There is a war going on, but it is a civil war within the "House of Islam" that occasionally spills over into non-Muslim countries. The three killers in Paris probably did not fully understand the role they were playing.
Two of these Muslim civil wars, in Afghanistan and Iraq, were ignited by US-led invasions in 2001 and 2003. Four others, in Syria, Libya, Yemen and the northern, mostly Muslim half of Nigeria, have begun since 2011.
In every one of these wars, the victims are overwhelmingly Muslims killed by other Muslims. From time to time, non-Muslims in other countries are killed too, as in New York in 2001, in London in 2007, in Bombay in 2008 and last week in Paris, and these killings do have a strategic purpose, but it's not to "terrify non-Muslims into submission". Quite the contrary.
The great Muslim civil war is about the political, social and cultural modernisation of the Muslim world. Should it continue down much the same track that other major global cultures have followed, or should those changes be stopped and indeed reversed? The Islamists take the latter position.
Some aspects of modernisation are attractive to many Muslims, so stopping the changes would require a lot of violence, including the overthrow of most existing governments in Muslim countries. But that is the task the Islamists in general, and the jihadi activists in particular, have undertaken.
As they are minorities in their own countries, the Islamists' hardest job is to mobilise popular support for their struggle. The best way to do this is convince Muslims that modernisation - democracy, equality, the whole cultural package - is part of a Western plot to undermine Islam.
This will be a more credible claim if Western countries are actually attacking Muslim countries, so one of the main jihadi strategies is to carry out terrorist atrocities that will trigger Western military attacks on Muslim countries. That was the real goal of 9/11, and it was spectacularly successful: it tricked the United States into invading not one but two Muslim countries.
But smaller terrorist attacks that lead to the mistreatment of the Muslim minorities in non-Muslim countries also serve the cause. They can create a backlash that victimises the local Muslim minorities, thus generating yet more "proof" that there is a war against Islam.
There will be more attacks like the ones in Paris, because lost young men seeking a cause abound in every community, including the Muslim communities of the West.
We can't arrest them all, so we will go on having to live with a certain amount of terrorism and trying not to over-react - as we have been doing for many decades.
-Gwynne Dyer is an independent journalist whose articles are published in 45 countries