Only a dwindling band of people now believe this, the official pretext for the twin-set of wars Israel is fighting on its northern and southern fronts. If it had been true, there was an obvious solution . . . swapping prisoners. Israel is currently holding 8,200 Palestinian fighters, as well as at least three Lebanese fighters who were seized in Lebanon itself during the long 18 years when Israel was occupying its entire southern region.

Both Hamas and Hizballah have said the Israeli soldiers will head home as soon as there is a fair swap.

This is such a wacky, left-wing idea that it was pursued by Ariel Sharon just two years ago, when he gave Hizballah 429 prisoners in exchange for an Israeli businessman and three corpses. The opponents of a prisoner-swap warn gravely that it would fire the starting gun for an open season on Israeli soldiers, with dozens being snatched. But previous prisoner-swaps have not been followed by a spate of kidnappings; indeed, they have led to a period of calm.

So what is the real reason for the bombing of Lebanon? The most obvious is a desire to permanently remove the Hizballah militia from its place nestling on Israel's borders, where it has amassed 13,000 rockets. This was a grievance just waiting for a casus belli.

But is this aim of disarming Hizballah reasonable? The Islamic fundamentalist group is indeed revolting. In its early days Hizballah imposed a savage code of "Islamic behaviour" on the Muslims of south Lebanon, imprisoning women in their homes and murdering gays.

Since then, it has endorsed the suicide-murder of Israeli children as they sit in pizzerias, and even in 1994 bombed a synagogue in Buenos Aires, Argentina, killing 85 civilians totally unconnected to this conflict.

Yet if being ideologically repugnant, snatching fighters and owning rockets were a reason for a war, then Lebanon would have an even greater right to invade Israel.

After all, it holds their snatched fighters, owns far more than 13,000 rockets (some nuclear) and has a history of invading their territory and committing mass slaughter on dishonest pretexts.

One Israeli general demanded this week, "How long can we live with a knife to our throats?" But the far bigger knife belongs to Israel. Is it really saying the right to self-defence and a buffer-zone of security belongs to it alone?

Hizballah is at its core a selfdefence organisation, however ugly, and its recent operations have been limited largely to this function. It was formed to expel Israeli troops who mounted an unprovoked invasion of Lebanon in 1982 in order to crush the Palestinian groups operating there. By the time the Israeli forces finally left in 2000, they had killed an estimated 17,000 Lebanese citizens and Palestinian refugees.

Since the end of the occupation, Hizballah had only fired across the border once, until Israel began its aerial bombardment last week. This was when the Israelis blew up Sheikh Ahmed Yassin, the spiritual leader of Hamas, outraging the world. (It is also worth remembering that half a million people in Lebanon get their drinking water from tanks provided by Hizballah. At least 100,000 people depend on the hospitals and health clinics they run. ) There was always a way for Israel to put Hizballah's rockets beyond use without a single innocent Lebanese child being bombed, and without anyone being deprived of safe drinking water. Hasan Nasrallah, the head of Hizballah, has been asked repeatedly if he would accept a two-state solution. He always replies that he will never sabotage "an internal Palestinian matter", and that if Israeli and Palestinian leaders negotiate a settlement both sides can accept, Hizballah's missiles will never be used across the border again. Hizballah will be reduced to a local Lebanese problem. Revolting though he is, Nasrallah has always kept his word on these matters: he even explained to Sharon back in 2004 that at some point in the future he would kidnap more soldiers in a bid to reclaim the remaining fighters Sharon clung onto.

But a real negotiated two-state solution is precisely what Ehud Olmert does not want. Here we get to the central reason why Olmert has chosen a violent nonsolution to Hizballah over a peaceful authentic solution. Uri Avnery, the veteran Israeli peace campaigner, explains, "[In Israel] we have an ongoing, partly hidden debate about what's really the main thing . . . achieve peace or create a bigger Israel? The people in power today still believe that a greater Israel is more important. They got away from the idea that all of the country of Palestine should become Israel, but they would still like to annex significant parts of the West Bank. That's their priority. As long as this is a priority. . . they think peace is a bad thing." Peace would create momentum towards negotiations with the Palestinians' democratically elected leaders . . . and that cannot be allowed to happen.

The Israeli newspaper Ha'aretz has just published a long, authoritative study of Olmert's motives, drawing on sources very close to the prime minister. It reveals that "Olmert has another consideration, of which he is not speaking [in public]. He wants to set a precedent for the convergence plan in the West Bank, to show that Israel won't accept terror from beyond the fence after it withdraws."

He knows the deal he plans to impose on the West Bank will be unacceptable to Palestinians. Not just to Islamic Jihad, but the vast majority. He has been proposing to seize strategically valuable chunks of the West Bank by annexing them to Israel since as long ago as 1978, after all. So he is trying pre-emptively to terrify them now so they will not dare fight back.

So here it is, the kernel of emotional truth behind this war. Its clearest expression can be found in the speeches of Ze'ev Jabotinsky, figurehead for the right wing of Zionism, the man Olmert was raised to revere. Talking of the Arabs in 1923, Jabotinsky insisted, "A living people makes enormous concessions. . . only when there is no hope left."

That is the true purpose of the wars in Gaza and Lebanon . . .

to ensure, at last, there is no hope left for the Arabs. But the Palestinians and Lebanese will not slump away. They will become gripped with a nihilistic hate, and long after Ehud Olmert is nothing more than a skeleton and a statue, the hate will still burn. Does he imagine this is good for the children of Israel?