This amplifies virulence as well: the Jew, for the anti-Semite, is not just a danger, but the greatest danger exerting the greatest powers. In current paradoxical parlance, the Jew is, in essence, a Nazi. The Jew does not just devour a Christian child’s blood, but the blood of all innocent children, and more completely, the blood of all innocents.

Is any evidence needed? Appearances are irrelevant; argument is illusion. What use is visible fact when the power of the Jew is in the web woven below the surface? Jewish autonomy is itself evidence of Jewish threat. Moreover, confrontation requires courage. Anti-Semitism never sees itself as a hatred; it views itself as a revelation. An attack on the Jew is never offensive; it is always defensive. This is precisely how the Nazis portrayed it. It is precisely how Islamist ideology does as well, evident, for example, in the principles and founding documents of Hamas and Hezbollah.

In a recent book, “Nazi Propaganda for the Arab World” (Yale), the historian Jeffrey Herf shows how Nazi propagandists literally taught Arab audiences the language of anti-Semitism through popular radio programs in Arabic. Nazi ideology bears many resemblances to that of contemporary Islamic extremism, some the consequence of careful teaching. That teaching is still present in the Arab world, amplified by political leaders and imams, often annexed to denigrations of Jews taken from Islamic sources

The result, Mr. Julius and Mr. Wistrich recognize, has been one of the most historically noxious forms of anti-Semitic mythology, which has also fed into political debates in the West and cannot be overlooked or easily dismissed. It is easy enough to discern when responsible criticisms of Israel veer into something reprehensible: the structure of anti-Semitic belief is not subtle. There is a wildly exaggerated scale of condemnation, in which extremes of contempt confront a country caricatured as the world’s worst enemy of peace; such attacks (and the use of Nazi analogies) are beyond evidence and beyond pragmatic political debate or protest. Israel’s autonomy  it’s very presence  is the problem. Mr. Julius writes, “Israel is the only state in the world whose legitimacy is widely denied and whose destruction is publicly advocated and threatened; Israelis are the only citizens of a state whose indiscriminate murder is widely considered justifiable.”

But even if we leave aside such manifestations, it is clear enough that anti-Semitism requires much deeper understanding than it usually gets. Last week, for example, Hannah Rosenthal, the United States’ special envoy to monitor and combat anti-Semitism, spoke in Kazakhstan, asserting the similarity of anti-Semitism and Islamophobia.

This is not an uncommon assertion (and cases of unwarranted discrimination are always similar) but Islamophobia is a concept developed within the last two decades by those who wish to elevate Islam’s reputation in the West; anti-Semitism was a concept eagerly embraced and expanded by haters of Jews. One was constructed by a group’s supporters, the other by a group’s enemies.

Moreover, much of what is characterized as Islamophobia today arises out of taking seriously the impassioned claims of doctrinal allegiance made by Islamic terrorist groups and their supporters. Anti-Semitism, though, has nothing to do with any claims at all.