The war isn’t over. That’s the big takeaway from the Boston Marathon bombing, like it or not.

A lot of Americans thought the war — which Congress had never formally declared to begin with — was already over. President Obama announced the withdrawal of American troops from Iraq and Afghanistan. The attacks on New York and on the Pentagon on September 11, 2001 are more than a decade past, and the attack on the American consulate in Benghazi, Libya was geographically distant. Osama Bin Laden was dead.

But this war — the one the Islamist extremists are waging against us, the one that Norman Podhoretz calls World War IV (World War III having been the Cold War) — can’t be ended unilaterally by American fiat. Even if we wish it could.

Within this basic framework, there are still plenty of things for Americans to debate. We can debate whether the amounts we are spending on national defense — $660 billion, or 4.1% of GDP in 2013, according to the White House Office of Management and Budget — is too little, or too much.

We can debate whether to treat American citizens such as Dzhokhar Tsarnaev as criminal defendants with the usual constitutional rights, or as wartime enemy combatants with lesser rights, as some Republican senators recommend.

We can debate whether the shutdown of a major American metropolitan area was an overreaction to the potential threat posed by a 19-year-old whose arsenal reportedly included pressure cookers and a BB-gun.

We can debate whether, given the death toll of terrorist attacks (compared to, say, heart disease, or fertilizer plant explosions, or school shootings), our response is proportionate to the threat.

We can debate immigration policies, and policing policies, and energy policies, and domestic surveillance policies.

But the Boston bombing, and the news that has followed about the careers and beliefs of the suspects, will constrain certain other debates, or puncture illusions.

There was this idea — apparently popular in some quarters — that we could defuse the Islamist extremist threat merely by electing a president with the middle name Hussein, or by withdrawing from Iraq and Afghanistan, or by killing Osama Bin Laden, or by instructing the NASA director that the American space agency’s “foremost” mission should be “to find a way to reach out to the Muslim world and engage much more with dominantly Muslim nations to help them feel good about their historic contribution to science … and math and engineering.”

Nonsense. Also false is the idea, apparently common on the right, that national security leadership is no longer a necessary or even desirable quality for Republican politicians. The Mitt Romney-Paul Ryan Republican ticket in 2012 was an example of this. Its main message was that the domestic economy and the federal budget were the big issues, not the global war against Islamofascism. That was true, until it wasn’t true anymore. Or at least it didn’t seem true to those imprisoned in their homes, or glued to the television screen or the Internet for updates on the Boston bombing suspects.

There’s something unnerving about this, which is why we talk about the attacks in terms of terrorism. The offense isn’t just the murder; it’s the infliction of fear, or terror, on the civilian population beyond those physically injured or killed in the attacks.

There is precedent in American history for a war-weary nation rising to a conflict not of its own choosing. After World War II, America answered the challenge of the Cold War.

Some may complain that the comparison with the Cold War is entirely inapt. The Soviet Union was a nuclear-armed superpower, while Dzhokhar Tsarnaev is a 19-year-old with a BB-gun, a pressure-cooker, and a degree from Cambridge Rindge and Latin. Maybe so. On the other hand, for all the grave crimes of the Soviet Communists, they never bombed the World Trade Center, the Pentagon, or the Boston Marathon.

Mr. Stoll is editor of FutureOfCapitalism.com and of Smartertimes.com.