How Paradoxes Populate Our Lives

We live our lives in paradoxes. Many are due to language. A friend recently told me that a scene she’d photographed was beautiful beyond words. She then showed me the photo to prove her point. What she had taken a picture of was indeed beautiful. But then I pointed out that in fact, she had used words very effectively to describe how beautiful what she’d photographed was. She looked at me, puzzled. I said:

Source: Eric Dietreich

“Your words, ‘This is beautiful beyond words’ actually do describe how beautiful that scene is. So what you photographed both is and is not beautiful beyond words. Hence it is paradoxically beautiful.”

A philosopher I know, despairing that his favored theory of the mind was likely false, said, “This is too sad for words.” I pointed out that the words he used, “This is too sad for words,” ably describe how sad the situation was. So, the falsity of his favored theory of the mind was both too sad for words and not too sad for words, since words did in fact describe how sad the situation really was. We knew how truly and deeply sad the falsity of his favored theory was by the very words, “This is too sad for words.” I said “The sadness you describe is paradoxical sadness.” I think my comment made him gloomier.

We routinely say things like, “No one goes to that restaurant: it’s too crowded.” The great, ancient Greek philosopher, Parmenides (late 6th or early 5th century BCE), pointed out that when we say things like “Zeus does not exist” we manage to refer to something. If we couldn’t refer to that thing, then the sentence “Zeus does not exist” would be meaningless, and it clearly isn’t. But what could “Zeus does not exist” refer to if not Zeus? Hence, “Zeus does not exist” implies that Zeus exists. “Santa Claus does not exist,” gives us Santa Claus; “unicorns don’t exist” gives us unicorns. In the same way we also get witches, ghosts, and werewolves, and everything else, including round squares.

Thomas Nagel, a well-known philosopher, has pointed out that when we humans adopt an objective point of view on something, we both view that thing from no point of view and from a point of view. He appropriately called that point of view, the View From Nowhere. (See his book by that that title. He claims that this view from nowhere is responsible for philosophy. Good hypothesis, since something has to explain why philosophy is so weird—and why it never makes any progress at all.)

And of course, we all know of the famous sentence:

This sentence is false.

which is false if true and true if false. But since it must be one or the other, it must be both.

The practical reader will at this point object:

“To say that something, X, is beautiful beyond words means only that X cannot be described directly with words. Of course, X might be described in some vague, indirect sense with the words ‘X is too beautiful for words’, but no one takes that seriously.”

Nature abhors a vacuum, according to Aristotle. And most people abhor paradoxes and contradictions. Hence the Law of Noncontradiction in classical logic: “No sentence is both true and false.” That Law turns out to be false (oddly, this Law was first robustly formulated and argued for also by Aristotle). The objector’s distinction between direct and indirect descriptions seems to save the day for someone willing to take that distinction seriously, but indirect descriptions are nevertheless descriptions. And they are paradoxical. Attempting to wall off the paradoxes behind a wall labeled, “Here be indirect descriptions—abandon hope all ye who enter here” only works if one pretends that the wall isn’t there. For to acknowledge the wall even a tiny bit is to conceive and acknowledge what is on the other side of the wall. Walls, it turns out, are themselves paradoxical—as with all boundaries. They both block and do not block our thoughts about what is on the other side.

I leave the reader with this: Physicists do not to this day know what motion is. (If you don't believe me, go ask them.) Zeno’s Paradoxes are as robustly potent today as they ever where, proving that motion is in fact impossible. Yet we move. So, my merely typing this blog and you merely reading it involve the both of us in contradictions.

Contradictions are everywhere. And that is a beautiful thing.