So John Kerry's frantic drive to settle the nearly seven-decade-long clash between the Israelis and Palestinians has come to nothing. Everyone who cares about Israeli security and the suffering of the Palestinians wished him well in his efforts, just as everyone knowledgeable about the conflict understood that those efforts would fail.

And yet surprisingly few on either side have drawn the proper conclusion — which is that, for now at least, there simply is no solution to the conflict.

It's easy enough to see why we're so reluctant to accept this harsh and ugly truth.

As inveterate optimists, Americans have a hard time accepting tragedy. We like to believe that any problem can be fixed with enough gumption and good intentions. We're even more inclined to believe it in the case of Israel and the Palestinians because our steadfast support of Israel over the decades has deeply implicated us in the intricate web of injustices that plague the region.

But our desire to find a way out of the impasse doesn't mean that one exists. Not every puzzle has a solution. Not every conflict can be resolved.

The Israeli-Palestinian conflict has had an intractable quality from the beginning: Two peoples with competing, exclusivist claims to one small parcel of land. That's one important reason why every attempt to broker a lasting peace agreement over the past 66 years has fallen to pieces in the end — because the end is unreachable.

For one thing, each group insists on making Jerusalem its capital city and claims to be unwilling to accept anything short of that. Yes, it's at least possible that this tension could be finessed by some kind of dual-sovereignty agreement. But there's no finessing this: The Israeli government demands that the Palestinians recognize Israel as the historic homeland of the Jewish people (meaning it will not be permitted to become a binational state), while the Palestinians insist on a "right of return" to land within Israeli territory, which would instantly transform it into a binational state — and one in which Jews make up a minority of the population.

That, my friends, is the very definition of an intractable conflict.

The only way out of such a conflict is for the incentives, priorities, and preferences of the parties to change, making accommodation more likely. But the unfortunate fact is that in recent years the parties have, if anything, been moving even further apart.

The Israeli side feels it got badly burned by the breakdown of negotiations at the Taba Summit in January 2001, and then by the Second Intifada that began soon afterward, unleashing deadly waves of suicide bombings throughout the country. Those bombings stopped not because of negotiations, but because the border fence constructed by the Israeli government greatly increased the difficulty of launching terrorist attacks inside of Israel from the occupied territories. The lesson Israel learned from this experience is that security can only be won through decisive unilateral action.

Unilateral action taught the Israelis a different and even bleaker lesson in Gaza. Dismantle settlements, pull back from occupation, and allow Palestinians to decide their own fate — and they will immediately elect an organization (Hamas) dedicated to annihilating the Jewish state. Israel now lives with a hostile power on its southern border that periodically rains down missiles on Israeli towns.

Add to that the anti-Israel Hezbollah faction (and Iranian proxy) in Lebanon to the north; the Syrian civil war, which pits the staunchly antagonistic government of Bashar al-Assad against even more radical Islamists, to the northeast; an unstable and intermittently hostile Egypt to the southwest; and of course the persistent threat of a nuclear Iran a thousand miles to the east — and one can begin to understand why Israel feels more surrounded and vulnerable than ever. The last thing it will do in such circumstances is undertake another experiment in withdrawal from the modest buffer zone of the West Bank on its militarily vulnerable eastern flank.

Attitudes on the Palestinian side have grown similarly intransigent. After having their hopes raised and dashed so many times, after decades of military occupation and ever-expanding settlement building on land that will ostensibly be part of any independent state, it's no wonder that popular support for a two-state solution is waning among the Palestinian people.

Then there's the fact that recent events seem to have shown the Palestinians that time is on their side. As the years have gone by without a peace deal and the population of the West Bank has increased, the world's outrage at the Israeli occupation and disenfranchisement of the Palestinians has only grown. In the past few years, this indignation has inspired the U.N. and other international bodies to begin recognizing, over strenuous Israeli (and American) objections, occupied Palestine as an independent state. This is an effort that Palestinian Authority President Mahmoud Abbas has now begun to pursue more actively than ever.

Not that such recognition will give many additional rights to the people living in the occupied West Bank. But that, in fact, is the point: To demonstrate to worldwide public opinion that the Palestinians have been consigned by the Israelis to live out their days in impoverished Bantustans where they are denied rudimentary rights to self-determination. The Palestinians hope that a growing chorus of global condemnation will eventually drive Israel either to pull back from the West Bank, thereby allowing the establishment of a fully independent Palestinian state, or to grant full political rights within Israel to the Palestinian people — a move that would turn Israel into a binational state.

Neither has any chance of happening.

Which means that the Israeli-Palestinian conflict has reached a condition that the ancient Greek philosophers would have described with the term "aporia" — meaning "to be at a loss" or "impassable." There is no peace process. No way forward. This might change down the road. But for now it is our lamentable but unsurpassable reality.