Paradoxes fascinate us because they mark the boundaries of our minds. When we try to fathom things that we weren't designed to fathom – like, say, the infinity of space – a paradox traps the train of thought in a nauseating loop-the-loop. We're intrigued by paradoxes because they hint at something beyond our mental reach, and they drive us mad for the same reason. We love them and we hate them, paradoxically.

Perhaps that's why paradoxes are so ubiquitous in language. They're even represented by their own stylistic device, the oxymoron. How many times haven't you heard "silent scream," "one-man band," "holy hell," or "Thinking SJW?" Entire sentences can be paradoxical as well, like this poignant bit of advice my brother once shared on Facebook:

"The moment you embrace imperfection, everything becomes perfect."

Source unknown

Imperfection and perfection are each other's opposites, so how could embracing one bring about the other? It's a good quote, but clearly ambiguous. Paradoxes also famously appear in art. Consider Ascending and Descending, a lithograph by master mindbender M.C. Escher:

"Bathrooms are on the top floor."
-Satan

You've definitely seen it before. The staircase that feeds into itself is a celebrity among optical illusions, even landing a role in Inception. The stairs can't really be going upwards, or downwards, because they end at the same elevation as where they start (wherever you consider the end point to be). But they can't be flat either; the angles and shading make that all too clear. It's a delightfully infuriating paradox that rouses the philosopher in all of us.

And then there are evil paradoxes like this:

"This statement is false."

Satan, again

This isn't a stylistic device, but a harrowing mind game. If we accept that the statement is false, then it must be true, thus making the statement false. Insane yet?

Okay, I've listed a number of paradoxes; now let's try to solve them. The perfection quote is the easiest, so we'll begin there. Perfection and imperfection are opposites, yes, but they're also nebulous words that easily overlap. I doubt you had a hard time gleaning the message: Allow your idea of perfection to encompass the little imperfections of life, and those will cease to bother you. The paradox isn't truly a paradox – it merely plays on the semantic flexibility of two abstract words, delivering an important message with a pseudo-paradoxical punch.

Seriously though, perfectionism easily gets toxic – you're already good enough 🙂

Escher's stairs are trickier, but we'll beat them by examining the properties of perception. We don't truly see in three dimensions, but two; the brain displays the third dimension of depth as diagonals on a plane. That's why this is instantly recognizable as a cube, despite the image being flatter than the one plastic glass of soda that went untouched at the party. Escher used this visual shorthand to his advantage for Ascending and Descending. He angled the lines to resemble our perception of three dimensions, alleging to represent reality. Then he went on to connect the lines in ways that are only possible in a drawing, swiftly abandoning reality. Once again, the paradox isn't truly a paradox. Escher isn't illustrating some glitch in existence; he's just pulling out the representational rug from under us. We can easily solve the paradox by denying the artwork its claim on the real world.

But the last example, the perplexing false statement, is impossible to resolve. There's no way to have those four words make sense without a referential cheat. Yes, this time, it seems like we've come upon a glitch in existence. A loop-the-loop on the fringe of our understanding. Contrast the perfection advice and the lithograph, which were paradoxes only at a glance. When we pondered the possibilities and limitations of their respective media – language and 2D art – we could reconcile them. They're solvable. With this example, however, there's no other medium to ponder, only the bedrock of our minds. It's a bona fide contradiction. Here's another example: If God is indeed all-powerful, could he create a boulder that's too heavy for even him to lift? If he can't, well, he's not all-powerful, because we just found something he can't do. But if he could, that would mean there's now a boulder that God can't lift – in which case you're also not all-powerful, are you God?

(Sorry, I don't know why I keep channeling Satan in this post.)

Let's distinguish, then, between two types of paradox: one that arises only in representations of reality, and one that arises in actual reality and proceeds to entangle our thoughts. We'll call them representational paradoxes and cognitive paradoxes, respectively. (I haven't done much research to find out if there exist better terms already, but that's old news to those of you who know me.) Oxymorons, contradictory quotes, and Escher's impossible buildings are representational paradoxes. They can be fun and stylistically potent. But they're only paradoxical because their media permit it. Step outside those media and into the world, and you'll render the contradiction moot. Cognitive paradoxes, however, can't be stepped out of any more than our minds can. They're the true paradoxes.

Or… and here comes a surprise that you all saw coming: Could it be that cognitive paradoxes are also representational paradoxes?

Perhaps human cognition is just another representation of reality – not truly reality? Maybe our way of thinking is its own medium, with a set of artificial possibilities and limitations? What if true reality is utterly unparadoxical, and cognitive paradoxes are just what happens when a flawed human brain tries to grasp it? In that case, paradoxes aren't cosmic adversaries on our philosophical ventures. They're just the result of flawed representation. Be it art, language, or human thought, they're all mere approximations that invite contradiction. Consider again the mind game with God and the boulder. It's impossible simply because our concept "all-powerful" is a faulty operation. It inevitably implodes. Our thoughts are like lines in a lithograph – able to combine in ways that true reality can't support. But if we could somehow escape our minds, perhaps we could understand the world without flukes. This implies that all paradoxes are solvable. Not by us humans, perhaps, but solvable in the reality that eludes us. Meaning that true paradoxes don't truly exist.

I have more to say, but I'll stop here before both our flawed brains simultaneously short-circuit. Not only from the subject matter, but from the countless little paradoxes I've contrived into the entire text (including its title). I've underlined them all, actually, to maximize both our existential headaches. Sorry, not sorry!