The Trouble With Symmetry

George Han · May 2026 · Philosophy Logic

Debates over burden of proof feel like a fair fight. But do both sides really start from neutral ground — or did one of them get a quiet head start that nobody noticed?

I came back from a run one morning with a question I could not shake. In a debate, one side says “X is right” and the other says “X is wrong,” and we treat it as a fair fight between equals. But did the two sides really start from the same neutral ground? Or did one of them get a quiet head start that nobody noticed?

Take burden of proof. We like to say it falls on whoever makes the extraordinary claim. It sounds fair. But it never answers the obvious question: who decides what is extraordinary?

To an atheist, saying God exists is the bold move, because it asserts that something is there. To a believer, saying God does not exist is the bold move, because it asserts that something is missing. Each side feels like the default. Each side feels like its opponent is the one reaching too far. So which one is actually the default? My answer, after a lot of circling, is neither. The neutral ground was never there.

What looks like a logical rule turns out to be a habit in disguise. And underneath it sits a quiet assumption we almost never question: that presence is the real thing, and absence is just the lack of it.

I do not think that is right. Absence is its own status. The fact that we usually notice a thing first and its opposite second tells you something about our minds, not about the world.

Where I First Felt This

I first felt this as an undergraduate, arguing about whether we should define imprisonment as negative punishment in an introductory psychology course. Everyone wanted to call it a loss of freedom. But you can describe the very same cell, the same prisoner, the same long hours, as a gain of confinement. Nothing physical changed. The only thing that moved was where I chose to put the zero.

Measure from a life of liberty and it looks like subtraction. Measure from empty space and it looks like addition. The words “positive” and “negative” were never properties of the punishment. They were properties of my starting point.

“Positive” and “negative” are not properties of the thing being measured. They are properties of where you chose to put the zero.

A Simple Test

That gave me a simple test. When you meet an asymmetry between presence and absence, ask one thing: does it live in the world, or does it live in where you chose to put your zero?

Sometimes it is just the zero. Take potential energy in physics. You can add any number you like to every value and not a single real prediction changes, because only differences ever show up. Whether something reads as plus five or minus five is a free choice. My imprisonment example is the same. So is most of the arguing about burden of proof. In all of these, the head start in the debate was a trick of the eye, produced by a baseline nobody agreed on.

And if someone ever insists the ground was perfectly neutral all along, you might gently ask them where, exactly, they put the zero.

This is a short thought, not a full argument. The test — ask whether an asymmetry lives in the world or in your zero point — has limits, and there are genuine cases where presence and absence are not symmetric in any trivial way. But as a first pass on a surprising number of arguments, it does more work than you might expect.