When my mother died, I wrote in a eulogy that one of the many things she taught me was to appreciate and understand paradox.  Paradox is more than merely holding two contradictory ideas at the same time.   What differentiates true paradox from contradiction is reflexivity.   A good example of paradox is the simple three-word statement “I am lying.”   If the statement is true then it is false, and if it is false it is true.   There is a “spinning” quality to a true paradox, like an echo in a canyon that reverberates repeatedly.

When Donald Trump declares that he is not a racist and then states that the judge in the Trump University fraud case must be biased because he (Trump) wants to “build a wall”– that is a mere contradiction.  It is not a true paradox because it lacks reflexivity- the self-invalidating component.    One can find truth in half a contradiction, but one cannot cut a true paradox in half because it is always both true and false simultaneously.

In flying airplanes, in business, and life in general, grasping paradox usually makes us smarter and better at what we do.   In flying, understanding how one can be “behind the power curve,” such that the more energy you add (power) the slower you fly, can save your life.  Or, the fact that when the airplane begins to fall out of the sky due to a wing stall, the solution to the fall is to point the nose down to the earth in order to gain lift.   It is the “Chinese handcuffs” of my youth, where in order to release oneself from their grip you had to push them together in order to pull them apart.

While paradoxes make for deeper understanding, we can also learn from contradictions.   My mother would tell me bedtime stories of how I should never forget that it was the “Christians” who built the concentration camps, and at the same time would instruct me that “if a priest or a nun were to get on a bus or train you should always give them your seat.”    There was no difference to her between “Christians” and Catholics, so her respect for those who she imagined built the camps was perplexing.  She would not, or could not, explain it to me, so I needed to draw my own conclusions.   Her life gave me what I supposed was the answer; when it came to loving her children and her husband, being dedicated in love meant an equal measure of forgiveness and compassion for one’s failings as admiration for one’s strengths.

Appreciating paradox and contradiction also tells us that life is not binary; there are always at least three sides to every story.   If we think we have a choice between the options given to us, we are likely missing something.   In a debate between the humanistic psychologist Carl Rogers and the Jewish philosopher-psychologist Martin Buber, the moderator asked them both if “man” was basically good or evil.   Predictably, Rogers said he thought man was basically good.   Buber, on the other hand, said he thought man was “basically good and evil, or not good and evil.”

In other words, it was the wrong question.   Being alive, being “engaged in life,” meant that one would do both good and bad things.   To not do good and evil meant that one was less engaged in life, less fully alive.

Life is full of paradoxes.   Bertrand Russell and Alfred Whitehead’s massive tome “Principia Mathematica,” which subsequently served as the model for the (now discredited) double bind theory of schizophrenia, was an attempt to solve the “simple” problem of whether or not the catalog of books in a library should itself be included in the catalog.   They concluded, after well over a thousand pages of mathematical computations, that it should not, because it was indeed a different “logical type.”  At that time, I suppose, paradox had no place in mathematics.  I am not sure that these days, in the era of chaos theory, they would have come to the same conclusion.

It is the appreciation of paradox, I believe, that leads one to understand how, in the words of Walt Kelly’s Pogo, “we have met the enemy, and he is us.”  It reveals how Nazi officers could engage in mass murder at 10 o’clock in the morning and come home to pet their beloved dogs and play with their children on their living room floors in the evening.   It is the awareness of the self-invalidating circularity within ourselves that allows each of us to understand how we can be the enemy.

If there was anyone who could hear the sound of one hand clapping, it would have been my mother.   There is a Zen koan in which two monks set out on pilgrimages from different places.   They each take vows to not retrace their steps, or to look too far ahead as they walk.   Unbeknownst to each other, they each set out to cross a deep chasm from opposite sides of a thin, reed bridge, and they meet in the middle.   If they were to go forward and cross each other, they would fall to their deaths, and if they were to back up, they would break their vows.    If my mother was one of the monks, I imagine she would have simply sat down on the bridge and spent the rest of her life getting to know the other monk.   She would have found a way to solve the unsolvable.