Stanley Fischer, vice president of Citigroup and former high World Bank and International Monetary Fund official, was sworn in on Sunday as the new governor of the Bank of Israel, Israel’s equivalent of America’s Federal Reserve Board. Although his appointment was already decided on last January, it had to wait until he completed his preparations for immigration to Israel and took out Israeli citizenship papers.

In the circles of those who support the free market policies of Finance Minister Benjamin Netanyahu, to which the Israeli economy has been responding most positively in recent months (unemployment is down, economic growth remains high, and the Tel Aviv stock market is at record peaks), there is little disagreement about Mr. Fischer’s qualifications for the job. He is an experienced administrator with an impressive record, and he and Mr. Netanyahu see eye-to-eye economically.

The criticism, rather, has been of the new governor’s provenance. Why was it necessary, it has been asked, to bring a Jew from America to head the Bank of Israel? Is the bank a basketball or soccer team that buys the best foreign players it can and brings them to Israel for a few seasons?

The debate around Mr. Fischer’s appointment has been an interesting one. True, some of it can be put down to professional jealousy. There are plenty of senior economists in Israel who wouldn’t have minded becoming governor of the national bank themselves, and one of them would have become it had Mr. Fischer remained in New York.

But that’s a side issue. The real question has to do with Israel’s relation to Diaspora Jews and with the nature of Jewish peoplehood. Do an American Jew (actually, Mr. Fischer was born in Zambia, but he has resided in the U.S. for the last 40 years) and an Israeli Jew belong to a single entity that makes the former eligible for a prominent position in the country lived in by the latter?

By international standards, after all, there is something definitely anomalous about Mr. Fischer’s appointment. It would be inconceivable for the government of the United States to appoint an Italian to head the Federal Reserve Board. No one in Paris, even in these days of European unity, would choose a German to run the Banque de France. It just isn’t done.

Nor, if he weren’t Jewish, would Mr. Fischer have been offered his new job. It was strictly as a Jew that he was chosen for it, just as was Albert Einstein when offered the presidency of Israel after the death of Chaim Weizmann in 1952. (Einstein graciously declined, which was probably just as well both for him and for Israel.)

The Jews, we are told, are one people. And yet what does belonging to this people mean? It’s certainly not a legal status like being French or American. Even though rabbinic law has its criteria for being Jewish, many persons who think of themselves as Jews do not meet these criteria and many who meet them do not think of themselves as Jews.

Does it have to do with a shared religion? It does in some cases – a synagogue-going Jew in London and a synagogue-going Jew in Buenos Aires have a lot in common. But many people who feel Jewish do not go to synagogue at all and would not even know how to behave in one.

Is it something cultural, then? Obviously not. You can come from Fez, speak Arabic, eat couscous, and listen to Um Kalthoum, and you can come from Detroit, speak English, and like hamburgers and Janis Joplin – and you can be just as Jewish in either case.

It’s the very amorphousness of being Jewish in fact, some writers on the subject have suggested, that helps explain the prevalence of anti-Semitism. What kind of group is it whose members have no outward sign, can be or pass for anyone, yet owe each other fealty and allegiance? It is as if being a Jew were tantamount to belonging to some secret society – and secret societies arouse fear and concern.

Jews know that this is not quite the case. There are no secret Jewish handshakes, no Jewish rings or cufflinks that we flash one another. We are not the Masons or the Rosicrucians.

Indeed, Jews themselves often can’t say what draws them to each other or doesn’t. Two Jews can meet and not even know that both are Jewish. I had a friend in college whom I knew for years without suspecting him of it. He wasn’t hiding it; it just didn’t matter enough to him to tell me. I discovered it when he married a non-Jewish girl and complained to me that her parents didn’t like the idea.

Are the Jews a people? The only answer one can give is that those who feel they are, are. Sometimes it’s easy to predict who these will be: Their education and upbringing account for it. Sometimes it’s impossible. I’ve known Jews who grew up in observant homes and went to religious schools and walked out the door one day and never came back, and I’ve known Jews who didn’t know they were Jews until they learned by chance and knew in a flash that a missing key to who they were had been disclosed to them.

Stanley Fischer isn’t one of your dramatic cases. He’s just an ordinary, year-round Jew who’s been to Israel often and even speaks a bit of Hebrew. As far as I’m concerned, he has as much right to his new job as anyone born in Tel Aviv. After all, this is – whatever that means – a Jewish country.

Mr. Halkin is a contributing editor of The New York Sun.