Israel is playing a tough military-diplomatic game with the noose it has thrown around the 6,000 Palestinians trapped in west Beirut.
The reason is simple. The Israeli government has never lost sight of its second major purpose, beyond ''peace for Galilee'' in its invasion of Lebanon: to make impregnable the hold it has slowly been establishing on the West Bank and Gaza.
The government of Prime Minister Menachem Begin is convinced that if it can smash the Palestine Liberation Organization (PLO) as a fighting force, it will simultaneously:
1. Establish the secure northern frontier until now lacking on the border between Galilee and Lebanon.
2. Destroy the influence of the PLO among the 1.25 million Palestinians living under Israeli occupation, and thereby cow them into accepting the absorption of the West Bank and Gaza into the state of Israel.
The temptation to achieve these two aims with a single blow is great - especially now that the Israelis, in conjunction with their hard-line Lebanese Christian Phalangist allies, have surrounded west Beirut.
This is the fifth Arab-Israeli war. And it is the first waged not with neighboring governments but head on with the Palestinians who are the direct challengers to Israel's right to the Holy Land.
Each of the preceding four wars, which ended in Israeli military victory, can now be seen to have had a specific aim or effect.
The first (1948-49) gave the Israelis their initial foothold in Palestine, despite efforts of Arab governments to stop them. Since the end of the 19th century, the Zionist movement had seen an Israeli state in Palestine as the only way to ensure survival of the Jewish people in a predominantly hostile world.
The second (1956) beat back attempts by the Arabs to question Israel's legitimacy and permanence through the use of Arab government-sponsored guerrillas (fedayeen) to render Israel's borders insecure.
The third (1967) - and Israel's most smashing military triumph - brought all of Palestine into Israeli hands and proved Israel's determination to maintain itself permanently as a Jewish state in the Middle East.
The fourth (1973) - launched by Egypt and Syria - saw Israel eventually come out on top, but only after things had come close to a draw. This established for the first time in more than a quarter of a century a climate psychologically opening the door to negotiation and compromise between Arabs and Israelis. But of the Arabs only Egyptian President Sadat was willing to take advantage of it.
Initially, negotiation - with United States participation - was between Egypt and an Israeli government of the Labor Party. But in the Israeli general election of 1977, Labor was ousted and the premiership passed to hard-liner Menachem Begin.
From the outset of his premiership - indeed throughout his political life - Mr. Begin has had one consistent aim: to extend Israel's frontiers to include Judea, Samaria - i.e. the West Bank - and Gaza. He and his supporters see these as included in the Old Testament ''Land of Israel'' (Eretz Israel) and therefore Israel's by right of the Scriptures. That precludes any territorial compromise.
From 1977 until April of this year, Mr. Begin used the negotiating process to establish for Israel (as he saw it) the most favorable conditions to force international acceptance of his intentions - which initially he was careful to soft-pedal. To this end he agreed to return to Egypt all of Israeli-occupied Sinai, seized in the 1967 war but not part of ''Eretz Israel.'' In return, he counts on being able to secure international acquiescence in Israel's absorbing the West Bank and Gaza.
The US and the international community, however, have continued to maintain that there must be negotiation with the Palestinians and the door kept open for self-determination and territorial compromise on the West Bank.
With Sinai returned to Egypt just over six weeks ago, Mr. Begin saw his country still facing two threats to its long-term survival and security: the porousness of its northern border to armed attack from Palestinians in Lebanon; and the likelihood of US and other international pressures for territorial compromise.
This is the broad context in which to place the Israeli military operations in Lebanon begun just over a week ago.
But there are many more Palestinians than those just in Lebanon (where according to the Palestinian Statistical Abstract for 1981, published by the PLO in Damascus, the total Palestinian population is about 360,000.) The same source gives the total Palestinian population of the world at 4.5 million. Other sources use a total figure of 3.5 million.
But can Israeli military operations in Lebanon, even if dashingly triumphant, stifle the nationalist irredentism of a Palestinian diaspora of that size?
After Israel's stunning victory in the 1967 war, then Prime Minister Golda Meir questioned the existence of both a Palestine and a Palestinian people. Her argument was that Palestine and Palestinians were relatively modern inventions and that those claiming to be Palestinians were in fact Arabs - period. Mrs. Meir's assertion, with its denial of Palestinian identity, played no small part in producing a Palestinian nationalism broader based, more determined, and more strident than had ever existed before.