One common response to the mass murder of innocent children in Newtown, Conn., has been calls “to do more” to help people with mental illness.

If that means providing adequate resources for community mental health services, fighting the stigma of mental illness that prevents people from seeking treatment and conducting outreach to people who may not know that they are ill, we are all for it, and were long before this tragedy.

If “doing more about mental illness” is a proposed alternative to gun control, however, we part company.

Protecting the public from mass shootings, which have become more common even as other kinds of violent crime decline, is complex in part because these attacks are still relatively rare and unpredictable. To think that we can somehow protect our children by identifying perpetrators before they go on a killing rampage is dangerous magical thinking.

No profile can isolate an Adam Lanza, a Jared Loughner (Tucson, Ariz.) or a James E. Holmes (Aurora, Colo.) from thousands, maybe millions, of troubled young men who exhibit some of the same symptoms but who will never commit a violent act.

In the end, what made them killers was access to high-capacity weapons that let them fire many deadly rounds very quickly. If these deeply disturbed young people had access to ordinary weapons, the death toll would have been much lower. If they had not been able to access guns at all, their rampages might have been limited to their fantasies.

The United States doesn’t have a higher incidence of mental illness than other countries. We do have more mass killings because the weapons are so readily available.

Unfortunately, mental illness is a silent problem until some extraordinary event occurs.

When a homeless, mentally ill woman walked out onto the Casco Bay Bridge in 2009 and threatened to jump, police from Portland and South Portland stopped traffic and subdued her, getting her into an ambulance. They saved her life, but others, just as troubled, went on slowly killing themselves with alcohol or drugs and did not get the help they need.

We should do more to treat mental illness, but not just in extraordinary cases. And not as an alternative to gun control.