which he found prevalent, but imposes a delay and cheek on its proceeding to extreme arbitrariness. He regulates and mitigates what he could not then extirpate. The husband must get drawn up by the proper authorities (the Levites) a formal deed stating his reasons (Isaiah 50:1; Jeremiah 3:8), and not dismiss her by word of mouth. Moses threw the responsibility of the violation of the original law on the man himself; tolerating it indeed (as a less evil than enforcing the original law which the people's "hardness of heart" rendered then unsuitable, and thus aggravating the evil) but throwing in the way what might serve as an obstacle to extreme caprice, an act requiring time and publicity and formal procedure.
The school of Shammai represented fornication or adultery as the "uncleanness" meant by Moses. But (Leviticus 20:10; John 8:5) stoning, not merely divorce, would have been the penalty of that, and our Lord (Matthew 19:3; Matthew 19:9, compare Matthew 5:31) recognizes a much lower ground of divorce tolerated by Moses for the hardness of their heart. Hillel's school recognized the most trifling cause as enough for divorce, e.g. the wife's burning the husband's food in cooking. The aim of our Lord's interrogators was to entangle Him in the disputes of these two schools. The low standard of marriage prevalent at the close of the Old Testament appears in Malachi 2:14-16. Rome makes marriage a sacrament, and indissoluble except by her lucrative ecclesiastical dispensations.
But this would make the marriage between one pagan man and one pagan woman a "sacrament," which in the Christian sense would be absurd; for Ephesians 5:23-32, which Rome quotes, and Mark 10:5-12 where even fornication is not made an exception to the indissolubility of marriage, make no distinction between marriages of parties within and parties outside of the Christian church. What marriage is to the Christian, it was, in the view of Scripture, to man before and since the fall and God's promise of redemption. Adulterous connection with a third party makes the person one flesh with that other, and so, ipso facto dissolves the unity of flesh with the original consort (1 Corinthians 6:15-16). The divorced woman who married again, though the law sanctions her remarriage (Deuteronomy 24:1-4), is treated as "defiled" and not to be taken back by the former husband. The reflection that, once divorced and married again, she could never return to her first husband, would check the parties from reckless rashness.
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Fausset, Andrew R. Entry for 'Divorce'. Fausset's Bible Dictionary. https://www.studylight.org/dictionaries/eng/fbd/d/divorce.html. 1949.