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.

For example, Mr. Carson has referred to the Affordable Care Act as “the worst thing that has happened in this nation since slavery” and compared it to slavery. He has implied that President Obama’s pledge to transform America was modeled after Cuba, Russia and other “places that have a Socialist/Communist base.”

Mr. Carson had expressed concern that if Republicans didn’t win control of the Senate in 2014, “there may be so much anarchy going on” that the 2016 elections couldn’t be held. He has endorsed the work of W. Cleon Skousen, a conspiracy-minded author and supporter of the John Birch Society. (Mr. Carson views Mr. Skousen’s work, especially “The Naked Communist,” as an interpretive key to America today.) He has also said that a Muslim should not be president of the United States, although he later insisted he had in mind Muslims who wanted to impose Shariah law on America.

Such rhetorical recklessness damages our political culture as well as conservatism, a philosophy that should be grounded in prudence, moderation and self-restraint. That doesn’t mean that conservatives should not use language that inspires people to act. But they should respect certain rhetorical boundaries. There are some places they shouldn’t go.

Mr. Carson doesn’t abide by such niceties, and he may be accurately gauging the mood of many Republicans. The Times reports that advisers who once fretted about his inflammatory rhetoric have now decided to “let Carson be Carson.” Mr. Carson has said that the message he’s receiving from supporters is, “Don’t stop. Don’t give in to the left-wing media. Go ahead and be yourself and talk about what we the people want to hear about.”

We hear similar expressions from supporters of Mr. Trump. Both Mr. Trump and Mr. Carson provide evidence that, for now at least, a large percentage of Republican voters are in a fiercely anti-political mood. As a result, the usual ways voters judge a candidate — experience, governing achievements, mastery of issues — have been devalued. People are looking for candidates not only to give voice to their anger but to amplify it. Reason has given way to demagogy. In a political context, Mr. Trump and Mr. Carson represent the id rather than the superego, not just in what they say but in how they perceive the world around them.

For the Republican Party to overcome this will require its presidential candidates to inspire voters to believe in the large purposes of politics. But it will also require Republican voters to lift their sights and raise their expectations about the goals of politics, which are to improve the lives of our fellow citizens in concrete ways; to advance, even imperfectly, liberty, opportunity and a more decent and just society.

Self-government requires more of people than pounding sand. There is vital work that needs to be done, including addressing sluggish economic growth, a widening opportunity gap and an unsustainable entitlement system. Because these things are hard doesn’t mean we can give up, and we certainly don’t need conspiracy-minded amateurs like Mr. Carson and Mr. Trump distracting our attention from them.

Politics isn’t meant to be a catharsis. Yet for many of my fellow conservatives, raging against the system — the much-maligned “establishment” — is just that. I get that it may be emotionally satisfying to cheer on careless rhetoric, to portray every political difference as a “give me liberty or give me death” moment, and to imply that America under Barack Obama is like Germany under Adolf Hitler. But it is also intellectually discrediting, politically self-defeating and unworthy of those who are citizens of a great republic.

Peter Wehner, a senior fellow at the Ethics and Public Policy Center, served in the last three Republican administrations and is a contributing opinion writer.