Was incest permitted between Lot and his daughters? Was it approved in the days of Adam and Eve and Noah?
In the case of the children of Adam and Eve and the grandchildren of Noah, marrying close family members was necessary, and at that time the children of such a union were not adversely affected. We might reasonably assume that the closer to creation, the more genetically stable reproduction was. Only over the centuries has genetic instability become a problem.
Abraham married his half-sister. Genesis 20:12
Amram, the father of Moses, married his father’s sister. Exodus 6:20
But daughters having children by their father was not the norm in any epoch. Lot’s two daughters found themselves in what they perceived to be difficult position, re finding a husband and having children to continue the posterity of Lot. Genesis 19:30-38 This was not a good decision on their part, but no adverse physical repercussions came of it. The sons born founded the Moabites and the Ammonites. Spiritually they abandoned the worship of the true God, who had saved Lot and his daughters out of Sodom, and became idolators. Their idolatry caused problems for Israel. 1 Kings 11:33
In the Law of Moses, some restrictions on sexual relationships were put in place. Leviticus 20:17-19
Outside of the Law of Moses, laws preventing the marriage of close relatives became necessary because it was found to result in mentally or physically disabled offspring.
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