[lbrandy]

It depends what you mean by free will. Non-philosphers almost always mean "libertarian" free will when they say that, and yes, this same argument also basically outlaws libertarian free will as well. There is no physical mechanism by which you can alter your brain physics to "choose" things.

Carroll and others have a compatibilist notion of free will which is a more subtle concept that I'm not sure I'm qualified to actually explain.