THERE IS A GROWING PUBLIC FEAR, which this book will not dispel, that the nuclear arms race is out of hand and that the Reagan administration is too much encumbered by theoretical luggage to do much about it.

Arthur Cox finds it deplorable that the emphasis in nuclear deterrence has shifted from "mutal assured destruction"--a theory that some strategists influential in the Reagan administration find "immoral" because it rests on the threat to annihilate civilian populations--to esoteric scenarios of counter-force and "limited" nuclear warfare. In his view, this new emphasis lowers the nuclear threshold and encourages the development of "hair-trigger" responses, increasing the risk of nuclear war by accident or miscalculation.

Cox is inclined to spread the blame impartially for this growing peril and confusion. On the American side, he argues, it was a major error to introduce the "mirving" of missiles in 1969: a breakthrough spurred at the time by technological advantage which has since been offset by the Soviet Union. A basic Soviet error, more political than military, was to launch new Soviet or Soviet-sponsored military adventures outside the traditional sphere of Soviet military interest--beginning in Angola in 1975.

Equally deplorable, as Cox sees it, is the present U.S. arms buildup, fed by the fear (which he believes to rest on a statistical miscalculation) that the Soviet Union has been dangerously outspending the United States on strategic weapons and is near achieving an edge.

The resulting alarmism (as he would have it) on our side, the talk of a "window of vulnerability" to a Soviet first strike, the casual theorizing about limited or battlefield-scale nuclear war: all of this exasperates Cox and elicits from him epithets like "madness" and "mindless" that shake the even tenor of what is otherwise a sober and factual, if tendentious, argument. Such influential Reagan administration theorists as Richard Perle (who attributes European anti-nuclear restiveness to "Protestant angst") and Colin Gray (who likes to think about the unthinkable) drive him up the wall.

Cox rejects the notion, more or less formally embraced by the Reagan administration, that the accelerated development of new strategic systems (the MX, the Trident, ground- and sea-launched cruise missiles) will or can stabilize the balance.

He is equally skeptical, on the same ground, of the contemplated deployment of new "Euromissiles." The deployment of the Pershing II in Western Europe would put its warheads five to six minutes from major Soviet targets; and Cox, with others, argues that this makes a "launch on warning" response by the Soviet Union more likely. He believes that when all relevant factors are considered--including the scale of Soviet strategic and conventional deployments against China--the overall arms balance is satisfactory now.

Finally, as noted above, Cox rejects the view that any one form of nuclear warfare is somehow nicer or more controllable than any other. "If," he writes, "the idea that some forms of nuclear war are more moral than others is ever accepted, the deterrent to nuclear war could be eroded seriously." He is, incidentally, in good company here: among warriors, if not among armchair civilian strategists. In a recent New Yorker report, John Newhouse recounts how the late General Creighton Abrams interrupted a theoretical discussion of limited nuclear war in 1973 "with an expletive, followed . . . by the statement, 'One mushroom cloud wll be reported as one hundred, and that will probably be the end of the world.' "

Detailed consideration of Cox's points, which strike me as compelling, is beyond the scope of a book review. In general, his view is worlds apart from the Reagan administration view of the arms control issue.

The critical question about Cox's argument, however, arises from the difficulty of detaching arms control issues from the political frictions that created the "cold war" in the first place. Cox clearly recognizes that Soviet interventions, directly in Afghanistan and indirectly in Angola, marked a new turn in the global rivalry. Still, he seems at times to minimize the pressure of political differences on the arms race.

Cox does acknowledge that the collapse of the shaky "detente" engineered by Nixon and Kissinger sprang from the Soviet failure to grasp the impact of its patronage of "national liberation" movements in the Third World. Thus one of his key proposals is for a separate negotiation leading to a sort of self-denying ordinance between the superpowers, limiting, and distinguishing between, forms of interventionism.

Cox is no doubt right in believing that these two interlocking factors, the nuclear and the political, must be separated and dealt with each on its own terms. But can they be? The Reagan administration is hardly the first to vacillate on the issue of "linkage." Politically, if not logically, arms control and geopolitics are linked at the deepest levels and affect one another.

In response to the structureless mishmash of self-justification that the Soviet Americanologist Georgy Arbatov contributes as a commentary to this book, Cox writes: "It is apparent that Mr. Arbatov does not present any criticism of his government. . . . If I were still serving in the U.S. government, I would not have said many of the things contained in this book. . . . One of the great tragedies resulting from the demise of U. S.-Soviet detente has been the snuffing out of voices of dissent in the Soviet Union."

But wait; something is wrong here. It is not because he is a Soviet official, but because he lives in the Soviet Union, that Arbatov toes the official line and probably would continue to do so if he were in private life. Moreover, "voices of dissent" in the Soviet Union did not commence being "snuffed out" because detente broke down but because the Sovied regime does not tolerate diversity at all, detente or no. Which is to say, as these surprising excerpts illustrate, that Arthur Cox takes too little account of the asymmetries between free and totalitarian societies, of the very different values and norms of criticism they permit and generate, and of the resulting difficulties of treating the arms control debate as if it were between societies sharing the same political assumptions.

Cox, though parts of his book show that he knows better, too often slides into the easy assumption that the arms race is a perverse eccentricity. Rather, it is a projection, made the more mortally dangerous by the accelerating pace of weapons technology, of a real and continuing clash of political, economic and social doctrines and values. It is therefore the more intractable. Pretending that competing views of the world have little to do with it won't make it easier to unravel.