Hillary Clinton has twisted herself into a pretzel on the subject of terrorism and its connection to Islam. Like many Democrats, she says that we must choose our words carefully to avoid scapegoating peaceful Muslims or driving them into the terrorists’ arms. But the words she has chosen won’t help achieve our foreign-policy goals or help peaceful Muslims — because they make no sense.

In a Nov. 19 speech on how to combat Islamic State, Clinton argued that our rhetoric is part of our strategy: “Islam is not our adversary. Muslims are peaceful and tolerant people, and have nothing whatsoever to do with terrorism. The obsession in some quarters with a clash of civilization, or repeating the specific words ‘radical Islamic terrorism’ isn’t just a distraction, it gives these criminals, these murderers more standing than they deserve. It actually plays into their hands by alienating partners we need by our side.”

These were prepared remarks. One might be tempted to give Clinton the benefit of the doubt anyway and assume she meant to imply that “most” Muslims are as swell as she says. Surely she doesn’t mean to deny that some Muslims leave something to be desired in the peaceful-and-tolerant department.

But other Democratic foreign-policy luminaries are saying similarly far-fetched things. John Kerry, Clinton’s successor as secretary of state, said a few days before her speech that the Islamic State’s barbarism “has nothing to do with Islam; it has everything to do with criminality, with terror, with abuse, with psychopathism — I mean, you name it.”

Nothing to do with Islam? Does anyone think we’re going to find professed atheists among these psychopaths? Kerry obviously wanted to condemn Islamic State and its allies while not lumping in most Muslims with them. He could have simply noted that most Muslims reject terrorism, that many call it a perversion of Islam, and that he hopes this view prevails among more and more of them. Unlike what he actually said, none of that would have been absurd.

Clinton also spoke for others in rejecting the phrase “radical Islamic terrorism.” Liberal pundits say it’s “ugly.” The Democratic Party is running an ad alleging that it equates all Muslims with terrorists and incites fear. But to invoke “radical Islamic terrorists” logically implies that it is possible to be other Islamic things: for example, a kindhearted Islamic scholar. So it wasn’t bigoted when Clinton, in 2005, gave a speech criticizing “radical Islamist extremists.”

It’s possible that some Muslims who hear that phrase will wrongly conclude that the speaker is expressing enmity toward all Muslims. But some misunderstandings are inevitable — and, in any case, Clinton’s preferred terminology does nothing to reduce their likelihood.

At the most recent Democratic debate, Clinton condemned “radical jihadist ideology” in her opening statement. She used versions of “jihad” five other times that night. Everyone knows the religion with which jihad is associated. She didn’t call it a “radical Crusaderist ideology.” She’s talking about a subset of Muslims, just as the Republicans who talk about “radical Islamic terrorists” are.

If using the word “Islam” in the vicinity of “terrorism” is a bad idea, then so is using the word “jihadism” to mean, well, Islamic terrorism. So it isn’t surprising that the J-word has run into the same criticism. In 2009, John Brennan, then an adviser to President Barack Obama and now head of the CIA, said that the administration disavowed the term “jihadism” for pretty much the same reasons Clinton dislikes “radical Islamic terrorism”: It “risks giving these murderers the religious legitimacy they desperately seek” and “it risks reinforcing the idea that the United States is somehow at war with Islam itself.”

All this tortured diction is pointless. We’re at war with people who believe that Islam justifies mass murder. There’s no way to conduct that war without giving some people the impression that we’re at war with Islam, period. And there is such a thing as going too far to try to avoid giving that impression. When that imperative leads officials to say things that can’t be believed, it sends the opposite message from what they intend: It suggests that our leaders are expressing obvious untruths because they can’t acknowledge that Islam really is our enemy.

I suspect, in other words, that the nothing-to-see-here denial of any link between Islam and terrorism has a symbiotic relationship with anti-Muslim prejudice. If you insist that the alternative to distrusting Muslims in general is to pretend that there’s no such thing as Islamist terrorism, then some people will figure that distrust is safer.

They’ll also figure that they can’t believe anything you have to say on related subjects. The latest Washington Post/ABC poll shows that 54 percent of the public opposes taking in Syrian refugees. Maybe the majority is right and maybe it’s wrong, but I can’t help thinking that the number would be lower if the people calling for letting the refugees come here weren’t the same people who say that “Islam has nothing to do with terrorism.”

Ramesh Ponnuru, a Bloomberg View columnist, is a senior editor for National Review, where he has covered national politics for 18 years, and a visiting fellow at the American Enterprise Institute.