Maybe we should think about the semantics as some have said.
In South Vietnam we fought Communism, yet if we had won in South Vietnam we would not have defeated Communism per se', but we would have slowed it's influence in Southeast Asia, appreciably.
Actually in retrospect, South Vietnam that is now just Vietnam could some day gradually democratize as the Northern governmental powers can't quelch the influence of the Western world from seeping into the South especially, as tourism dollars/Euros roll in.
Similarly, Tiananmen Square isn't something the Chinese government has brought to an end. There is such a strong capitalistic movement in the Republic of China, and such a strong under-ground Christian church too, that nothing is going to stop folks from gradually attaining liberty, and freedom, even with the strong arm of Maoist type pressure.
Likewise, in Iraq, if we bring hostilities down to a minimum and basically neutralize AQ's influence, then that probably isn't a defeat of AQ, but it sure will have knocked some perverbial wind out of their sails, and probable their influence in other countries too.
To "win" is in some ways in the eye of the beholder, as a "win" can be just hanging in there long enough for the present Iraqi government to gets it's walking legs going, and for a National police and military force to get established. It doesn't end Islamic militancy, but it bloodies it's perverbial nose, and surely causes it setbacks in other parts of the world.
I don't think we will ever get the "hugs and kisses" from any of these Islamic governments or their populous that we would desire, as their ethical/religious motivations and culture go very "cross-grained" to our Western culture and religious/ethical basis of life and how we look at human, both male and female.
Islam and Democratization seem to be like water and oil. They aren't mixing too well at this time. Something has to "give" or we are in for some real problems........Thats reality.
To be moderately Islamic is to be un-Koranic, and that just makes for some problems for the continued future.
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Win, stablize, whatever, we have to pull out when we think these folks can self govern and self defend from within and without. We can still be a force to quick-deploy, as is the case with our presence in South Korea, and for years in West Germany, before the USSR cave-in.
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I wish that somehow when we invaded in the last conflict that we could have somehow partitioned-off the Kurdish, Sunni, and Southern Shiite Muslims areas into "three states" within the larger country of Iraq, and then had a central government with basically loosely governed states based on their strong religious differences and cultures. Call them provinces, states, whatever, but maybe that would have made a difference.
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Seems to boil down to the American people perceiving a personal threat upon themselves with whats going on in the Middle East. If it doesn't touch our physical shores, then it isn't a threat.
I tend to be "far reaching" in my way of seeing or perceiving threat. I don't like it to sneek up and bite me in the perverbial arse. I'd rather smack the enemy down early than late. Often this saves lives, but I'm sure the war detractors will have another angle on that one.
I also see it like Vector control. Get those critter while their larvae's before they are blood sucking Mosquitoes.