He is also stressing the leading role of Kurdish peshmerga (armed forces) on the ground, to which Britain, France, Germany and others have promised to supply weapons and equipment. Cameron does not seem to have grasped that the Kurds' very limited objective is the securing of their own territory in the northeast, not the wider pacification of Iraq's Sunni Muslim belt.
2. Could the campaign be extended into Syria? Would President Bashar al-Assad's co-operation be necessary?
Cameron (and US President Barack Obama) have left unanswered the key question of whether a stepped-up military campaign would pursue Isis beyond Iraq, into its strongholds in Raqqa and elsewhere in northeast Syria. Cameron last week described the Damascus Government of Assad as "illegitimate", implying that Britain and the US could act in Syria with impunity.
But this position is legally questionable, given that Assad won recent (admittedly highly manipulated) elections and the divided rebel factions do not constitute an alternative government. Russia, Assad's ally, would be likely to veto any attempt to gain United Nations authority for air strikes. And Assad can deploy sophisticated Russian-made air defence systems and fighter planes.
3. What about putting troops on the ground?
Pentagon analysts are said to believe Isis will be permanently suppressed only by sustained action by ground troops, either Western or local or a mixture of both, whose task would be to physically wrest control of those areas currently occupied by the Isis "caliphate".
Past experience in Afghanistan (after 2001), Iraq (after 2003) and Libya (after 2011) certainly suggests that air power alone, even if unchallenged, cannot achieve a clear and lasting victory.
But there is zero appetite in the US or Britain, so soon after the end of the deeply scarring eight-year occupation of Iraq, for a resumed large-scale ground troop deployment in the Middle East.
Even if it were thought desirable, capacity would be lacking, given Nato's still incomplete withdrawal from Afghanistan and the new demands posed by the "rapid reaction force" envisaged for Eastern Europe in response to Russia's military intervention in Ukraine.
4. Is there an alternative to large-scale action?
A middle path might be pursued involving the temporary hit-and-run insertion of British and US special forces, working with the peshmerga forces and a rehabilitated Iraqi Army, and backed by fighter/bomber and drone strikes, whose aim would be to disrupt and demoralise the Isis command structure. But such joint action, which would be problematic in the extreme, would be unlikely to have a lasting or definitive impact.
5. Enhanced regional co-operation became the key phrase of last week. What does it mean and how could it defeat Isis?
Much attention is now focusing on alliance-building across and around the region, including with countries previously ostracised by the West, with a view to isolating and squeezing Isis out of existence.
The most remarkable and potentially significant of these developments is the thaw in US-Iran relations. Recognising the common threat posed by the Sunni extremists of Isis, Iran, which is overwhelmingly Shia Muslim, has made no objection to the American air raids in Iraq. It also joined with Washington in forcing the resignation of Iraq's Shia Prime Minister, Nouri al-Maliki, in favour of a less divisive figure.
Iran has meanwhile initiated talks with its great rival and sparring partner, Saudi Arabia, on security issues. For its part, the US appears to be pulling out all the stops to achieve a final compromise agreement with Iran on its suspect nuclear programme by the November deadline. A nuclear deal could clear the way for a new era of bilateral engagement and co-operation on Iraq and on Syria, where Iran currently backs Assad, and an end to Israel's oft-repeated, destabilising threat to attack Iran.
6. What about the wider world?
Despite the confrontation with Russia over Crimea and eastern Ukraine, the Western powers have a shared interest with Moscow in combating Islamist extremism. That reality was underlined last week by a video in which Isis fighters mocked President Vladimir Putin and vowed to "liberate" Chechnya and all of the predominantly Muslim Russian Caucasus.
A similar coincidence of strategic interest arises in respect of Gulf Arab leaders, who are increasingly alarmed at the threat to their domestic hegemony by the radicals' iconoclastic ideology, and with Egypt, the traditional leader of the Arab world. Having overthrown the Muslim Brotherhood Administration that replaced Hosni Mubarak's regime, the military-dominated Government of former general Abdel-fattah al-Sisi in Cairo appears keen to take a lead in curbing regional extremism. Recent unconfirmed reports suggested it assisted a long-range bombing raid on hardline Libyan Islamist factions by aircraft from the United Arab Emirates (UAE).
