Know Your Enemy
It seems to me that the Islamist movement is not as different from the other nihilistic, revolutionary ideologies of the last hundred years or so as we tend to believe. Like the communists, anarchists, fascists, and others, the Islamists are basically a small group of disaffected intellectual types with delusions of global domination through a bloody mass mobilization of the "people" (proletariat, whatever). All these groups have utopian fantasies-- whether a workers' paradise or a restored caliphate-- and all have strong notions of purification-- whether genetic or spiritual.
In defeating the other "-ists" it was as important to make the world understand why our way of doing things was better as it was to prove we were stronger. World War I defeated the Germans, but it did not discredit their nationalism, expansionism, or notions of being instruments of social Darwinism. To the contrary, the handling of the victory by the allies allowed all of these virulent strains to grow into the full-blown horrors of Nazism. The same mistakes were not repeated in WW II, and our post-war handling of the peace contributed to the total discrediting of the violent pathologies of Germany (and Japan, which had its own form of quasi-religious nationalism). Of course, during the Cold War, while it was America's nuclear umbrella that kept the Red Army at bay, it was in the marketplace of ideas (and the marketplace of, well, markets) that the battle was fought and won.
In our current struggle against the Islamists, we are doing well on the military front (leaving aside for the moment the controversies over going to war in Iraq in the first place and the ongoing deficiencies in securing our ports and borders), but we have barely joined the battle on the intellectual front, and where we have tried we seem to be failing. People keep talking about "losing the peace" in Afghanistan and Iraq, but that's wrong. What we are losing is another phase of warfare. War is the application of violence for political ends. How can a war be successful if the violence goes great, but we don't meet the political goals?