In determining Jewishness, usually several traits are lumped together: Jewish birth, Jewish descent, and Jewish way of life. A person of Jewish birth can be baptized and to all practical purposes cease being Jewish. A convert can lead a perfectly Jewish life, but he would still not be a Jew in the historical sense: for example, our experience of persecutions is rather impersonal for him. Someone with merely a Jewish grandfather may come to Israel, serve in the army, and come to identify himself with Jewish people. Though the definitions have much in common, they refer to different objects.
The best definition of Jewishness would refer to someone whose children—and preferably grandchildren—identify with the Jewish people. Arguably, such a definition is dynamic. Let’s assume realistically that 80 percent of the grandchildren of Israeli Jews identify as Jewish; Israeli-ness is therefore a very strong trait of Jewishness. About the same proportion holds for Orthodox Jews and converts; religious observance, therefore, is also a powerful trait. Jewish birth is a weak trait: the Diaspora Jews massively intermarry and assimilate.
The definitions’ stickiness varies between Israel and the Diaspora. The barest relation to Jewishness suffices in Israel because one’s Jewishness is confirmed by practical actions such as army service. Jews even by a grandparent are likely to fight as Jews, pay taxes as Jews, and marry Jews.
In the Diaspora, Jews by grandparent bear no relation to the Jewish people whatsoever. And on the contrary, some religious Jews in Israel defy the definition of Jewishness: Satmar Jews refuse army service, entreat the Arabs, and detest their fellow Jews. One definition cannot fit all Jews, we need at least two. In Israel, Jewishness is predominantly political: atheists of Jewish birth, traditionalists of remote Jewish ancestry, and religious Jews are all equally Jewish. In the Diaspora, the only operative criterion is religious observance; Jewishness simply cannot be demonstrated in any other way there.
Fringe cases exist for both definitions. In Israel, those are the atheists who refuse to serve in the army, people with remote Jewish roots who serve in the army but remain anti-Semites. In the Diaspora, we can imagine atheist Jews or non-observant Reformists who are nonetheless involved with Jewish organizations. Their Jewishness is extremely weak; it is highly implausible that their grandchildren would remain Jewish.
Jewishness has no clear-cut boundaries. Defined as the propensity to have Jewish grandchildren, Jewishness has fuzzy borders. For the vast majority of the people, their Jewishness is demonstrated by their peculiarly Jewish way of doing something, whether in the religious or political sphere.