In less than two weeks, Western Europe has witnessed the calm of everyday life repeatedly shattered by high-profile, indiscriminate acts of savagery, raising the sense that violence is becoming a new normal.

After the Bastille Day massacre in Nice, then an ax attack on a German train and a shooting spree in Munich, the list of violent acts grew again on Sunday not once, but twice. One Syrian asylum-seeker allegedly hacked a woman to death with a machete in southern Germany; police said it didn’t appear connected to terrorism....