Will we in the future look back upon a George W. Bush era or merely a George W. Bush presidency?

This is a question that is almost never asked of a single-term president. The most significant one-term president may have been the often-forgotten, often-misunderstood James K. Polk. In four years he signed a treaty with Great Britain over the Oregon territory, prosecuted the controversial Mexican War, brought down tariff rates, appointed two associate justices to the Supreme Court, and presided over the incorporation of Texas, Iowa and Wisconsin into the Union. And yet no one has ever spoken of the Polk era in American history.

Nor of the Taft era, or of the Harding era, or of the Ford era, or, more recently, of the Carter era.

The kind of impact that comes from transforming an era – from defining a period of time by the personality of a president – usually requires two terms. (Grand exception: Abraham Lincoln didn’t serve his full two terms, of course, but he was elected twice and used his years in office not just to change the country but to preserve it.) And though second presidential terms are both burdens and opportunity, putting pressure on an administration that may be exhausted of energy and ideas, they also provide the time and opening for a president to make lasting changes in the executive branch, the government and the nation.

Franklin Delano Roosevelt, who in slightly more than three terms and in four presidential elections certainly stamped his impact on an era, once argued that greatness in the presidency required a significant alteration in the way the nation thought. “All of our great presidents,” he said, “were leaders of thought at a time when certain ideas in the nation had to be clarified.”

In his brilliant essay opening each volume of the new “American Presidents” series that he edits, the historian Arthur Schlesinger Jr. takes his own stab at defining greatness in the presidency. “Crisis widens presidential opportunities for bold and imaginative action,” he argues. “But it does not guarantee presidential greatness.” Mr. Schlesinger points out that secession did not inspire James Buchanan to greatness, nor did economic distress inspire Hoover to the greatest heights of presidential achievement. And it is interesting for us to note that the presidents who succeeded them (Lincoln and Roosevelt) were the ones who did the clarifying.

All of which makes us wonder whether Bush will clarify issues left unclarified by Bill Clinton (whose name does not adorn an era, only an attitude) or whether Mr. Bush’s successor will be called upon to clarify the issues the 43rd president leaves unresolved.

We cannot know for sure right now, of course, but we can speculate on what those issues might be – and in setting them forth we can clarify for ourselves what our own time is about, and what it might be remembered for by our children and grandchildren. Here’s a guess at what historians – who call the period at the end of the 19th century the Age of Imperialism, who regard the ’20s as the Age of Isolationism, and who regard the period that followed the New Deal as the period of increased government intervention in the economy and domestic affairs – might consider the contemporary questions that beg clarification:

What is the role of the United States in the period that followed the Cold War, when no nation-state was a credible rival to American power? Mr. Clinton had his own answer, oddly derivative from Mr. Carter: that the United States be the guarantor of human rights in regions of contention and disorder, and the “indispensable” partner and participant in multinational efforts to police and preserve the peace. Mr. Bush came to office questioning both parts of that approach, though events prompted him to take a kinder look at “nation-building,” in Iraq and Afghanistan, than he ever contemplated in his debates with Al Gore Jr. in 2000.

This question, which Mr. Clinton bequeathed to Mr. Bush, remains fundamentally unresolved – especially since it may be that the greatest threats to American security and independence aren’t nation-states at all but aggregations of the aggrieved that take terror as a tactic and then transform it into a crude ideology.

Now that communism is gone, is it still in the American interest to promote democracy abroad, and is it reasonable to think that American-style democracy has worldwide appeal or applicability? This is one of the most beguiling questions in the American debate, and it is important to remember that Mr. Bush did not put it on the American agenda. It was there, implicitly, during the Cold War and before, when American policy-makers reached a conclusion, in places like Guatemala, Iran and Chile, that is at odds with the instincts of the Bush team.

Many of the people who surrounded Mr. Bush in the early years of his presidency argued that the greatest benefit of the war to topple Saddam Hussein might be to use Iraq as a laboratory of democracy that would eventually infect the entire Middle East. Writing in The New York Times earlier this month, however, Francis Fukuyama, of the School of Advanced International Studies at Johns Hopkins University, offered a counter-argument:

“We need in the first instance to understand that promoting democracy and modernization in the Middle East is not a solution to the problem of jihadist terrorism; in all likelihood it will make the short-term problem worse, as we have seen in the case of the Palestinian election bringing Hamas to power.”

How do we make a graceful transformation from post-industrial manufacturing to whatever will follow the information-age economy? We struggled with similar questions when the railroad, shoe, textile and steel industries collapsed, and now we are struggling with these difficult dislocations as the American automobile industry is under siege. This comes at a time when old-style health-care and retirement benefits themselves are being altered. Right now, few politicians in either party are looking at these two problems as two sides of the same devalued coin. But these issues, like the two questions before it, are a reminder that any politician who wants his name on an era is going to have to come up with solutions posed by the end of an era.