Donald Trump is still on top of the polls even after saying things that would doom any candidate in a normal year. The horrors inflicted by Islamic State have given his campaign a lift.

The would-be president said he would register Muslims in a national database and probably close some of their mosques. He charged that Muslims in Jersey City, N.J., cheered the collapse of the World Trade Center in 2001, even though nobody else remembers such a thing.

He warned that President Barack Obama plans to admit 250,000 Syrian refugees next year; the real number is 10,000. He sent out bogus statistics claiming that 81 percent of white murder victims are killed by black people; after Bill O’Reilly of Fox News told him that wasn’t true, Trump shrugged and said he didn’t have time to check the facts. And that’s only in the last week.

How can a figure this gratuitously divisive hold on to his place atop the GOP presidential standings? Anger and fear.

The anger of conservative voters has been evident all year, but this week the nonpartisan Pew Research Center released an important study that added new detail to the picture.

The report’s headline was that only 19 percent of Americans say they can trust the federal government most of the time, one of the lowest levels in half a century. But among Republicans, that disaffection runs much deeper: 32 percent say they not only mistrust the government but are “angry” with it.

The angriest voters, Pew found, are politically engaged conservatives, the Republicans most likely to vote in primary elections. Most of them say an ordinary citizen could do a better job in the White House than a professional politician. Among that group, Citizen Trump scores high.

“We’re sick of career politicians,” explained Marenda Babcock, 60, a Trump supporter in Indiana, at a focus group sponsored by the University of Pennsylvania’s Annenberg Center last month.

“We did what we were supposed to do. We wrote the letters, we made the phone calls, and they did not listen. And we’re out to clean house.”

Now add another inflammatory element to the mix: fear. After the Paris attacks, polls showed that terrorism had jumped to first place among voters’ concerns, displacing even the economy and jobs.

Trump was quick to take advantage. Not only did he reject Obama’s proposal to admit more Syrian refugees; he called for deporting any refugees who have already arrived.

Other candidates tried to match him — Ted Cruz said he’d admit only Christians, Chris Christie said he’d deny entry to children — but nobody does truculence as convincingly as Trump. Ben Carson, who delivers his conservatism in more soothing tones, sounded uncertain, and lost some of his support.

An ABC-Washington Post poll released this week found that 42 percent of Republicans named Trump as the candidate they trusted most to handle terrorism, far ahead of any of his competitors.

The public’s heightened fear may not last until next year’s general election, but it will surely remain fresh until the Iowa caucuses in January.

Even so, Trump is the preferred candidate of only about one-third of Republican voters. By all rights, something should happen to unseat him. But what?

I consulted several strategists for Trump’s competitors — and came up empty.

“I wish I knew,” said the adviser for one candidate. Maybe the voters will wise up, he ventured.

“When it’s time to cast a real ballot, they’re going to think about electability, about which candidate can win the general election against Hillary Clinton.”

Or maybe Trump will come in second in Iowa, he continued, and decide to withdraw, because he doesn’t want to look like a loser.

Trump is still a long way from becoming his party’s presidential nominee, but by all logic, he shouldn’t even be this close. This campaign, however, hasn’t been governed by logic; it’s been governed by anger and fear.

Doyle McManus is a columnist for the Los Angeles Times.