THE image of a dead Syrian boy washed up on a Turkish beach has inspired a wave of Western soul-searching, with much talk about how “the world” failed 3-year-old Aylan Kurdi, who drowned along with his mother and brother while trying to escape their country’s civil war.

This reaction is understandable, but its policy implications are unclear. And since policy questions are where outrage ultimately cashes out, it makes sense to try to think through what it really means to say that we . America, the West, the world . failed the Kurdi family, and helped consign them to their fate.

One thing it might mean is that the world’s powers, the United States chief among them, had a responsibility to prevent the Syrian war from developing, and a responsibility to protect its victims once it did.

To a point, this seems plausible. The U.S. has very consciously accepted stewardship of global stability, and in Syria the Pax Americana has developed an ugly crack. And since our various Syrian forays . clandestine aid to rebels, airstrikes threatened and then held back, explicit aid to rebels . look like failures at the moment, we’re partially implicated in the continuing catastrophe.

But this argument is usually linked to demands for military intervention, and there it becomes less persuasive. It was precisely the “responsibility to protect” theory that justified our intervention in Libya’s civil war, and today Libyan refugees, too, are dying in the Mediterranean, and their country is in its own kind of bloody chaos.

This outcome is characteristic of many humanitarian interventions, unfortunately: They save some lives and extinguish others, they deal with one group of thugs only to empower worse successors. And the case that a humanitarian intervention in Syria would actually succeed has never been particularly strong . a cold reality unchanged by the image of a tiny body on a beach.

Of course military intervention is not the only way that the Kurdis might have been protected. They could also have been granted the opportunity so many Syrians are desperately seeking, to be airlifted to another country, and welcomed as refugees.

But then the question becomes, which country has that responsibility? Who should have taken them in?

One answer is that nations that are directly implicated in Syria’s agony have more responsibility to accept refugees than nations that are not. The strongest obligation would belong to those countries . the Gulf States and Iran, above all . who have fed arms and money into the Syrian conflict. A weaker-but-still-meaningful responsibility would attach to the United States, because we too have sent arms and because of the links between our Iraq intervention and the region’s current chaos. Other countries would have more attenuated obligations, or none at all.

But the reality is roughly the reverse. Countries like Qatar and Saudi Arabia are basically accepting no refugees. The U.S. is accepting relatively few. And the countries that have opened the door widest are places like Germany and Sweden, which are motivated by a different theory of moral obligation: A utilitarian universalism, which holds that the world’s wealthy nations have an obligation to accept refugees, period, regardless of whether their own governments bear any responsibility for the crisis that produced them.

This theory has the advantage of eliminating any messy haggling over who bears responsibility for what. When tragedy strikes, everybody above a certain level of G.D.P. just has to open the gates. (Or, perhaps, to have them open permanently.)

But it has the disadvantage of being completely unworkable over the long run, as Europe is beginning to discover. The utilitarian theory is blind to the realities of culture, the challenges of assimilation, the dangers and inevitability of backlash. It takes what is a deep, long-term issue for European society . one way or another, over the next century the continent will have to absorb large numbers of new arrivals, from Africa especially . and brings things to a crisis point right now. And then it tries to evade that crisis by treating dissent as illegitimate, which only works until it doesn’t: One day you have a pro-immigration “consensus,” and the next a party with fascist roots is leading Sweden’s polls.

So prudence has to temper idealism on these issues. There may be a moral obligation to accept refugees in wealthy countries, but there cannot be a moral obligation to accept refugees at a pace one’s own society cannot reasonably bear.

Which means that every country’s obligations may be different. It seems reasonable to believe that by accepting so very, very few refugees . only 1,500 so far . from a conflict our Middle Eastern misadventures worsened, the United States is failing in its obligations to the Syrian people.

But it’s also reasonable to worry that by accepting hundreds of thousands of refugees on a continent already struggling with assimilation, and making itself a magnet for still more, Germany is failing in its obligations to its own.