For weeks now, I have watched friends, family and fellow travelers on the left – and myself too – torment ourselves over this conundrum: Israel is right to defend itself against a murderous Hamas shelling our cities, yet Israel cannot defend itself without killing innocent Gazans, which is wrong.

Our Facebook feeds are filled chock-a-block by people who don’t see the dilemma. Some, certain that Israel is in the right, post snapshots of rockets in the sky over Tel Aviv, hidden exits of Hamas tunnels at the perimeters of kibbutzim, and pictures of missiles cached in the basement of Gaza elementary schools. Others, sure that Israel is in the wrong, upload photos of wreckage in Shijaiyah and corpses of kids covered in sheets.

The rest of us roll the awful images around in our minds, trying to make sense of them together. It is true, we tell ourselves, that Hamas started this war, and that no country would allow rockets to be fired on its citizens without returning fire. And it is true that Hamas spent $900 million of aid money to build a network of tunnels terminating in Israeli villages and towns because it hoped, some day, to kill Jewish civilians, the more the better. And it is true that Hamas has fought this war in a way calculated to cause Israel to kill more Palestinian civilians, not fewer. And yet, it is true too that hundreds of innocent Gazans are dead – kids, parents, grandparents – and that Israelis killed them. And it’s true that Israel’s coarse treatment of Gaza before the war destined many Gazans to lives without means and without hope before the first bomb fell. We scroll through these things in our mind and we cannot make them fit, like a ledger we cannot balance.

And that is because these things don’t balance. The expectation that they might is based on the false assumption that the morality of this war is a “zero-sum” affair, and that to the degree that we are right, they (Hamas, the Palestinians and their supporters) are wrong, and the reverse. In fact, something like the opposite is true. Israel is right to defend itself. But as we do so, the Palestinians grow more right, too: right that they deserve an end to the suffering we are causing them. Our being right does not negate, but rather abets, their being right. And, equally, our being right leads us to do things that are, in truth, wrong.

Here is why we find ourselves in this horrid position. As a philosopher named Thomas Nagel once observed, there is such a thing as “moral luck.” This, he wrote, is when “what someone does depends on factors beyond his control, yet we continue to treat him in that respect as an object of moral judgment.” The very notion of moral luck seems paradoxical, because we are used to thinking that we are only morally accountable for things that we control. But that is not quite true. Like well-meaning American whites who never questioned segregation, sometimes we end up culpable for choices we never made.

Hamas is a factory of moral bad luck. Its leaders aim to trap Israel in situations from which only bad can come, either dead Israelis or dead Palestinians or both. They began their barrage of rockets on Israel because they knew Israel would respond, killing innocent Gazans, including kids, along the way. They unleashed their evil because they knew that Israel would, in response, unleash evil of its own.

What are we to make of this? For one thing, we can understand that both things are true. It is true, as Ari Shavit recently wrote, that “in this sad war story, Israel is in the right,” and it is also true that in this sad war, kids are dying at Israel’s hand. It is true that Israel is right and Israel is wrong. And it is true the right and the wrong are irreducible, and do not cancel each other out.

Also, we can conclude that there is no place for righteousness in the conflict. When we fight this war, as I think we have to, we must do so with grim knowledge that every violence done to civilians, and their homes and schools, is a tragedy in which we have a hand. Equally, those who piously condemn Israel should know that, were they in our position, they could scarcely act differently than we do.

Finally, perhaps, we can understand why this war is so sad, and so confusing, to so many of us, and how we can be so certain that we must fight and, at the same time, shattered by the results of the fighting.

I realize that there is little comfort in any of this. But, then, comfort belongs to people with better luck than ours.