President Bush plunged into tangled Middle East problems this week as both Egyptian President Hosni Mubarak and Israeli Prime Minister Yitzhak Shamir trekked to Washington on separate visits to discuss what to do with the Palestinian question.

Unfortunately, while all parties are making optimistic noises, any actual breakthroughs appear a long way off.Mubarak edged closer to agreeing with the Israeli view that the 16-month Palestinian uprising and civil unrest in the occupied West Bank and Gaza Strip must be reduced before peace negotiations can begin.

While that may soothe Israel's feelings, it's hard to see what Egypt can contribute toward easing of tensions in the occupied territories where 1.7 million Palestinians have been under Israeli rule for 21 years.

Mubarak himself admits that the unrest will not subside until Palestinians have some reasonable hope for an independent homeland. One of the best ways to encourage that hope is for a dialogue to begin.

Dialogue first or peace first? Trying to resolve which must prevail is like finding the answer to the old teaser: Which came first, the chicken or the egg?

Shamir has been under pressure from the Bush administration to find peace openings and has come to Washington with a pledge to work with the United States in searching for solutions in the Middle East. In his pocket is a plan for Palestinian elections in the occupied territories.

This sounds promising, but the plan depends on finding Palestinian leaders not connected with the Palestinian Liberation Organization. That approach is doomed to defeat from the start. The PLO is accepted by most Palestinians as their voice and already has begun a sort of government-in-exile.

Even though Israel endorses the idea of Arab self-rule in the occupied territories, as long as it refuses to sit down and talk with the PLO, the Palestinian deadlock will persist.

The refusal to deal with the PLO is not simple hard-headedness on the part of Israel. Real questions of military security and even survival are at stake. But at this point, Israel is the only party able to cause a breakthrough by agreeing to negotiate with the PLO.