First let me apologise for my snarky comment regarding JD's original question.

Yes, it is possible, in fact essential, to fight any war at all with ideas. They are an essential part of the armoury. Clausewitz specifically recognised this in stating that war was diplomacy by other means, and in stating that the objective was to break the enemy's will to fight.

If you study the end of WW1, it was the German General staff that lost its nerve and then put it's faith in Woodrow Wilson's ideas for a negotiated settlement.

The cold war involved a massive multi-country intellectual confrontation with the Soviets, that, in my opinion, dwarfed the military efforts.

This was aimed at firstly selling the benefits of free market capitalism as well as highlighting the downside of command economies and repression. About the only thing left of this today is the Peace Corps. the Voice of America and perhaps some aid programs.

If you lived in America, you would have seen very little of this effort as Europe was the main theatre. Typical programs were endless scholarships for any communist intellectual who wanted to visit and study in the west, multiple "friendship societies" and similar organisations aimed at getting the good news about western capitalism to the eastern bloc and taking any opportunity to pour scorn on the Russian "workers paradise" propaganda that they tried to foist on "non aligned" nations.

Fruits of this program were "Prague Spring" and the Polish Solidarity movement

The Russians simply gave up when they realised that the entire "workers paradise" charade simply couldn't be carried any further (it certainly would not have survived the internet). All of this infrastructure has been dismantled since the end of the cold war.

Which begs the question - where is the similar and complementary effort to demonise Al Qaeeda in muslim eyes and win over the muslim world to our way of thinking??? It appears that only Dr. Kilcullen is trying to do this, and I suspect most of his efforts may simply be undoing some of the harm earlier "policy" decisions has done.