Behind the gush of peace talk from the White House, even President Reagan's trusted advisers express uncertainty and skepticism about prospects for any sort of U.S.-Soviet nuclear arms-control agreement in a second Reagan term.

Reagan, as always, is hopeful. Intimates say he has become convinced that he could be "a peace president" who could score a real breakthrough in dealing with the Soviet Union. They say Reagan believes that the Soviets will take him seriously if he is reelected, recognize that the U.S. defense buildup is not a passing fancy and bargain seriously on nuclear-arms reductions to reduce their military costs.

The president's advisers acknowledge that they have no hard facts on which to base this glowing assessment. Curiously, however, the dubious quality of a foreign policy based largely on faith has been obscured by the election-year oratory of the Democratic opposition. Thanks to Walter F. Mondale, who compares Reagan's belated interest in improved U.S.-Soviet relations to a "deathbed conversion," much of the political dialogue has been focused on the motives of the president's peace offensive.

Reagan can be trusted to win any debate whose issue is one of motives rather than results. In 1980, when President Jimmy Carter said the election would determine "whether we have peace or war," Reagan turned this hyperbole into a debate on the character of Carter, who he said was trying to portray him as "a mad bomber." Reagan said claiming that anyone would deliberately want a war was "beneath decency."

The real problems have little to do with Reagan's motives or the auspicious timing of his interest in international peace. The problems, apart from the Soviets themselves, are that Reagan knows little about his subject matter and even less about the struggle in his own administration over arms control.

For those interested in what Reagan doesn't know, the recommended reading is Strobe Talbott's new book, "Deadly Gambits," a veteran diplomatic correspondent's fascinating account of the bureaucratic struggle over arms control that has been a feature of the Reagan presidency.

Sprinkled throughout the book are some frightening Reaganisms. Reagan stated inaccurately that submarine-launched ballistic missiles could be recalled. He asserted that the only nuclear-tipped missiles are land-based, not on bombers or submarines. He discovered that a submarine could be "sunk." And he confessed that he didn't realize when he submitted his first proposal for reducing U.S. and Soviet strategic nuclear forces that most of the Soviet nuclear arsenal was concentrated in large, land-based missiles.

Had Reagan realized this elementary fact, part of any primer on arms control, he also would have realized that the Soviets would think that his first arms-reduction package, announced with great fanfare May 9, 1982, was too inequitable to be taken seriously.

By themselves, these considerable knowledge gaps would not necessarily stop Reagan from reaching an agreement with Soviet leaders. He is consciously a delegator, who prides himself on decision-making ability rather than on what he knows. But, as Talbott makes clear, the delegating of arms-control decisions flowed to negotiators deeply divided in strategy, purpose and understanding.

In his heart, Reagan may have wanted arms control and a safer world. In his head, he had no independent knowledge of how to achieve an agreement with the Soviets, even if they had wanted one, or of how to resolve the conflicts in his bureaucracy. Since it is always easier to block a proposal than advance it, Reagan's ignorance gave arms-control opponents within his administration a huge advantage.

Nearly four years after he took office, Reagan has learned a bit about weapons systems but given no sign to his subordinates that he is prepared to make personnel changes that a genuine arms-control effort would require.

Reagan never fires anyone unless forced to and certainly isn't going to get rid of longtime loyalist Caspar W. Weinberger, a capable defense secretary who is hostile to arms control. Nor is Reagan likely to make arms control the personal priority it would have to be if he wanted his administration to speak with a single voice. Reagan's advisers say they will address this question after Election Day.

The irony is that polls show that Reagan, despite his huge lead, still comes up short when his intentions toward the Soviets are measured. At the same time, Americans overwhelmingly view him as a strong and decisive leader.

The evidence of his first term contradicts the public perception. Reagan may be totally serious about using the U.S. defense buildup as a platform for negotiating with the Soviets. But he has given no sign of willingness to make the changes and assume the leadership that could make these negotiations a success.

Reaganisms of the Week: Speaking to the United Nations Monday, the president said: "I believe that the future is far nearer than most of us would dare hope."

Explaining to Bowling Green State University students two days later why he seeks better relations with the Soviets, he said: "We want it because peace in America is such an attractive way to live that war is a terrible interruption."