Plato's Theory of Forms: the measure no one gave you

Imagine two white cats, lying side by side. You look and say, without a second thought: they're equal. Except they're not. One is a bit bigger. One's fur leans more toward cream. One has a gap near the ear that the other doesn't have, and if you measured with a better instrument, it would match even less. Even so, you called the two of them equal, and you were not wrong: you did it with confidence, and you would do it again right now. The question that carries the whole class by Professor Rodrigo Bitencourt on Plato is this: where did you get that equality from?

A measure the world never gave you

In the world you see, it is not there. No pair of things you have ever seen in your life has been perfectly equal, not one. And even so, you recognize equality when it shows up halfway, and you know how to say that the two cats come close, and that a cat and a cabinet do not. You have, in your head, a measure the world never gave you.

The one who first asked this question was Plato, and he did not use cats: he used stones and pieces of wood, whatever was at hand in Athens. He inherited the problem from earlier masters, among them Heraclitus, for whom everything flows, everything changes, nothing stays the same for two instants in a row. If that is taken all the way, the consequence is harsh: there is nothing stable to know, and if there is nothing stable to know, there is no knowledge at all, only opinion. Lucky opinion, when it happens to be right.

Except the equality you see in the two cats should not exist, if that consequence were correct. And it does exist. You do not hesitate to say the two of them look alike, and you do not hesitate to say a cat and a cabinet look nothing alike. Something in you already knows how to measure an equality it never saw in full anywhere. That is the crack through which the Theory of Forms comes in.

What eidos actually means

When you hear "world of ideas," your head probably goes to somewhere inside you: an idea is what I have in my head, what I think, mine. Everyone falls for this, because in English the word pulls that way too. But that is not what Plato is talking about.

The Greek word is eidos, and it means appearance, it means essence. Eidos is a thing's metaphysical structure, its ontological structure. What is at stake here is form and the essence of reality, not an idea sitting in your head. Further on, Professor Rodrigo Bitencourt, in the class, also distinguishes substantial form from intentional form: the same form present in the substance, in the real cat, is the form present in your mind when you think about it, except there it is intentional. That is why, for Plato, reality lies in the eidos, in the essence, and concrete things take part in that essence.

So when Plato talks about something "equal in itself," he is not referring to your personal concept of equality. He is saying that there is a thing called Equality, which is not any pair of equal objects, which does not change when your mood changes, and which is exactly what allows you to recognize the equality in the two cats.

The Equal itself, in the Phaedo

It is in the Phaedo that Plato works out the argument most carefully. In Maria Teresa Schiappa de Azevedo's Portuguese edition (Coimbra, Livraria Minerva), translated here, he states: "the existence of something 'equal' [...] I do not mean a piece of wood equal to another piece of wood, or a stone equal to another stone, or anything of that kind, but a reality distinct from all of these, standing beyond them [...] the Equal itself" (Phaedo, 74a).

And he adds, a few lines later, that the equal things of this world tend to identify themselves with that Equal itself, but "fall well short of it" (Phaedo, 75a-b). They owe it something. And no one can owe something to a thing that does not exist.

Notice that the argument does not even need your eyes to work, which is why it is stronger than it looks at first read. Plato asks, still in Phaedo 74b, whether it is not true that the same stones and the same sticks "seem equal to the eyes of some and not to the eyes of others." If equality depended only on what each eye captures, it would change from person to person, and from instrument to instrument, exactly like what happened with your two cats when you went to measure them up close. The standard that lets you call two things equal, even when the senses disagree with each other, cannot come from the senses.

More real than the cats

Here is the bold step, the one that crosses two thousand years: that thing, Equality itself, is more real than the cats. And it is not a metaphor. Plato means real, literally.

The two white cats are going to die. The equality between them is not perfect today, and it will be less perfect tomorrow, for instance when one of them puts on weight. Everything you point at with your finger is on its way to stop being what it is. Equality is not: it does not gain weight, does not age, does not change depending on the day. Two thousand four hundred years after that conversation in Athens, it is still exactly the same thing.

So answer this: which of the two deserves the name "real" more? What exists today and vanishes, or what never stops existing?

A new criterion for real

We are used to calling real whatever can be seen and touched. Plato proposes another criterion: real is what endures, what does not change. And, by that criterion, what you touch is nothing more and nothing less than the shadow, and what you only reach by thinking is the body.

If Equality is not in any object of this world, you did not learn it by looking at the world. No teacher taught it to you, you did not memorize it, and even so you have it. That is the account that opens the class's next question, the one about exactly where this knowledge that no one gave you comes from, and it is worth going back to it after watching the whole video.

This also explains why the change of criterion is not a matter of vocabulary. If real were only what you touch, the two cats would beat Equality without a fight, because they are right there, lying down, and Equality is not anywhere you can point your finger at. But if real is what endures, the contest flips: the cats will change until they stop existing, and Equality will not. Plato is not asking you to look down on what you see. He is asking you to notice that what you see never stays still long enough, on its own, to hold up the word "real."

Go back to the two cats. They are still not equal, and nothing about that changes. What changes is that now you know what you were doing when you said they were: you were using a measure no one gave you, that you did not buy, and that is not registered in your name.

Continue: Plato's second sailing: the method of the Forms · Plato's Phaedo: three passages to read first · Recollection in Plato: recognizing what you never saw · Truth as coherence
Source class: F&T 2.4 - Platão I: o Mundo das Ideias e a busca pela transcendência