The average Islamic extremist when he has time to think about anything other that licking his favourite pig, is under the mistaken belief that the western world is fundamentally weak. Weakened by our dissipated and irreligious lives; weakened by our usual sympathy for the underdog.
This is perfectly understandable for the moronic medieval minds that most Islamic extremists carry around with them. Because in some ways the west does look weak.
But the west is not weak as it has shown again and again since the start of WWII. However it is reluctant to start anything without taking care that it is doing the right thing. Time and again, whenever the west has gotten involved with something without thinking enough in advance (Vietnam, Iraq, etc.) it has gotten bogged down in something it realises that it shouldn’t have started.
But the west will get involved if it is provoked enough and it believes that it is on the right side.
The beheading of James Foley by the pig-licking thugs sometimes known as ISIS, ISIL, IS or just Daesh would appear on the surface to be an attempt to discourage the US and the west from getting involved. It would seem that the US air strikes and the push by the Kurdish and Iraqi military have started making things difficult for IS, and they would like to stop the US air strikes.
What they have accomplished is to encourage the US and the rest of the west to stay involved and take more measures.
They may regard themselves as some sort of ultra-religious freedom fighters, but anybody who uses extortion, flogging, amputations, rape, and indiscriminate killings are nothing more mindless pig-licking thugs.