Twice in the space of a few days, I came across a dictum attributed to Niels Bohr, the renowned Danish physicist who in 1922 received a Nobel Prize for his work on the structure of the atom.

“The opposite of a correct statement is a false statement,” Bohr reportedly said. “But the opposite of a profound truth may well be another profound truth.”

Bohr’s paradox has been quoted for decades. But his observation was new to me when I encountered it in a commentary by the late Rabbi Jonathan Sacks on the biblical book of Ecclesiastes, then saw it cited again by Dr. Lewis Thomas, who was famous for his essays in The New England Journal of Medicine.

I was puzzled to understand Bohr’s meaning. If a “profound” statement is true, how could its opposite be true? When I put the question to a friend of mine, a professor of philosophy at the University of Massachusetts, he replied noncommittally. Good teacher that he is, he wanted me to work it out for myself. So I started thinking harder.

I realized that there are many accurate statements the negative of which is also accurate. For example, “A lot of people like chocolate” is true, and so is “A lot of people don’t like chocolate.” But those aren’t really opposites, since “a lot of people” by definition excludes other people. Besides, Bohr’s aphorism refers to profound opposing truths — he surely had something more in mind than shallow statements of taste or opinion.

Nor was he likely to be merely restating the truism that life is full of seeming paradoxes, many of them captured in proverbs that contradict each other. “Never judge a book by its cover” discounts the importance of external appearances, while “Clothes make the man” emphasizes their importance. “Absence makes the heart grow fonder” articulates an emotional reaction that countless people have experienced — but so does “Out of sight, out of mind.” All such clichés are astute in some situations and clueless in others. Like much folk wisdom, they are context-dependent — not expressions of fundamental and immutable truths.

As I mulled the question, I began to come up with answers.

Bohr was a pioneer of quantum theory — a field famous for addressing apparent internal contradictions. For centuries, scientists had debated whether light consisted of waves or of particles. Bohr was among the earliest physicists to understand that both approaches, though apparently mutually exclusive, are true. Light behaves like a particle and like a wave — profound truths whose opposites are also true. Eureka!

Just as science can supply illustrations of Bohr’s observation, I reflected, so can faith. As a religious believer, I am certain that God is omniscient and has knowledge of all events past, present, and future. I am also certain that human beings have free will and choose their actions. That sets up an inescapable paradox: If God has perfect foreknowledge, how can human actions be freely chosen? Yet if people truly have free will, how can God know the future in advance?

To be sure, philosophers and theologians have grappled with this tension and proposed various ways of reconciling it. Still, it strikes me as an elegant demonstration of Bohr’s maxim that contradictory truths can both be profound and meaningful.

And so — to offer one more interpretation of Bohr’s remark — does Abraham Lincoln’s lapidary description of America in the Gettysburg Address as a nation “conceived in liberty, and dedicated to the proposition that all men are created equal.”

Liberty and equality are fundamentally at odds. If Americans have complete liberty to pursue their interests and ambitions, everyone will not be equal; yet if equality for all is to be ensured, American liberty must be curtailed. As a matter of public policy, this duality is less a contradiction to be resolved than a tension to be constantly recalibrated. But it also fits Bohr’s formulation. At the heart of the American experiment is a classic inconsistency: liberty vs. equality. They are always in conflict, yet always interconnected.

I initially tackled Bohr’s paradox as a riddle to be solved. What I take away from it is a challenge to embrace complexity. Truths can be profound and contradictory — a timeless reminder that life’s greatest insights sometimes defy logic.