There are arguments in favour of expanding the Canadian military mission from Iraq into neighbouring Syria, and on Tuesday the Prime Minister stood in the House and made them.

The so-called Islamic State controls territory in Iraq, and Canada's air strikes are targeting it there. But much of the ISIS quasi-state, including its nominal capital city of Raqqa, is across the border in Syria. Stephen Harper spoke of "denying safe haven" to ISIS by sending Canadian warplanes, which are now restricted to Iraqi airspace, into Syria. The Prime Minister also stressed, as he always does, that ISIS is a terrorist organization that regularly threatens to attack Westerners, including Canada and Canadians. Fighting ISIS over there, goes the argument, is the best way of preventing terrorism over here. All of this has a certain logic to it.

But the logic behind the Harper government's Syrian plan has gaps, inconsistencies and blind spots. And that's why the plan for limited Canadian military action and assistance in Iraq makes sense – while a plan to expand the mission to Syria does not.

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There are four primary reasons for our opposition to mission creep into Syria.

In Syria, who would Canada be fighting for? In Iraq, the question is easy to answer. The bulk of the Canadian mission is about supporting Iraq's semi-autonomous Kurdish region, which has its own long-standing, motivated military force, the peshmerga. In Northern Iraq, Canada has a real partner on the ground – it has a government, a functioning state and a high level of public support. It is defending its territory against ISIS.

Iraq as a whole may be a dysfunctional mess, but in Iraqi Kurdistan, Canada is not trying to conjure up a state; it is assisting one that is solid and very real. The contrast with Syria could not be more stark. Canada has no significant ally on the ground. ISIS is the opponent, but ISIS's main adversary, the government of President Bashar al-Assad, is also our adversary.

In Northern Iraq, Canadian advisers and aircraft are working with our coalition partners and our allies on the ground to push ISIS back. Who are our allies in Syria? What's the endgame?

International law: Syria is a failed state, with millions of refugees and most of its territory contested between a brutal dictatorship and an Islamic death cult. But it is worth remembering that, with the exception of the United States, our NATO allies fighting ISIS in Iraq have not authorized their aircraft to bomb Syria. The mission in Iraq exists because the recognized government of the country requested it; it is perfectly legal under international law. No such situation exists in Syria. This is not a United Nations mission, or even a NATO mandate. National sovereignty is not sacrosanct, especially in a case like Syria's. But it is not nothing.

Acknowledge our limits: Given the West's overwhelming military superiority compared with ISIS – we have the most powerful air forces in history; they don't even have planes – it becomes easy to assume that success is ours for the taking, and that all that's needed is a bit of willpower. Pursuing ISIS across the border into Syria (and beyond) starts to look like a moral imperative. If we try, we will surely win.

The past decade and a half of Western involvement in the Middle East should be cause for a hefty helping of that most Canadian of virtues: modesty. Good intentions backed by massive military force do not always yield success.

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The American mission in Iraq ended in total failure; 10 years and hundreds of billions of dollars left behind a state of semi-governed chaos that opened the door to ISIS. In Afghanistan, it would not be fair to call the mission that Canada was a part of a failure – and it would be just as inaccurate to call it a success. The bombing campaign in Libya achieved its objective of removing dictator Moammar Gadhafi, but the country is now largely ungovernable and a haven for terrorists. That, too, is not a success story.

Military intervention is not always doomed to fail. Canadian CF-18s can accomplish real and important things, but we have to acknowledge that even the smartest bomb is a blunt instrument. The limited mission in Northern Iraq is a rare case where a military response is called for and has a decent chance of achieving its objectives. Syria looks nothing like that.

The thin link to terrorism in Canada: Mr. Harper has repeatedly tried to closely tie ISIS to the terrorist threat in Canada. The truth is that the same nihilistic ideology may motivate both. But so far, the actual connections are thin to non-existent.

For example, Chiheb Esseghaier and Raed Jaser, recently convicted of plotting to blow up a train and commit other acts of terrorism in Canada, hatched their schemes before ISIS even existed. Parliament Hill shooter Michael Zehaf-Bibeau was not sent here by a foreign power. Unfortunately, long after ISIS has collapsed, there will still be small numbers of frustrated men throughout the world, susceptible to catching a virus that makes them long for purification through violence.