The eighth day is the answer to a careful question: how soon can a newborn be brought under the covenant? Targum Pseudo-Jonathan on Genesis 17:12 settles the timing and then pushes the circle outward.
Every male in your generations, circumcised on the eighth day. But not only the child of the household. Also he who is brought up in your house. Also he who is bought with your silver. And, the Targum adds, every son of the peoples who is not of you — any male from outside Israel who enters the household, all the way down to the one acquired in a transaction.
The verse is doing theological and ethical work at once. Theologically, the eighth day is already understood in rabbinic tradition as a deliberately late-Sabbath moment — the child lives through one full Shabbat before being covenanted, as if the universe itself must greet him first.
Ethically, the Targum is refusing to let the covenant become a private bloodline. Anyone in Abraham's extended house — home-born or bought — is swept into the circle. A foreign servant is not a tool. He is a future covenant-bearer. The knife travels wherever the household travels.
The Maggid hears both ideas at once. The covenant waits a week for the infant. And it travels across ethnic lines for the servant (Genesis 17:12). Jewish identity, in this verse, is not a closed gene. It is a generous threshold. Anyone inside Abraham's tent for long enough gets the mark.