The number two has no physical existence, yet no one doubts it's real.

Dismissing justice as "just an idea" is an argument that also eliminates math.

Numbers and ideals differ in precision, not in reality.

Every act of counting already depends on Platonic Forms.

I've written before about how we're all already Platonists when it comes to geometry—nobody looks at an imperfectly drawn circle and concludes that circularity itself is "just relative." But recently I realized there's a stronger version of this argument, one that's harder to sidestep.

A drawn circle is at least something physical. You can see it, touch it, erase it. The skeptic can still say, "Circles are grounded in physical reality. Justice is different; it's just an idea in your head."

So let's talk about the number two.

Point to it. Not two apples, not two fingers, not a numeral on a page—that's just a symbol. Point to twoness itself.

You can't. Two has no weight, no color, no location. It's never been photographed or observed under a microscope. It has zero physical existence.

And yet would anyone argue that two is "just relative"? That mathematics is merely a cultural construction? Of course not. Two is one of the most reliable, universally functional realities we know. It works across every culture, language, and historical period. It works whether anyone believes in it.

Two is a purely mental reality that exists nowhere in the physical world, and it's among the most real things in human experience.

Now tell me again that justice can't be real because "it's just an idea."

The Skeptic's Dilemma

The standard objection to ideals like justice goes like this: You can't point to it. You can't measure it. People disagree about what it means. Therefore, it's not real.

Every one of those claims applies to the number two. You can't point to it. You can't measure it. You measure with it, which is a different thing entirely. People across history have used different numeral systems. Yet the underlying reality of twoness is as solid as anything we've encountered.

The person who dismisses justice as "just an idea" while relying on arithmetic has already conceded the principle. They've accepted that non-physical, purely intelligible realities can be reliable and functional. They just haven't noticed they've done it.

Not Equally Precise, but Equally Real

I'm not claiming justice works like arithmetic. Numbers map onto experience with extraordinary precision: two plus two equals four, no exceptions. Justice is messier. Reasonable people disagree about its requirements in particular cases.

But this is a difference of precision, not of reality. A compass is less precise than a GPS. Nobody concludes from this that North doesn't exist.

Plato understood this gradient. In the Republic, he placed mathematics at the second-highest level of knowledge—it's the clearest example of the mind grasping non-physical reality. But he placed Justice and the Good above mathematics. Not because they're less real, but because they're more fundamental and therefore harder to see clearly. The difficulty of defining justice isn't evidence that it's unreal. It's evidence that it's deep.

The ancient Greeks didn't consider one to be a number. They called it the monad, the unit. It wasn't first in a sequence; it was the principle of unity that made counting possible.

When you count three apples, each one is unique: different size, different blemishes. No two are identical. Yet you call them all "apples." You can only do this because you possess the concept of apple-ness (the Form), and the numbers count instances that participate in it.

This means every act of counting is implicitly Platonic. The "one" represents the unifying idea. The numbers enumerate particular instances. You've been a Platonist every time you counted your change.

Justice works the same way. It's the unifying principle that lets us recognize a fair trial, a returned wallet, and an equal division of resources as instances of the same thing—the way we recognize different objects as instances of "apple." The Form of Justice is less precise than the Form of Apple, which is less precise than the Form of Triangle. But the structure is identical, and the reality is of the same kind.

Justice doesn't exist the way a rock exists. But neither does the number two. Neither does a proof, a theorem, or a perfect circle.

Yet these things are real enough to build civilizations on. They're intelligible realities—they exist in the mind, and they work.

The number two doesn't exist, in that you can't find it in the physical world. But it really does, in that it's one of the most reliable realities we know. Justice doesn't exist, in that no one has ever held it. But it really does, in that every functioning society depends on it.

The question was never whether these ideals are physically real. The question is whether ideas can be real. You already know the answer. You've known it every time you counted to three.

© Psychology Today