Mayor Rudolph Giuliani, who says he has given "no thought yet" to national aspirations, is campaigning for Republican candidates in Iowa, New Hampshire (those are the first two states he mentions; he is such a tease), South Carolina, California, Florida and elsewhere. This stirs speculation that there might be a national role for him in 2000, even though:

He supported Mario Cuomo's re-election in 1994, is pro-choice, favors gun control, rent control and has implemented for city workers one of the nation's most liberal "domestic partners" policies, one that grants the same rights to married couples and unmarried couples of various sexual configurations. Furthermore, Americans want presidents to be their pals, but Giuliani's personality is sandpapery.In 1993, voters liked Giuliani just enough to give him a narrow victory over his calamitous predecessor, the courtly David Dinkins. They did so precisely because Giuliani is not likable, any more than surgery and cold showers are. Since 1993, he has been trying to "give people more freedom in a realistic way" and to give them "more ability, within reasonable bounds, to make choices in their lives."

Such was the filth and fear in New York's public spaces in 1993, he is not exaggerating when he says that his task has been "to convince people that things are not hopeless." There is simply no precedent for the reduction of crime produced largely by his insistence that the phrase "petty crime" is oxymoronic.

Graffiti, menacing panhandling, boom boxes, subway turnstile jumping, even jaywalking - these are offenses that suggest disorder will breed disorder. Today, the Fear City of 1993 is the nation's safest big city, with the lowest violent crime rate. Crime is down 49.3 percent (homicides 69.3 percent, to a 32-year low) in the first half of this year from the same period five years ago. There were 2,005 murders in 1992. There probably will be fewer than 700 this year.

"I get the murder statistics every morning," he says, and notes that nowadays most victims were known to their killers. That is, stranger-on-stranger killings, the sort that drive people indoors and tourists away, are down even more than the general murder rate. When a reporter asked about criticism that he had not done enough for minorities, he replied, "They are alive; how 'bout we start with that." In 1997, he carried 43 percent of Hispanics, the city's largest minority (almost one-third of its population).

Welfare rolls soared from 200,000 to 800,000 under Mayor John Lindsay's policy of making welfare "user friendly." The ratio of working people to welfare recipients went from 10-to-1 in 1960 to 5-to-1 in 1970. Rolls almost reached 1.2 million - more than the populations of 15 states - under Dinkins, when 80 percent of applicants got assistance because, Giuliani says, social workers "stopped asking questions."

Even before federal welfare reform in 1996, Giuliani's policy of "restoring work to the center of New York life" had trimmed the rolls by 250,000. This February, they fell below 800,000, having shed more people than the population of the state's second largest city, Buffalo. Welfare offices are now called Job Centers where, Giuliani says, applicants for aid "don't get to talk about welfare" - first, jobs - "until a few days later."

Giuliani is the only New York mayor in this century other than Fiorello La Guardia to serve two terms as a Republican. (Lindsay became a Democrat in his second term.) He may be a wine too vinegary to travel west of the Hudson, but here he has been medicinal.