PARIS -- Remember the Nixon Doctrine? The promise that post-Vietnam America would provide its Third World allies with the weapons and training to fight their wars but would not fight those wars for them?

That doctrine reached its zenith in the Persian Gulf, when Richard Nixon promised in 1972 to sell Shah Mohammad Reza Pahlavi any conventional weapons system the Iranian monarch wanted. But it slid into ignominy with the collapse of South Vietnam in 1975 and the fall of the shah four years later.

Now the Reagan administration has succeeded in turning the Nixon Doctrine on its head, and the locale is again the Persian Gulf. It is there that the administration is sending Americans to fight for Arab states it will not or cannot arm.

To be fair to the White House, this is not a result that it set out to achieve. It is Congress that has religiously blocked arms sales to Saudi Arabia, Kuwait and Bahrain -- the same countries that the administration is deploying American ships and men to protect from Iran. As for Iraq, Iran's main enemy, Congress has hung out a sign: Don't even think about arming these guys.

The incoherence of the administration's response to this dilemma was on display Thursday. As the White House was backing away from its proposal to sell Maverick missiles to Saudi Arabia and Stinger missiles to Bahrain, American helicopters were busily attacking four Iranian patrol boats in the gulf after the Iranians were foolhardy enough to fire on a U.S. observation helicopter.

Can we really be willing to ask American sailors and airmen to be ready to die for Kuwaiti tankers and thus "reassure" our Arab allies of our reliability, but not be willing to provide those Arab allies with modern weapons to protect those tankers themselves? Taken together, the policies of Congress and the White House have created an absurdity that not even the combined brilliance of Caspar Weinberger and George Shultz, those veterans of forceful U.S. policy days in Beirut, may be able to resolve.

The fear that the U.S. weapons would one day soon be turned against Israel helps explain Congress' share of the American dilemma in the gulf. That is a problem to be explored another day. What is important at this point is not to lose sight of the accidental nature of the growing U.S. involvement in the gulf and the vulnerability of American designs to forces that have no particular reason to wish us well -- not only Iran, but also Iraq and the Soviet Union.

It is, in brief, the kind of situation that gave rise to the Nixon Doctrine in the first place.

In the understandable pleasure that Washington takes in the Iranian-bashing opportunities of the moment, it is too easy to forget that 37 American sailors have already died in this conflict, and not at the hands of the Iranians. The mistaken Iraqi attack on the USS Stark in May forced the administration to explain why those men had been put in harm's way, and then to design a policy to fit that explanation.

Originally we were told that the Stark got shot while preempting Soviet moves in the gulf and guaranteeing freedom of navigation. As circumstances have changed, and particularly as Shultz prepares to go to Moscow to seek Soviet cooperation on the gulf, the rationale has also been reshaped. It boils down now to a desire to develop a long-term, un-Nixonian military presence in the gulf (which, incidentally, the Arabs we are protecting show no signs of wanting).

The sizable American force that has been assembled since the attack on the Stark could well change the nature of the Iran-Iraq war in ways other than the beneficial ones that Washington hopes and predicts. It could help undermine a tacit but clear system of constraints that has held damage in the war to acceptable levels in recent years.

Last winter, when Iraqi air attacks were devastating Iranian refineries and cities, Kuwait and Saudi Arabia understood that they would feel the sting of Iranian retaliation if the attacks continued. The deep air raids soon stopped and are only being resumed now that the Weinberger Shield surrounds Iraq's two allies. The thresholds of acceptable violence appear to be on an escalator that Iraq controls more fully than does the United States.

Washington has succeeded in reducing the worries of Kuwait, Saudi Arabia and Iraq, as the State Department's Arabists promised. After all, Iranian retaliation would now hit American sailors and soldiers, and not something that Congress and the Arabs seem to think worth hoarding far more: sophisticated weapons.