Not coincidentally perhaps, the UAE, a close US ally which attended the Nato summit as an observer, called last week for a "unified effort" to root out the "global scourge of terrorism" and radical militancy in Iraq, Syria, Yemen, Somalia and Afghanistan promoted by Isis and al-Qaeda.
The UAE call echoed efforts by congressional Republicans to authorise sweeping military action against not only Isis but also the al-Qaeda-linked al-Nusra Front in Syria, al-Shabaab in Somalia, Boko Haram in Nigeria, and any other organisation sharing "a common violent extremist ideology with such groups, regional affiliates, or emerging terrorist groups".
7. What could such measures mean for the future of the region?
Analysts suggest these - and other efforts to more deeply engage and co-ordinate with regional powers such as Turkey and moderate pro-Western states such as Jordan - could ultimately produce a "grand bargain" creating a new order in the Middle East underwritten by the US, Russia, Iran and the Sunni monarchies of the Gulf. Its primary raison d'etre would be the crushing of Islamist extremism wherever it is found and bridging the Sunni-Shia schism.
On the other hand, such a dramatic reformation could resurrect George W. Bush's discredited "global war on terror" and simply escalate violent confrontation with radical Islam. Another key stumbling block remains the Assad regime. Cameron and Obama say they will not countenance any kind of deal with the Syrian leader, whom they accuse of war crimes.
But a growing number of military and diplomatic commentators believe that an accommodation allowing Assad to remain in power in return for his help, distasteful though it would be for many, is unavoidable if the relatively more dangerous threat posed to Western interests by Isis is to be defeated.
8. Can Isis be defeated from the inside?
Isis has been described as the wealthiest terrorist group in the world, with a monthly income of about $9.6 million. Its funds are said to come from wealthy Sunni Arab donors who share its fundamentalist ideology, from taxes and protection money levied in the territories that it controls, from northern Iraq's captured government banks, and from the sale of oil through unscrupulous middlemen.
Millions of dollars have also been obtained from the ransoming of hostages. In Raqqa and elsewhere, Isis has established entrenched governance structures funded by its large income. To bring Isis to heel, it is argued, ways must be found, principally by Arab governments, of cutting off or sequestrating this flow of money and thus reducing its economic and political influence in Iraq and Syria.
9. Are there lessons from Iraq's recent history?
As happened during Iraq's so-called "Sunni awakening" in 2007, the key may lie with the Sunni Arab tribes whose alienation by Maliki's Baghdad Government led them to acquiesce in last northern spring's Isis insurrection. Now that Maliki has gone and Sunni interests are likely to be better represented, it may be that the tribal leaders (who are said to deplore the extremists' excesses and do not share their grandiose caliphate ambitions) can be encouraged to turn on Isis, just as they turned on al-Qaeda in 2007 with the help of US General David Petraeus.
A "local" solution of this kind, which uprooted Isis governance, administration and money-making schemes as well as its military bases, would be more likely to endure than one imposed from outside through Western military intervention.
10. What can be done to rescue Western hostages held by Isis?
Cameron read the riot act to fellow leaders at the Nato summit, insisting that paying ransoms only encouraged hostage-taking and increased the security threat to countries such as Britain. The objects of his wrath were said to include the French and Italian governments, which are believed to have acquiesced in the buying off of kidnappers with large amounts of cash.
Cameron's unyielding stance, though principled, coupled with the apparent absence of negotiations or a negotiating channel, may make it more likely that Isis will carry out its threat to murder the British hostage and aid worker David Haines following its beheadings of two American journalists. But this does not necessarily follow; Isis does not appear to want money. Rather, its videos demand an end to US bombing. If Britain joins in those attacks, the vulnerability of British hostages could increase.
A special forces rescue of Western hostages was attempted by the US a few months ago, but it failed to locate them. Unless better intelligence is obtained on the ground, any repeat rescue attempt looks unlikely to succeed. Overseen personally by Cameron, every arm and branch of the British security establishment is currently focused on saving Haines.
- Observer