Moisés Naím / Financial Times

This week's terrorist attacks not only killed people; they also killed ideas. Many of the certainties and assumptions that guided position papers, policies and budgets will not survive the deliberate crash of jetliners into the World Trade Center and the Pentagon. Some of the ideas that passed away last Tuesday had been with us for decades; others were as new as the Bush administration. The attacks have also brought about new ideas, some of which are likely to be as misguided as those discarded.

First and foremost among the ideas now buried beneath thousands of tons of rubble is the notion that technology could make the American homeland impregnable. Whether this idea's demise will also kill plans to build a missile shield that would protect the US from the intercontinental ballistic attacks of rogue states remains to be seen. There is too much money to be made and too many careers are at stake for this programme to die quietly or quickly.

What is certain is that proponents of missile defence will have a much tougher time persuading Americans that this is the best use of their tax dollars. The terrorists made everyone fully and painfully aware of the concrete meaning of asymmetric war: enemies that respond to high-technology weapons with low-tech tools. The idea that, in some instances, the brilliance of scientists and engineers is no match for the suicidal motivation of fanatics is no longer just a experts' prediction: it is now a conviction burnt into the minds of all those who saw Tuesday's harrowing scenes.

Those scenes also destroyed the idea that military superiority ensured national security. Military might may be necessary but, contrary to what was frequently implied in the haggling over military budgets, it is not sufficient to guarantee national security.

The terrorist attacks have sparked new ideas that will inform debates and shape policies. The main one is the need to wage a global war against terrorism. While the idea may not be new, it is now high in the minds and the agendas of politicians, policymakers and the public. Giving more attention, money and priority to efforts to prevent and to fight terrorism is long overdue and absolutely necessary. But this idea may lead to two other, more problematic ones.

The first is that the fight against terrorism is a war and can therefore be won. The second is that other foreign policy problems that confronted the US before the terrorist attacks of last Tuesday can be put on the back burner while the war against terrorism is being waged.

Terrorism has always existed and will not be eradicated. In fact, by increasing the terrorists' mobility, agility and global reach, globalisation has made them much tougher adversaries. Nor does the world lack fertile breeding grounds for future terrorists. These may be refugee camps that are home to millions displaced by war, ethnic strife or failed states, or neighbourhoods as big as entire cities where the only way out of despair and hopelessness is the promise of martyrdom: the supply of volunteers will continue to be steady, diversified and abundant.

The idea that the elimination of Osama bin Laden and his network would substantially curb the terrorist threat may prove to be as misguided as the hope that the elimination of Pablo Escobar, once the leader of Colombia's most powerful and violent drug cartel, would thwart drug trafficking. After the Colombian police killed him, Escobar was quickly replaced by other drug lords at least as cunning and violent. Today the drug war shows no signs of abating and is in fact fiercer than ever.

There are no reasons to believe that the war on terrorism will be any different: it will be permanent, with elusive and changing enemies - and even important victories will not ensure that the enemy has been defeated. Calling this conflict a war may feel right but what is being fought is very different from what we used to know as war.

The second idea engendered by recent events is that in the foreseeable future there will be no foreign policy priority more important for the US than defeating terrorists. Yet before Tuesday the US was facing, in addition to terrorist threats, myriad other challenges for which it had no obvious response. It still is.

While the terrorist attacks can and should be used as an opportunity to improve the US's relationship with Russia and China, the stubborn fact remains that the Bush administration is still in the process of defining its long-term strategy with those two countries. It is not clear, for example, what stance the administration will take towards China: strategic ally or future threat. Will it ignore Russia or actively engage it? While the Nato alliance has unequivocally and strongly supported the US, multiple rifts and disagreements on issues including missile defence and the Kyoto agreement - still plague the relationship between Europe and the US.

In a few months, the World Trade Organisation summit in Doha will highlight the sorry state of the world's trade regime and the need for the US to build and to lead a coalition that could break the stalemate that has paralysed trade talks for years.

Plan Colombia. Tensions between India and Pakistan, China and Taiwan, or on the Korean peninsula. The Balkans. Nuclear proliferation. Africa. Aids. Poverty. Global economic slowdown and financial instability. Argentina and Turkey. Last but not least, the Middle East. The list is long and well known. Some of these are chronic problems and will not go away. Some are dormant and do not require immediate attention. Others will not directly affect important American interests. But sooner rather than later, one or more of them that does touch vital American interests will flare out of control. And the US will not have the luxury of not getting involved. It may even be that in a year or two the fight against terrorism is itself displaced as the highest priority.

The good news is that another idea rising from the ashes of Tuesday's tragedy is that even a superpower cannot afford to go it alone. Many of the unilateralist instincts that were so much in evidence at the beginning of the Bush administration will, one hopes, now be tempered by the realisation that the long-term fight against terrorism requires close co-operation with other countries. That lesson will come in handy when the need to deal with the other foreign policy challenges facing the US arises. Few if any of the problems listed above can be effectively confronted by America acting alone. We all need friends and allies. Even a hegemon.