Like so many American children, I spent a small portion of every afternoon in the company of Fred Rogers. Mr. Rogers' Neighborhood followed an hour of Sesame Street on our local PBS station. This was back when Sesame Street could occasionally still be weird, though Mr. Rogers was the same steadying presence he’d been, and would continue to be, for years to come.

I have only vague memories of the episodes themselves, but the show’s cheerful, friendly, and intensely singable intro has stuck with me. It ends with a question that has become synonymous with Mr. Rogers himself: “Please won’t you be my neighbor?”

Now that Fred Rogers has entered the canon of secular saints, not to mention the pantheon of people played onscreen by Tom Hanks, that friendly question has acquired a kind of moral force, an undeniability. Who could ever say no?

I have a deep appreciation for Mr. Rogers. But I can’t help wondering whether a small part of his legacy was fostering, intentionally or not, some ambiguity about the very idea of neighborliness. After all, when he invited television viewers across the country to be his neighbor, he didn’t exactly mean that everyone should move to Pittsburgh.

He was stretching the meaning of the term “neighbor.” You might say he helped broaden the idea of neighborliness. He was offering an answer—or at least attempting to reframe—a question that has troubled humanity for some time: Who even is my neighbor?

A pretty compelling, if enigmatic, answer to that question was given awhile back, but we wrestle with it still. Current debates over globalism and nationalism could be described broadly as attempts to come up with an answer. So could arguments over funding for public schools and universities or, for that matter, the decisions of local zoning boards.

Once you’ve gone about the tricky business of deciding who your neighbors are, you’re quickly faced with the question of what you owe to those neighbors. Figuring that part out is no easier.

Many conversations about philanthropy can be understood as competing attempts to answer these two questions (that is, “Who is my neighbor?” and “What do I owe to my neighbor?”). How you respond will undoubtedly inform the way you go about practicing charity.

Way back in 2006, sociologist Emily Barman, in a fascinating book about workplace giving campaigns, drew a contrast between “communities of place” and “communities of purpose.” The former, she says are rooted in “place and propinquity,” while the latter are “based on meaning: the collective imaginings of members with a shared characteristic or interest.”

In the book, she suggests the United Way and its traditional fundraising campaigns rely a notion of the community as a place, while “alternative funds” draw on notions of the purpose-centered communities. She seems to view favorably the rise of these purpose-centered communities, enabled as they were by burgeoning forms of communication.

In other words, our neighbors aren’t who they once were. You can just as properly refer to fellow environmentalists in Copenhagen as your “neighbors” as you do (or don’t) the Trump-flag-waving family across the street. Barman examines how shifting concepts of community can affect what kinds of nonprofit organizations attract support from donors.

Fred Rogers himself seemed to endorse an idea of neighborliness that extended far afield of place and propinquity. He spread welcome messages about the value to you of every child, no matter who they were, where they lived, what they looked like, or what connection they might have to you. Everyone is our neighbor.

It sounds good, but if we agree that neighborliness comes with certain obligations, in what ways can we meaningfully be obligated to everyone? We must demonstrate respect, decency, and kindness, of course. But is it wrong to think that you might owe something even more to the people you actually see and interact with every day? Is it possible that “place and propinquity” engender bonds and duties that can’t be replicated by ideologies, politics, and personal interests?

I’m as guilty as anyone of giving more thought to friends and strangers half-a-world away than to the people on my street. Good and noble things can be accomplished when, linked by the Internet, people forge communities of purpose. But it’s also possible that something irreplaceable is lost when those communities of purpose siphon resources from communities of place.

I’m glad Fred Rogers offered his invitation to neighborliness, and I’m glad that so many people have chosen, metaphorically, to accept that invitation. But it’s worth remembering that we only get to choose some of our “neighbors.” The ones who live next door and down the street, the ones whose kids attend the same public school as yours, the ones at the local homeless shelter—they’re already your neighbors. No invitation needed. And they deserve a little neighborliness too.