U.S. Sen. Rand Paul, R-Ky., speaks with the media at the Peppermill restaurant Friday, Jan. 16, 2015, in Las Vegas. (John Locher/AP)

TWO POTENTIAL Republican presidential candidates, Sen. Rand Paul (Ky.) and New Jersey Gov. Chris Christie, have made irresponsible comments about vaccines at a time when measles has reappeared in the United States. Their remarks call into question their judgment and their fitness for higher office.

Mr. Paul, an ophthalmologist, said in a television interview, “I’ve heard of many tragic cases of walking, talking normal children who wound up with profound mental disorders after vaccines.” He added that he vaccinated his own children: “I’m not arguing vaccines are a bad idea. I think they’re a good thing. But I think parents should have some input.” Mr. Christie, visiting a medical research laboratory in Cambridge, England, said that he, too, had vaccinated his children, but “I also understand that parents need to have some measure of choice in things as well. So that’s the balance that the government has to decide.”

Both comments reflect a streak of libertarianism, a political philosophy that champions the individual and freedom to choose. In principle, this isn’t irrational. The United States has often stood as a beacon of individual liberty over tyranny. But it becomes destructive when people resist government because of irrational fears and suspicions. To protect people from threats, government has a legitimate role. In the case of measles, the threat is a highly contagious virus that can bring serious consequences. According to the Centers for Disease Control and Prevention, “Measles is so contagious that if one person has it, 90% of the people close to that person who are not immune will also become infected.” This is why states have passed laws mandating vaccination for children attending public schools (although 17 states, including California, scene of the outbreak at Disneyland, have waivers for personal beliefs, and 48 have waivers for religious beliefs).

Both the governor and senator seem to be suggesting that it is fine for parents to avoid vaccinations for their children. But is this really a matter of individual rights? Liberty does not confer the right to endanger others — whether at a school or Disneyland or anywhere else.

More broadly, a president must make decisions every day about science, and it is not always easy; consider the struggle over climate change, the hard-fought debate over the impact of the Keystone XL pipeline, the promise of genetically modified foods, the intensifying threat of cyberattacks and the growing danger of antimicrobial resistance. Every one of these requires decision-makers to be rational and clear-eyed, the president most of all.

In the case of measles, proven science is well in hand. The vaccine has a half-century record of safety and effectiveness. The study linking it to autism has been discredited and retracted. Mr. Paul’s reporting of anecdotes that he has “heard” is particularly insidious. Measles was eliminated in the United States by 2000 with widespread use of the vaccine. No presidential candidate should endorse parental “choice” that could reopen the door to an ugly and preventable disease.