According to Orthodox Jewish tradition, in addition to the possibility that one becomes a “naturalized Jew” by means of conversion to Judaism, the religion one is born into is determined by the religious status of one’s mother, religious lineage being defined as matrilineal. The biblical basis for this assumption is Deuteronomy 7:3-4 :
Neither shalt thou make marriages with them (the non-Jewish nations that will be encountered when the Jewish people enter the land of Israel): thy daughter thou shalt not give unto his son, nor his daughter shalt thou take unto thy son. For he (the non-Jewish father) will turn away thy son from following Me, that they may serve other gods…
The Oral Tradition in Tractate Kiddushin 68b interprets the implication of these verses:
How do we know that her children bears her (religious) status? — R. Yochanan said on the authority of R. Shimeon b. Yochai, Because Scripture saith, “For he will turn away thy son from following me”: thy son by an Israelite woman is called thy son, but thy son by a non-Jewish woman is not called thy son. Ravina said: This proves that thy daughter's son by a non-Jewish man is called thy son.
The subtle inference drawn by the Talmud from the biblical verses is that since despite the fact that Deuteronomy 7:3 mentions both possibilities, i.e., a Jewish man marrying a non-Jewish woman, as well as a Jewish woman marrying a non-Jewish man, the specific fear delineated in 7:4 regards exclusively concerns itself with what will happen to a son who will come under the influence of a non-Jewish father. Consequently, when the mother is Jewish, the child is “your son”, but, by implication, not when the mother is not Jewish. The Codes accept this definition, as in Shulchan Aruch, Even HaEzer 4:5.
Consequently, with respect to the specific question whether the child of a Jewish mother is considered Jewish, the answer according to Orthodoxy is yes. As to whether that individual’s children are Jewish or not, that would then depend upon the individual’s gender. If the person is a woman, then just as she is Jewish, her children are similarly Jewish. On the other hand, if we are speaking about a man, then it would depend upon with whom, i.e., a Jewish or non-Jewish woman, he has children.
However, even if an individual is “technically” Jewish by virtue of his biological origins, whether or not he views himself as Jewish, let alone if he lives in accordance with the dictates of a Jewish lifestyle, is certainly within his own purview. Ideally, being Jewish is not just a matter of biology and/or conversion, but also includes the means by which an individual chooses to live his or her life.
Rabbi Jack Bieler