WASHINGTON — Sudden, horrific events in the middle of a presidential campaign provide an X-ray of the instincts and thinking of the candidates. We can see what their priorities are, and pick up clues about their character.

The terrorist attacks in Belgium brought out the worst in Ted Cruz and Donald Trump. Cruz demonstrated that his only focus right now is to find ways of out-Trumping Trump. He seeks words that sound at least as intolerant and as dangerous to civil liberties as the formulations that regularly burst forth from the Republican front-runner.

Thus did Cruz declare: “We need to empower law enforcement to patrol and secure Muslim neighborhoods before they become radicalized.” He happily intruded on Trump’s trademark issues by emphasizing the need to seal the nation’s southern border against “terrorist infiltration.”

Cruz touched so many hot buttons that it’s a wonder he did not have to wrap his hands in heavy gauze. And it tells us something about how far the Republican Party has veered to the right that its more moderate conservatives, including now Jeb Bush, have decided that Cruz is their best hope to stop Trump. It is hard to imagine Bush offering sentiments about Belgium remotely similar to Cruz’s.

But being more out there on these matters than Trump is, as the man might say, a huge reach. Not content to imply that he’s for torture, he embraced it outright. He insisted that it could have helped prevent the attacks in Belgium. Speaking of Salah Abdeslam, the terror suspect captured last week, Trump told CNN’s Wolf Blitzer: “Well, you know, he may be talking, but he’ll talk a lot faster with the torture.”

You don’t have to be a socialist to share Bernie Sanders’ view that Cruz’s proposal to single out a religious group for special police treatment is “unconstitutional” and “wrong.” Hillary Clinton responded characteristically this past week with a policy-heavy speech. She upbraided Cruz, saying that he was “treating American Muslims like criminals,” which was both “wrong” and “counterproductive.” She also condemned torture “anywhere in the world.”

Before the age of Trump, we valued sobriety in leaders when the country faced severe challenge. Clinton and Sanders apparently still think we do. But in the Republican primaries, sobriety has gone out the window.

The one Republican hopeful who hasn’t gotten that message yet is John Kasich. True, he did some partisan pandering, saying President Obama should not have gone to a baseball game in Cuba after the attacks. If he were president, Kasich added, he would have canceled the rest of the trip and returned to the White House to organize new anti-terror efforts.

But overall — and this is to his credit — Kasich’s reaction to Belgium contrasted sharply with the extremism of his competitors. “We are not at war with Islam, we are at war with radical Islam,” he said. “In our country, we don’t want to create divisions.”

In a more functional democracy, the campaign might provide the occasion for a serious debate on Obama’s strategy against the Islamic State (which, by the way, is what Clinton tried to start). Should the United States be more aggressive, or would such an approach, as the president seems to believe, lead us into unsustainable commitments? And how can we promote greater intelligence cooperation across Europe and give our allies a lot more help?

But such a discussion would not provide the incendiary sound bites that so much of our media seem to encourage and that Republican primary voters seem to reward.

With large parts of the Republican establishment giving up on Kasich and embracing Cruz as the last anti-Trump hope, we can now look forward to a GOP race to the bottom in which fear itself is the only thing its leading candidates have to offer.

E.J. Dionne is a columnist for The Washington Post. His email address is: ejdionne@washpost.com. Twitter: @EJDionne.