THE TANTALIZING question raised by the life of Moshe Dayan was whether Israelis can find in themselves the resources of courage and imagination not only to defend their country but also to reach out and live in peace with all their Arab neighbors. Certainly Mr. Dayan, as much as any single Israeli since the state's founding, proved the first task could be accomplished. With his signature eye patch, he came to symbolize the Israeli "David's" prowess against the Arab "Goliath." Not even his failure as defense minister to prepare adequately for the Arabs' surprise attack of 1973--the ultimate tribute: his tactic--dulled the luster he had won in earlier wars.

Yet Gen. Dayan was no cardboard warrior. As a boy he had lived alongside Arabs and, even as Jewish life in Palestine (later Israel) became more urban and "modern" and concentrated on military confrontation, he kept a deep fascination with the desert and with the Arabs who lived in Palestine and with the potential of peace. The 1967 war, ending with the West Bank and Gaza in Israel's hands, let him test his practical ideas for Jewish-Arab coexistence. He conducted what was, by comparison with any other occupation you can think of, a mild and progressive regime. His response to the troubles that inevitably arose was not automatically to retreat to more repression but to try sinuous new ways of cooperation. Speaking colloquial Arabic, sipping coffee with Arab friends on the West Bank, he could claim as few Israelis could to have the respect of the Palestinian Arabs and to know them.

As the years passed, his conviction grew that he and perhaps he alone could lead. Yet the war of 1973, though it perhaps added a desire for personal vindication to his political motivation, had hurt his public standing and, with his loner's style, he had burned his bridges to his old Labor home. He parlayed his personal prestige into a position in Menachem Begin's post-1977 cabinet and as foreign minister made important contributions at Camp David. But he wanted more, and in the elections earlier this year he tried to fashion for himself a swing man's power. He failed. To his dismay, to Israel's dismay, perhaps even to the dismay of those Arabs who saw in him levels of desert perceptiveness quite apart from the Israeli norm, he had not established by the time of his death yesterday whether a true peace can be had.