THE KIDNAPPING of Aldo Moro constitutes a fundamental threat and challenge to the Italian state. The terrorists are pressing the question whether a government actually exists - or is it only the legal shell of a government, with noting inside? Is is capable of acting, at last, to preserve itself and public order? Mr. Moro has been Italy's premier repeatedly over the past 15 years, and he is a leading candidate to be its next president. The government knew that he was a target, and he moved about the city under heavy guard. The kidnappers, armed with submachine guns, slaughtered his driver and four bodyguards. If a small group of terrorists can commit a crime on this scale, and make off with a politician of Mr. Moro's rank, the state itself is in jeopardy.

This kidnapping is only the latest and most spectacular in a series of terrorist crimes reaching back for a decade in Italy. There have neen recurrent waves of bombings and shootings. In recent months there have been increasingly frequent attacks on prominent people - businessmen, journalists, politicians. The Moro Kidnapping is evidently the work of an organization that calls itself the Red Brigades. A court in Turin has been attempting for two years to try 49 people accused of being members. In the spring of 1976, terrorists murdered the chief prosecutor and his two bodyguards. Last spring the trial was postponed when the president of the city's bar association was assassinated and half the jury panel suddenly refused to serve. Last week the gunmen killed a policeman who had been in the antiterrorism squad, and one of the defense attorneys quit the case.

The most dismaying thing about this succession of outrages is that arrests have been very few. In the rare instances where there have been arrests, the delays in bringing defendants to trial have typically been inordinate. One reason for the rise in terrorism is, very simply, that over this past decade the great majority of terrorists in Italy have gotten away with arson, assualt and murder. Alond with the political crimes, incidentally, there is a brisk business, often conducted by the same people, in robbery and kidnapping for profit. As this pattern has continued, the effect has been to generate a rising contempt for public authority among the vast majority of Italians who are totally law-abiding. This kind of terrorism has afflicted all of Western Europe in recent years. But it is only in Italy that the enforcement record is so poor that the gunmen are able to operate on their present scale.

The background to these events is, of course, the Italian tradition of weak government. It never found a way to use the country's new prosperity, in the 1950s and 1960s, to build the social structure that a modern industrial state requires. One poignant example is the University of Rome, which currently has some 160,000 students in facilites capable of accommodating fewer than one-tenth as many. How did it happen? Because, in the demonstrations in the late 1960s, the admissions system was attacked as an unjust and repressive relic of the class structure. The government's response was open admissions. As standards plummeted, the students became unemployable. Those tens of thousands of bitter young people, with no hope of the professional carrers that they sought, are now the sea in which the terrorists swim. If the failures of social policy are most visible in the educational system, they are only marginally less disastrous in housing and health. The unemployment rate in Italy is the higest in any major European country. So is the inflation rate.

The crucial thing now is the Italian government's answer. If it lashes out blindly and illegally, that would be as harmful as doing nothing. But it looks as though the old tradition - weak governments and ingrown politics, dominated by a small circle of perennial figures preoccupied with self-preservation - may be coming to a dramatic end. This crime may now precipitate the kind of crisis throughout Italy from which a ver different style of government must emerge.