Leading article: The Obama doctrine comes into focus

This US President is a pragmatist - he will act when he believes it is in the national interest to do so

For an American president and US public opinion, foreign interventions are often a case of damned if you do, damned if you don't. The current war in Libya is a classic example, and in his televised speech on Monday night aimed primarily at a domestic audience, Barack Obama made a well-reasoned attempt to square the circle, and explain exactly what the US is doing in Libya. In the process, he set out what may be described as the "Obama doctrine", building on the themes he set out in Oslo, when he accepted the Nobel Peace Prize in December 2009.

Americans are extremely lukewarm about the involvement in Libya. A vociferous minority criticises Mr Obama for not stepping up the war, to get rid of Colonel Gaddafi as soon as possible. A majority is above all fearful of a repeat of Iraq, but for the time being is willing to go along, provided American lives are not lost and US troops are not dragged into another ground war in a Muslim country.

It is equally certain however that had the US not become involved when the regime launched its bloody counterattack, this president would have been castigated for sitting on his hands as a massacre unfolded. And so Mr Obama presented the humanitarian argument as the main justification for intervention, and he had good news to report: the avoidance of a potential slaughter at Benghazi, and a rebel advance that brings nearer the undeclared goal of the war (and most people's profound wish), the removal of Gaddafi himself. But he left two crucial questions unanswered.

The Obama doctrine essentially draws a distinction between America's vital and non-vital interests. In the case of the former, the country will act unilaterally if required. Libya however does not fall into that category. Even though the President insisted that the US had a national interest in ensuring that a bloodbath in Libya did not derail the fragile progress towards democracy in Tunisia and Egypt, this war is one of choice, not necessity. In these cases, America should act not as the world's policeman, but as its "police chief", at the head of a multilateral coalition. Hence the handover to Nato, in which (lest anyone has forgotten) the US is the overwhelmingly dominant partner. For Washington to use its military might explicitly to topple Gaddafi would split the coalition, Mr Obama argued, just as had happened in Iraq.

So far, so clear. But what if the Libyan war drags on? For how long is the US prepared to sustain an involvement that, if the Iraq and Afghanistan precedents are any guide, will become steadily more unpopular? What if, despite Nato's aerial shield, the rebels are thrown back by regime forces? And what if civilians loyal to Gaddafi fight back against the rebels – would not the alliance be obliged to let a civil war take its course?

The second point on which Mr Obama was largely silent was the precedent set by the Libyan operation: whether the US would now intervene elsewhere if a similar crisis erupted. A Libyan massacre would have "stained the conscience of the world," the President declared. But what of the stain of Robert Mugabe's brutality in Zimbabwe – or more pertinently, what if the Assad regime in Syria, the mullahs in Iran, or that vital US ally, the Saudi monarchy, "do a Gaddafi" against their own people, amid the turmoil sweeping the Muslim world?

This President is a pragmatist and he has left his options open. America could not use its military everywhere, he said, "but that cannot be an argument for never acting on behalf of what's right." In short, this President will act when he believes it is in the national interest to do so. That has been realpolitik throughout the ages. It is also the Obama doctrine.