I hear, "I'll do my best" a lot. In my experience, it almost always has been a cop-out for the end result of something. You can't blame the person for doing a shitty job at something, because of the, "I did my best" excuse. It drives me nuts, but when I hear someone else say it, I give them the benefit of the doubt that they mean it. In that case, it doesn't bother me.
Anti-intellectualism has been a constant thread winding its way through our political and cultural life, nurtured by the false notion that democracy means that 'my ignorance is just as good as your knowledge.' -Isaac Asimov-
