If what people do is any reflection of who they are, then Devin P. Kelley, who slaughtered 26 churchgoers on Sunday in Texas, surely was a madman.

Before the atrocity, he had attempted to sneak weapons onto an Air Force base after making death threats to his superiors, according to a local police report. In 2012, he had escaped from a mental hospital in New Mexico to which he had been sent after assaulting his wife and fracturing his stepson’s skull.

A video of the church killing reportedly shows Mr. Kelley working his way methodically through the aisles, shooting some parishioners, even children, at point-blank range.

“I think that mental health is your problem here,” President Trump told reporters on Monday.

It is true that severe mental illnesses are found more often among mass murderers. About one in five are likely psychotic or delusional, according to Dr. Michael Stone, a forensic psychiatrist at Columbia University who maintains a database of 350 mass killers going back more than a century. The figure for the general public is closer to 1 percent.