LIKE many other political autodidacts, Ben Carson has an odd obsession with Nazi Germany.

On several occasions, the pediatric-neurosurgeon-turned-Republican-presidential-candidate has compared the United States to the Third Reich. Mr. Carson has warned that a Hitler-like figure could rise in America. To understand what is happening in the Obama era, he recommended that people read “Mein Kampf.” And he won’t let go of the myth that the Holocaust would have been “greatly diminished” if Jews in Nazi Germany had been allowed to possess guns.

To declare the United States to be “very much like Nazi Germany” is a special kind of libel, yet Mr. Carson is clearly drawn to it. Part of the explanation may be that people who want to impress sometimes invoke imbecilic historical analogies, with the default one often being Nazi Germany. Some part of the answer has to do with his staggering ignorance when it comes to the unique malevolence of Hitler’s Germany. And for still others, it’s a way to convey alarm and mobilize supporters. In the case of Mr. Carson, it also appears to be based on the belief that progressive ideas share intellectual roots with fascism, with Nazism — the National Socialist German Workers’ Party — being an extreme version of progressivism.

One might expect a fringe presidential candidate to resort to the Nazi analogy. But what is disturbing is that in this case the person making the comparison is polling second in the Republican race for president. In the most recent Fox News national poll, Donald J. Trump drew 24 percent support while Mr. Carson had 23 percent. Between them, then, they are pulling in just under half of the support among Republicans.

In one respect, Mr. Carson is the antithesis of the crude and boisterous Mr. Trump. In tone and style, Mr. Carson comes across as calm, reasonable and agreeable. But in fact he is more rhetorically intemperate than even Mr. Trump.