Jimmy Carter and Ronald Reagan come from the two sides of the oldest political argument in America, even if they are both reluctant to say so during this presidential campaign.They disagree on the most fundamental issue of American government -- just what should the government be?

Reagan's answer has long been "not much," though he has modified it extensively during this campaign. The Reagan canon from the first dozen years of his political activism (1964 to 1976) is filled with the rhetorical consequences of his conservative impulses: "Government does nothing as well or as economically as the private sector of the economy," he said in countless speeches during the '60s. The government, he said, should stick to its "legitimate function," which he defined in the narrowest sense -- maintaining the national defense, preserving a national currency and the like.

The idea that government should do as little as possible is one that Jimmy Carter has never uttered. He did campaign in 1976 on a promise to cut the number of government agencies from 1,900 to about 200, but that stillborn and long-forgotten proposal was meant to increase efficiency, not to make the government more passive.

Though Carter may be less "liberal" than other Democratic presidents since Roosevelt, he is no less activist, as the two new cabinet departments he created indicate. He has happily volunteered a governmental role in many of society's private sectors, and promises more of the same if he is reelected.

Reagan -- at least the old Reagan who spoke his mind bluntly -- would say that willingness to use the federal government to meddle with society is just the government's existing table of organization, a decision that would probably determine his behavior in the White House if he is elected president. He is giving up his best and probably only chance to build a national consensus in favor of abolishing specific government programs. Without campaigning on promises to do so, it seems unlikely that a President Reagan could later find the political influence he would need to eliminate functioning government organs.

The most radical Reagan proposals the candidate is still making call for the transfer of some federal programs to the states, particularly welfare. If put into practice, such transfers could dramatically alter the role of the federal government, but in the campaign Reagan insists he only wants to relocate these programs, not abolish them.

So the differences that do exist between Carter and Reagan are not simple matters of one candidate supporting Program or Agency X while the other opposes it. The differences are significant, probably, for the effect they would have on the philosophy that would govern either man as chief administrator of the federal establishment.

Put another way, the different attitudes of a President Reagan and a President Carter are more likely to appear in their appointments of subordinates and the aggressiveness with which they pursue different kinds of programs than in any radically different approach to the structure of government itself.

As Reagan has been saying during this campaign, different approaches to administration can substantially alter the way government action is felt in the private sectors. In a statement last week -- the same one in which he said that "air pollution has been substantially controlled" -- Reagan assailed the Carter administration for proliferating government regulations. He promised new measures to simplify regulations and suggested new legislation that would allow others to be revoked.

The environment is a vivid example of an area in which the attitude of the executive branch can determine the rigor of federal regulation regardless of existing statutes or agencies. The Carter administration has taken an activist position on enforcing environmental laws, purusing alleged violations with a vigor that was not always required by the letter of the law, according to some of the officials involved in the process.

These are presidentially appointed officials, whose policy decisions largely determine bureaucratic behavior. Presidential appointees less interested in agressive enforcement could substantially reduce federal pressure to diminish pollution, they concede.

Similarly, the Carter administration has sanctioned aggressive federal action, mostly by the Interior Department, to protect and expand national parks and wilderness areas. For environmental reasons, the administration has curtailed energy exploration by private interests in federally controlled lands, most dramatically in Alaska but elsewhere, too.

Reagan has spoken out against these policies, too. "The government owns such a vast amount of the United States," he said last year, "and has now closed such a vast amount of known mineral lands and possible sources of energy and will not allow exploration or drilling or leasing for those things. This should be relaxed."

As that quotation suggests, environmental questions are now inextricably bound up with the energy issue. Here, too, the two major candidates differ significantly.Both favor higher energy prices and a freer run for market forces, but Carter energy policies include a heavy dose of federal action both to limit energy consumption and share the benefits of price decontrols with the federal treasury.

"I would get the government out of the energy industry and turn it loose in the marketplace," Reagan has said repeatedly. This is "an energy-rich nation," Reagan says, whose "state of Alaska alone has more oil than Saudi Arabia [a contention disputed by many experts]." He disputes the need for strong conservation measures that the Carter administration has favored.

In other areas where the philosophy of the governors can alter the impact of government, potential differences between Reagan and Carter are less clear. For example, Reagan's attorney general and assistant attorney general for the antitrust division could markedly alter the environment in which America's biggest corporations operate, but candidate Reagan has not advertised his intentions in this field. Appointments to the Federal Trade Commission could transform that body -- newly aggressive in the Carter years -- into a less stringent guardian of business behavior. Many businessmen express the belief that Reagan will make changes in these areas consistent with his less-government-is-better philosophy, but this remains to be seen.

Reagan used to speak forcefully against the use of federal funds to prop up faltering private enterprises or municipalities, particularly the Chrysler Corp. and New York City. Carter showed no reluctance to help them both. But the 1980 Reagan says he now sees the merit of both those programs, and does not forswear similar uses of federal power in a Reagan administration.

Carter has forsworn some traditional liberal uses of federal power in ways that distinguish his administration from some of its predecessors. For example, Carter has refused to entertain proposals for gasoline rationing or allocations, or for wage and price controls, despite many Democrats' approval of both. Reagan, too, opposes all these proposals.

Carter has been a deregulator, signing legislation removing most of the federal controls from the airline, trucking and railroad industries. In his campaigning this fall, Reagan calls Carter a reluctant deregulator who only accceded to Congress' wishes in these cases, but in fact both candidates come out about the same on the issue.

One of the assertions made repeatedly this year by Reagan's aides and supporters is that the former governor should be judged by his behavior as California's chief executive, not just by his rhetoric. He was pragmatic and moderate in Sacramento, they say, and will be the same if he gets to the White House.

Reagan's eight years as governor did indeed demonstrate political flexibility. Reagan did not dismantle the state government, he presided over its growth. He did not cut taxes, but raised them substantially. He did not take the state out of regulating business and industry.

For all of that, though, Reagan insists that he still believes what he said he believed in years past. "Look," he said last week, "I've been on the mashed potato circuit so long, I was on radio so many years with those five-day-a-week commentaries, I had a twice-a-week column in more than 100 newspapers throughout the country -- how could I change my positions?"

If he still is the true-blue conservative he once claimed, his campaigning this year has raised a curious anomaly.

In traditional political parlance, a liberal-conservative fight was supposed to involve promises from the liberal for ever more federal largesse, and stern warnings from the conservative that the federal honey pot was empty. In 1980, Jimmy Carter is at least the most liberal candidate, but he makes no new promises of federal help for the traditional beneficiaries of Democratic Party liberalism. Carter is the first modern Democrat to preside over a national economy that promises less for all than it used to.

Ronald Reagan, the conservative, rejects the view that the days of big economic growth are gone. He promises to bring them back. And in this presidential campaign he is the candidate who proffers new federal goodies to the electorate, from new Social Security benefits to tuition tax credits for parents of children in private school to big pay raises for the military.