"Start a war between Islam and the rest of the world. Since our religion basically teaches that we are inevitably going to conquer the world by force, we will be guaranteed victory in such a war."
I agree with this to a large extent.
But it would be an extremely bad thing if it happened at all, regardless of whether they win. So playing into their hands is probably not a good idea anyway, even though they are wrong.
Assuming that's true, it's still not like the situation where your adversary is an evil genius so that doing what he wants you to do is likely to be helping him succeed in his evil goals. In this situation, it's not worth it to put much stock in whether the West is playing into Isis' hands.
But it would be an extremely bad thing if it happened at all, regardless of whether they win.
It depends how far they get in their war, it seems to me.
ISIS (or any enemy, for that matter) doesn't need to be led by evil geniuses in order to know how to set a trap for the West to fall into. With 9/11, Al Qaeda set a perfect trap for the U.S. to be blinded by pain and rage (having the simpleminded W. in office certainly helped) and, as a result, the U.S. engaged in what from the White House looked like a righteous campaign for the liberation of oppressed masses, but to those masses looked like a meddlesome intrusion into their already complicated lives. In this case (in every case, actually), I think it's absolutely essential to consider what our enemies are counting on us to do.
Here's my op-ed that uses long-term orientation, probabilistic thinking, numeracy, consider the alternative, reaching our actual goals, avoiding intuitive emotional reactions and attention bias, and other rationality techniques to suggest more rational responses to the Paris attacks and the ISIS threat. It's published in the Sunday edition of The Plain Dealer, a major newspaper (16th in the US). This is part of my broader project, Intentional Insights, of conveying rational thinking, including about politics, to a broad audience to raise the sanity waterline.