ISIS / IS / ISIL / The Islamic State

It's pretty well accepted by serious commentators that bombing by 'great powers' almost always leads to increased recruitment for these sorts of groups. So I guess recruitment would be down? Attacks like Paris are specifically designed to encourage these kinds of kneejerk bombing campaigns which kill civilians and feed the narrative being peddled.

I wouldn't recommend not intervening, and I can't say I've heard any serious commentators suggest not intervening. The aim of those opposed to nonsensical air campaigns is simply to have a proper UN mandate for intervention, to restore some semblance of international law in these cases.

The idea 'we bomb and a ground-based guerrilla outfit whom we support will sort out the aftermath' simply wouldn't work. That would only mean that civil war would continue to simmer under the surface even if it could ever end (there is no guerrilla campaign in the world which isn't bitterly opposed by some).

A negotiated peace settlement which brings lasting peace and stability and would be accepted by all could only be brokered by the UN. Needless to say, certain Western powers have no interest in bringing stability to the region, as this would mean an increased oil price.

However that may be (and I'm obviously not naïve about the UN's capabilities), it is very important to move away from the Bush Jr. way of starting illegal wars just to remove a formerly compliant American puppet governor who knew too much about the Bushes and their cronies--oligarchy at its worst.

Let's try the other side of the coin.

Let's say the great powers, including Russia, all just backed off and left Daesh alone. What would you expect to happen?

Depends what you mean by back off. Leave them alone totally or not carry out direct attacks? If you leave them alone totally then either they will succeed and establish a power block, or local groups will fight them for power and absorb them and their supporters into their ranks.

I've heard some interesting arguments and explanations recently for the rise of Islamic extremism. One that has really struck me is that it is rooted in the under representation of the Islamic states on the world stage after the fall of the Ottoman Empire. Tied to that is also the lack of stability caused by the fall of the Ottoman Empire and the West's subsequent medeling.

Linking this to your question... The logic is that you need to stabilise these countries and empower them. This can only be done by the local/regional groups. That then means that a proxy war makes the mors sense than direct action. Ultimately though in this argument you need to allow stronger Islamic states to exist and allow them a voice on the world stage.

Let's say the great powers, including Russia, all just backed off and left Daesh alone. What would you expect to happen?

ISIS would start to organise itself better, as it would be able to move people, materials, fuel and equipment more easily without fear of airstrikes. It would develop an infrastructure, an economy, and trade with it's neighbours would increase. Places like Saudi Arabia would begin to openly recognise ISIS as a state. I personally don't think we would be any safer.

Let's also say the west backed off and Russia didn't. What would you expect to happen then?

As above, but the Russian economy is fucked, and when they lose the war Putin is replaced by someone more isolationist.

Western agression definitely aids the recruitment of western Muslims to ISIS, but they would continue to grow without this.