President Barack Obama’s reluctance to intervene in Syria has occasioned yet another round of soul-searching on America’s role in the world. His reflective speech at the U.N. General Assembly has led commentators to wonder whether the United States remains willing to play its traditional and indispensable role in maintaining world order. “Nation-building at home” is the newest term of art, and even the dreaded I-word is making one of its periodic comebacks. Bill Keller of The New York Times sees a “new isolationism” creeping across the land, while Sen. John McCain alleges that there are 15 isolationists in the Senate GOP caucus.

This debate on America’s role in the world is not new — indeed, it is a constant and a healthy conversation. America’s expansive commitments and unique power deserve constant re-evaluation. But however one feels about the wisdom of deeper involvement in Syria — and the two of us disagree among ourselves on that point — it should be easy to see that Obama’s America is not retreating and will not retreat from the world.

More than 50,000 U.S. troops remain in Afghanistan — more than when Obama took office in early 2009. The president has committed to do what is necessary to prevent Iran from getting a nuclear weapon. Recent events have created greater hope for a diplomatic resolution with Iran, but the United States is still committed to that promise and the military option is still on the proverbial table. That is a huge prospective commitment, even if the odds of that being necessary in the future may be (thankfully) declining. The “rebalancing” to Asia has manifested itself in numerous military and nonmilitary measures that have certainly gotten China’s attention, among its other effects.

Obama’s record shows that he recognizes America’s capacity to project military power around the world is its unique strength and an underpinning to the global order. He has therefore used American military forces repeatedly in such diverse locales as Afghanistan, Pakistan, Yemen, Libya, Somalia and Uganda, among others. The U.S. military retains its global presence and American forces continue, again uniquely, to patrol every ocean and to protect the global commons.

But Obama also sees an America that is weary of war, fiscally constrained and in the view of many sometimes reckless in its use of force. Whatever one’s views on the latter point, there is little doubt in the eyes of most Americans that the wars of the past dozen years have been very difficult and costly — and that they are not to be repeated.

The president has sought to acknowledge those two truths both by sharpening America’s nonmilitary tools for international engagement and by exercising greater prudence and restraint in the use of force than some of his predecessors. This reflects a sense that American power is not enhanced by unnecessary wars that waste resources and erode American will. He also talks about ending the major wars in Iraq and Afghanistan even while continuing to prosecute military operations on several fronts. To some, his rhetoric is not sufficiently Churchillian; to others, he may hedge and cover his political flanks more than would be advisable. But whatever one’s take on his communications strategies, the actions should not be forgotten.

Obama’s priorities are clear: maintaining great-power peace, preventing the proliferation of weapons of mass destruction and combating Al Qaeda and related groups — on these matters, very little retrenchment is visible in U.S. policy. Creating stability in places like Syria, Libya, Iraq and Egypt, while desirable in principle, is a second-tier priority in the president’s eyes — especially in light of the evident difficulty of making a difference for the better in such places over the past decade.

Within the confines of that overall approach, it is possible to differ on very important specifics about how best to deploy scarce U.S. resources and political capital. Are U.S. military forces in Europe still necessary or useful? Did the United States do enough in Libya, where the world’s collective role in helping Libyans build a post-Qadhafi state has been minimalist? Should the United States intervene militarily in Syria? They are not easy questions, and at times this administration has stumbled in trying to answer them. So has Congress, especially in its willingness to tolerate sequestration and even a government shutdown and a debt default — blunders that could pose far greater threats to American internationalism than anything emanating from the White House.

Overall, Obama’s approach to foreign policy is a form of selective yet still robust engagement. It’s a far cry from isolationism. We would be wise to remember that — and so would any potential challengers to America’s global role.