The nakedness of your sister, whether she is the daughter of your father or the daughter of your mother, whether she is born at home or outside, you shall not uncover… (Leviticus 18:9)
A woman who shares a parent is a sister. Same mother, same father, born in wedlock or out of it, even the product of an illicit relationship, she’s off-limits. The reason is similar to what we said previously: we’re overly familiar with relations and they’re always around. The incest taboo is a successful impediment. Plus, there’s the whole “danger of inbreeding” thing.
In Leviticus 20:17, regarding sexual relations between brothers and sisters, the Torah says, “chesed hu.” Most commentators translate that “it is shameful,” but we are all familiar with the far more common meaning of chesed: an act of kindness. Rashi quotes the Midrash that there was one sanctioned situation in which siblings were permitted to wed: Cain, the son of Adam, was permitted to marry his sisters because there simply weren’t any other women and the propagation of the species depended on it. “Chesed hu,” this was a one-time exception that God made in His kindness.
This mitzvah applies in all times and places. In the Talmud, it is discussed in the tractates of Kerisos (2a) and Yevamos (22a). It is codified in the Shulchan Aruch in Even Ha’Ezer 15. It is #332 of the 365 negative mitzvos in the Rambam’s Sefer HaMitzvos and #127 of the 194 negative mitzvos that can be fulfilled today as listed in the Chofetz Chaim’s Sefer HaMitzvos HaKatzar.