Story highlights

• Peter Bergen: Trump's recent speech was long on invective but short on policy specifics
• Trump's claims are erroneous, and his plan to suspend immigration won't work, Bergen says

Peter Bergen is CNN's national security analyst, a vice president at New America and a professor of practice at Arizona State University. He is the author of the new book "United States of Jihad: Investigating America's Homegrown Terrorists."

(CNN)To paraphrase an observation made by the American writer H.L. Mencken: For every complex problem, there is a solution that is simple, neat and wrong.

Peter Bergen

Donald Trump's Monday speech in New Hampshire was billed as his big statement on terrorism. Coming a day after the deadliest terrorist attack on U.S. soil since 9/11, the speech was his opportunity to lay out one of his campaign's signature claims in considerable detail: that he will be really tough on terrorists, including torturing them and killing their families.

Instead, Trump's speech was an oversimplification of Mencken-like proportions. It was long on invective against Hillary Clinton -- such as "Clinton wants to allow radical Islamic terrorists to pour into our country" -- but short on policy specifics. The speech did briefly flesh out Trump's one big counterterrorism idea. In his words, "I will suspend immigration from areas of the world where there is a proven history of terrorism against the United States, Europe or our allies."

Trump failed to elaborate or specify which countries would be affected, but presumably this ban would apply to countries such as Afghanistan, Iraq, Libya, Pakistan, Syria and Yemen, all of which have significant ISIS or al Qaeda presences within their borders. The ban could also include countries such as Indonesia and Saudi Arabia -- longtime American allies that are, respectively, the world's largest and richest Muslim countries -- that also have been sites of terrorist attacks against Western and American targets.

Here's the critical question. Would this vague plan to suspend immigration solve the problem of terrorism in the States? Hardly. Since 9/11, every lethal jihadist terrorist attack in this country has been carried out by an American citizen or legal resident.

Take Carlos Bledsoe of Memphis, Tennessee, whose family members have served in the U.S. military since the Civil War. He was a convert to Islam who killed an American soldier in Little Rock, Arkansas, in 2009.

Or Nidal Hasan, born in Arlington, Virginia, 4½ decades ago, a U.S. Army major who killed 13 people at Fort Hood, Texas, in 2009.

And Syed Rizwan Farook, who was born in Chicago in 1987. Together with his wife, Tashfeen Malik, a legal U.S. resident by virtue of her marriage to her American husband, he killed 14 in San Bernardino, California, in 2015.

Now Omar Mateen, who was born in New York in 1986: He killed 49 people early Sunday at an Orlando nightclub. (In his Monday speech, Trump claimed that Mateen was Afghan but failed to mention the two of them were both born in Queens.)

For Trump's plan to work, you would somehow have to wind the clock back a half-century and ban immigration from all Muslim countries until now. Since even Trump doesn't claim he can reverse time, his proposal for a temporary ban is fatuous.

It's the sort of idea that your opinionated and tiresome uncle who always has the "easy" answer to every difficult problem trots out at Thanksgiving dinner and everyone ignores because it's clearly just dumb. But instead of holding your tongue or rolling your eyes until someone changes the subject, in this case your uncle could become the 45th president of the United States.

Not only would the ban be useless to efforts to combat lethal acts of terrorism in the United States, but by imposing what looks like a religious test on immigrants it would also be open to serious legal challenges. Not to mention that it's a fundamentally un-American idea. The United States didn't ban Italian immigration in the 1920s because a small minority of Italians became members of the Mafia, and the country is a richer place for it.

In his speech, Trump went on to make other vague, unsubstantiated or outright erroneous claims. For instance, that President Barack Obama is not letting law enforcement "do their job." Really? The FBI said it's investigating some 900 terrorism cases in all 50 states. Sounds like it is not being hindered by Obama.

Trump also claimed that the Obama administration, with support from Hillary Clinton, is "restraining our intelligence gathering." Tell that to Osama bin Laden, who is dead as a result of a CIA operation and SEAL raid authorized by Obama and whose most prominent supporter was Clinton. Or to the 1,000 ISIS fighters a month who have died in U.S. airstrikes since the summer of 2014.

He railed against the "tremendous flow of Syrian refuges into the United States." The war in Syria has generated the largest number of refugees since World War II, a total of 14 million between those displaced internally and those who have left the country. Yet the United States has only taken so far less than 4,000 Syrian refugees -- a paltry figure that future historians will bracket with the failure of the Roosevelt administration to take in more Jews fleeing the Nazis.

Perhaps most irresponsibly, Trump demanded, "Muslims have to work with us." News flash: They are. Around a third of all the terrorism cases investigated since 9/11 originated with a tip from a member of the Muslim community or a family member, according to research by New America. In quiet ways far too complex to hold Trump's interest, Muslims in the United States and around the world are helping every day to prevent massacres such as Orlando from happening.

Mencken's words were more prescient than even he knew. He might as well have been writing about Trump's counterterrorism plans, which may be simple but have no hope of being effective.

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Peter Bergen is CNN's national security analyst, a vice president at New America and a professor of practice at Arizona State University. He is the author of the new book "United States of Jihad: Investigating America's Homegrown Terrorists."