The Paradox of Not-Knowing: A Lesson from Professor D. Dubrovsky

Some lecturers transmit facts. Others transmit a way of seeing. D. Dubrovsky, who taught philosophy at the Donetsk Medical Institute (now University), belonged unmistakably to the latter category. Educators of his caliber are rare, and those of us who studied under him understood, even then, that we were witnessing something more than a standard course in philosophy—we were being initiated into a mode of thought.

It was Dubrovsky who first opened philosophy to me as a living discipline rather than an academic requirement. That early exposure has stayed with me, eventually giving me the confidence to attempt my own modest philosophical excursions within my field—among them, a continuing inquiry into what might be called the philosophy of health and illness.

The Lecture: Two Circles on a Chalkboard

I recall one of his earliest lectures with unusual clarity. Dubrovsky approached the chalkboard and drew two circles—one small, one substantially larger.

"Everything within the small circle," he said, "belongs to you, the students. Everything within the larger circle belongs to me."

On its surface, the statement seemed unremarkable: professors know more than students. But Dubrovsky was not making a claim about the content of knowledge. He was making a claim about its geometry.

He directed our attention away from the interiors of the circles and toward their circumferences—the boundary lines separating what is known from what is not. The student's circle, being small, has a correspondingly short boundary. The professor's circle, being large, has a boundary that stretches on considerably further.

This was the insight he wanted us to sit with: the boundary between knowledge and ignorance does not shrink as knowledge accumulates. It expands—and it expands faster than the knowledge itself. The more one comes to know, the larger the surrounding territory of the unknown becomes. Dubrovsky's world of not-knowing, precisely because his circle of knowledge was so much larger than ours, was correspondingly vaster than any student's.

Rediscovering the Story

I might never have returned to this memory had I not recently encountered it again—preserved as an anecdote still passed among alumni of the institute, apparently having taken on something of a legendary status among generations of students since. Coming across it unexpectedly brought the lecture back into focus with unusual vividness, and with it, a renewed appreciation for how much that early lesson had shaped my subsequent thinking.

The Paradox, Revisited

Years later, I find that Dubrovsky's demonstration was not merely a clever pedagogical device—it articulated a genuine epistemological paradox, one that philosophers from Socrates onward have circled in various forms: the more rigorously one pursues knowledge, the more acutely one perceives the scope of what remains unknown.

My own circle of understanding has grown considerably since those student years. Yet the boundary separating it from the unknown has grown in proportion—if not faster. Each answer acquired seems to generate several further questions; each field mastered reveals adjacent fields barely glimpsed. This is not a failure of inquiry but its natural consequence.

A Familiar Tradition

Dubrovsky's chalkboard diagram, though drawn with no more than two circles and a piece of chalk, belongs to a lineage of thought stretching back to Socrates, who claimed that his only wisdom lay in knowing that he knew nothing. It resonates, too, with the epistemic humility that later thinkers—from the skeptical tradition through to contemporary philosophy of science—have insisted must accompany any serious pursuit of knowledge. Karl Popper's view of scientific progress as a series of ever-more-refined conjectures, each opening new avenues of uncertainty rather than closing them, echoes the same geometry Dubrovsky sketched on the board that day.

What distinguishes his version is its visual economy. Where Socrates required paradox and argument, Dubrovsky required only two circles and their circumferences—a demonstration immediate enough for a room of medical students to grasp on first hearing, yet deep enough to still be worth turning over decades later. That, perhaps, is the mark of genuine philosophical teaching: not the transmission of a conclusion, but the installation of a question that keeps working long after the lecture ends.

Dubrovsky's diagram, drawn decades ago, continues to describe the shape of intellectual life with unsettling accuracy: genuine learning does not diminish ignorance. It discloses, with increasing precision, just how much of it there is.

 Mykola Iabluchanskyi