It's worth recalling the brief history of Gulf War III.

Cheated of an attack on Syria late last year by the British Parliament's refusal to go along with it, the United States backed away from an attempt to destabilise Iran's ally President Bashar al-Assad. Australia, which had been talking it up, of course did too. Then in June, Islamic State (IS), which the Obama administration had tolerated, if not created, in Syria, turned on vulnerable areas in north-western Iraq. With a new government in transition, Baghdad's authority was more fragile than ever. But not so fragile, it seems, that President Haider al-Abadi was in any hurry to throw open Iraq's borders again to Western military.

After a Western emergency mission in the summer to help evacuees, foreign planes kept flying into Iraq, and the mission crept from humanitarian to interventionist. Gruesome video images of IS militants executing hostages and displaying severed heads were trailed like bait to lure the US and its coalition partners back onto the hook.

For nearly four months, we heard repeatedly that Australia had been invited to send aircraft and special forces to Iraq, but details about it have been scarce. An invitation from the US to join in bombing raids is not the same as an invitation from Iraq to put troops – trainers, special forces, or any others – on the ground. In late October, Foreign Minister Julie Bishop went to Baghdad determined to secure a Status of Forces Agreement (SOFA), and the Defence website then announced that 'legal protections' had been agreed, that would spare Australians being tried for crimes by Iraqi courts. Under the previous President, the SOFA was a sticking point that led to coalition troops leaving at the end of 2011.

Administrative arrangements, the Defence website says, are 'being finalised'. Meanwhile our Special Operations Task Group is still not in Iraq. It is 'deployed in the Middle East Region'. If that means it is at Al Minhad Air Base, in the United Arab Emirates, what it is doing there is not revealed. It is 'prepared to act', says the website, but that doesn't mean it is in action.

If and when the SOFA results in a formal invitation from Baghdad, the Task Group will presumably begin its special operations. After a decade, the Iraq armed forces must by now have had enough Western advice and training. But if IS continues expanding, we will almost certainly be into mission creep, hearing that we need more equipment, regular troops on the ground, more air support. We could be on the way to the hundred-year war that former general Peter Leahy anticipates.

So what, in the age of global communication, is holding up Haider's letter of invitation? Without it, Australia's armed presence will be illegal and could amount to a crime of aggression. This may be why we have heard so much from the Abbott Government about the 'global threat' posed by IS, as if our forces are defending Australia. IS, the Prime Minister told the UN in September, declares 'war on the world'. Yet clearly IS, with some 20 000 men, no air force, and no navy is not about to invade Australia. Mr Abbott won't give us all the facts, so Australians are left to choose between at least three possibilities.

First, it might be that Baghdad's Shiite regime doesn't want Western observers interfering in its dealings with its Sunni and other minorities. According to Human Rights Watch, pro-government forces killed 34 people in an attack on a mosque in late August. President Haider's government may not want witnesses to such events, over and above the 1600 American troops currently advising and training the Iraqi army and intelligence.

A second possibility is that the Iraqis, after a decade of Western military presence, sense American war weariness, and don't rely on Obama's resolve. In spite of the fire-breathing John McCain, the latest venture into Iraq has been criticised in the New York Times, the Wall Street Journal, and even in Quadrant. Haider's government may find an ally that is never going away, like Shiite Iran, more reliable.

Third, if Haider doesn't formally invite Australia to put any forces on the ground in Iraq, we will either have to introduce them by some legal sleight of hand, or confine ourselves to bombing missions (which Iraqis who are their victims must regard as terrorism and assassination). Either way, mission creep will be off.

Other countries offering troops presumably face the same situation. That could even mean Gulf War III is over sooner than we have been led to expect. Lives, money and resources would be saved, international law could be maintained, and IS hopes of dragging the West into a religious war would be thwarted, in favour of a season of peace and goodwill. Religious differences would be left to their sectarian adherents to sort out.

What would Australian taxpayers prefer? That we are left guessing about such important matters, with sketchy information, is further evidence of the need for Parliament to debate the deployment of Australian troops abroad. Parliamentarians have time, in the next session, to ask the Government to make whatever invitation it has public, and if it has none, to demand the Australian contingent be brought home by Christmas.

Dr Alison Broinowski, formerly an Australian diplomat, is a member of Australians for War Powers Reform.