Plato's Forms, Naturally

04 Feb 2021

Imagine drawing a diagram, like in Pictionary, of what an idea is. There are people. There is this cloud-like thing, the idea. The people have a relationship that we might call "knowing", from the people to the idea. That's fine, but can we go further?

Let's ramify the diagram a little bit more. There are still people, but each of them has (within their heads) a mental workspace. Within the mental workspace are things that we might be tempted to call ideas, but for the sake of less confusion, let's make a distinction and call these representations. The distinction is that ideas are common across people, while representations are inside of some particular person.

There is a relationship, that we might call "recognizing" from representations to other, hopefully corresponding, representations in other people's workspaces. I think of this recognition relationship as something analogous to Masonic lodges recognizing one another.

For example a representation in Johnicholas's mental workspace that we might call Johnicholas::Foo might be definitionally (according to Johnicholas) Johnicholas::Bar plus Johnicholas::Baz. Then it would probably recognize a representation Katie::Quux if Katie::Quux was defined as the sum of two of Katie's representation, and Johnicholas::Bar recognized one of them and Johnicholas::Baz recognized the other one.

In C.S. Lewis's The Last Battle, there is a great quote:

So I went over much grass and many flowers and among all kinds of wholesome and delectable trees till lo! in a narrow place between two rocks there came to meet me a great Lion. The speed of him was like the ostrich, and his size was an elephant's; his hair was like pure gold and the brightness of his eyes, like gold that is liquid in the furnace. He was more terrible than the Flaming Mountain of Lagour, and in beauty he surpassed all that is in the world, even as the rose in bloom surpasses the dust of the desert. Then I fell at his feet and thought, Surely this is the hour of death, for the Lion (who is worthy of all honour) will know that I have served Tash all my days and not him. Nevertheless, it is better to see the Lion and die than to be Tisroc of the world and live and not to have seen him. But the Glorious One bent down his golden head and touched my forehead with his tongue and said, Son, thou art welcome. But I said, Alas, Lord, I am no son of Thine but the servant of Tash. He answered, Child, all the service thou has done to Tash, I account as service done to me. Then by reason of my great desire for wisdom and understanding, I overcame my fear and questioned the Glorious One and said, Lord, is it then true, as the Ape said, that thou and Tash are one? The Lion growled so that the earth shook (but his wrath was not against me) and said, It is false. Not because he and I are one, but because we are opposites. I take to me the services which thou hast done to him, for I and he are of such different kinds that no service which is vile can be done to me, and none which is not vile can be done to him. Therefore if a man swear by Tash and keep his oath for the oath's sake, it is by me that he has truly sworn, though he know it not, and it is I who reward him. And if any man do a cruelty in my name, then though he says the name Aslan, it is Tash whom he serves and by Tash his deed is accepted.

In my (admittedly somewhat creative) interpretation, Lewis is claiming that Aslan's representation of Aslan recognizes any representation of honorable behavior as an instance of itself and refuses to recognize any representation of cruel behavior as an instance of itself. In particular Lewis is saying that Aslan::Aslan recognizes Emeth::Tash.

This system, the recognition thing, is a form of holographic self-representation. Holographic self-representation occurs when the whole consists of many parts, each of which has an (approximate) map of the whole. There are a lot of people (the knowers) who each have mental workspaces containing representations that (among other things) have a recognition criterion or function, and these recognition principles generally pick out a class of representations distributed over knowers.

What's the payoff? Well, I think this story helps explain in what sense Plato's or Decartes's dualism is useful even if it is not strictly true. That hyperbole about perfect, timeless, eternal, locationless forms located in a separate realm is literally nonsense, but metaphorically it's teaching us true facts about ideas and giving us tools for working with them.

Why are ideas durable and long-lasting (qualities are similar to, but not quite the same as, timeless and eternal)? Well, the aggregate knowers of an idea are actually pretty large. Ideas are durable like mountains. Second, the aggregate knowers of an idea are fertile and replicate. Ideas are durable like a species. Third, a knower can infect an ignorant person with the idea. Ideas are durable like a disease. Fourth, the idea was invented at some point, and whatever caused it to be invented might still be around and cause a reinvention. (Salt crystals and pyrite plus human genetics might inspire the idea of cubes or right angles).

Why are ideas similar to a cloud in that they have no precise location? It's because they are distributed entities across many knowers; the knowers have location, but it's not valuable to average their locations together to find a center of the idea.

It also moves attention to (in my opinion) important and interesting aspects of ideas:

How does a representation recognize another representation? Maybe it can empathetically model what the other representation would do, by stipulating observable differences (such as "I'm in this head, it's in that head"), and then use itself to predict what the other representation would or definitely would not do. Anything that the other representation does that doesn't match is possibly grounds for refusal of recognition; on the other hand, there's always a possibility that the stipulations might be wrong (Duhem-Quine?).

How should we act at the borders between two historically-separate traditions? Well, we want to merge the same ideas, and we want to distinguish different ideas, right?

In what sense are ideas such as morality universal, and in what sense are they history-dependent? There might be symmetries (Rawls's veil, Kant's Categorical Imperative), and moral rules that respect the right symmetries might be able to replicate (self-assembly means symmetry) across populations. The constraints of "it needs to be highly symmetrical" and "it needs to function", might be stringent enough that some very simple moralities are universal.