Two children that have the same father but different mothers are forbidden to have relations on grounds of incest. If their father is a gentile (and they have different Jewish mothers), it is not really their father, therefore are they still forbidden to have relations?
1 Answer
This question was raised by the Assia journal conjunction with artificial fertilization.
It is a problem to take sperm from another Jew because the child could marry his brother. It may be permitted to take sperm of a non-Jew in this case because they are not considered to be brothers.
, שהטעם "עיקרי לאיסור הזרעה מיהודי זר לאשת-איש - "שמא ישא אחותו מאביו" - לא קיים במקרה שהזרע הוא של גוי. זאת מכיון שאין הולד מתייחס אחר אב-גוי גם כשהוא נולד כדרך כל הארץ, לא כל שכן בצורת הזרעה מלאכותית.
http://98.131.138.124/articles/assia/assia1/r001128.asp
( for some reason the link doesn't work as a link; if you'd like to see the article you can copy-paste the link from here )