But back to the relevant question, if I do something and blame it on a fake belief, is what I pretend to believe in at fault?
I fear you have little understanding of what Muslim extremists believe in. They most certainly are killing people in the name of Allah, and they most certainly do believe they are Muslims. Do you think the murders of those poor innocent Parisians, or the Charlie Hebdo cartoonists, or the murderers of Theo Van Gogh in Holland, or the murder of the soldiers in Woolwich, or the fatwa applied by millions of Muslims on Salman Rushdie is pretend Islam or something? From the murderer of Theo van Gogh:
At his trial, Bouyeri was unrepentant -- and absolutely clear about why he murdered van Gogh. “I did what I did purely out my beliefs,” he explained, Qur’an in hand. “I want you to know that I acted out of conviction and not that I took his life because he was Dutch or because I was Moroccan and felt insulted…. If I ever get free, I would do it again.” He was, he said, acting in accord with Islamic law: “What moved me to do what I did was purely my faith. I was motivated by the law that commands me to cut off the head of anyone who insults Allah and his prophet.”
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