Here's the Obama doctrine.
'Obama's Libya policy may not amount to a doctrine, but it did establish two principles. Last March, Obama explained that we must intervene when there's a risk of massacres or genocide, but we can never do so alone unless Americans are directly at risk.At face value, I find this borderline repugnant. America shouldn't be the world's policeman, but neither should we make it a matter of principle to say we won't stop genocide when and where we can simply because no one will join our posse. - Jonah Goldberg
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I doubt that the Libyan war established the principles that Goldberg claims here. But I do think the war established a principle, and a very important one at that: the U.S. will no longer be an occupying power.
The Libyan war, combined with the Obama administration's lethal expansion of special forces and drone attacks in Somalia and Yemen, drive this point home. The U.S. will continue to wage what can only be called a "war" on terror, but one that is far more asymmetrical and under the radar. This is almost certainly for the good. While drone campaigns will undoubtedly radicalize some (especially if they're used hyper-aggressively), they're far less radicalizing than a large scale troop presence in a foreign country.