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Why is it so that if a Jew has a male child with a non-Jewish woman the child is not circumcised, even though, like Ishmail, the child is under Abrahamic (but not Mosaic) covenant, since the father is of "seed of Abraham"? (I assume Abrahamic covenant status follows the father, since it descends from Abraham to Ishmail and Isaac, and from Isaac to Jacob, from Jacob to all the other Jews and their offspring).

Also, such a child is not Jewish (not under the Mosaic covenant), but Genesis 15:18–21 promises all the descendants of Abraham specific land and to curse those, who curse them. This is different than for Bnei Noah where no such promises are made, so wouldn't that imply a sign of the covenant should be made for all the descendants of Isaac (Ishmail did not inherit the covenant:

וַיֹּאמֶר אֱלֹהִים, אֲבָל שָׂרָה אִשְׁתְּךָ יֹלֶדֶת לְךָ בֵּן, וְקָרָאתָ אֶת-שְׁמוֹ, יִצְחָק; וַהֲקִמֹתִי אֶת-בְּרִיתִי אִתּוֹ לִבְרִית עוֹלָם, לְזַרְעוֹ אַחֲרָיו
וּלְיִשְׁמָעֵאל, שְׁמַעְתִּיךָ--הִנֵּה בֵּרַכְתִּי אֹתוֹ וְהִפְרֵיתִי אֹתוֹ וְהִרְבֵּיתִי אֹתוֹ, בִּמְאֹד מְאֹד: שְׁנֵים-עָשָׂר נְשִׂיאִם יוֹלִיד, וּנְתַתִּיו לְגוֹי גָּדוֹל


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the child may be circumcised if the parents wish but is not given a brit milah -- a religious service which includes language pointing out an obligation as a jew – Danno Dec 11 '12 at 16:46
@Dan, thank you. I am curious if it is a sin not to circumcise a son in such a case, and if, like for Bnei Noah, there is a framework for those under Abrahamic but not Mosaic covenant in Judaism so they could follow the Torah as applied to them? – MichaelS Dec 11 '12 at 16:57
@MichaelS If your question is more general than just Brit Milah please edit that into the question. – Double AA Dec 11 '12 at 17:05
Gen. 21:12 establishes a special "official descendant" status for Isaac. (May flesh this out into an answer later if someone else doesn't.) – Isaac Moses Dec 11 '12 at 17:05
@IsaacMoses As does Gen. 28:4 to Jacob. – Double AA Dec 11 '12 at 17:15

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