Wednesday, April 29, 2009

The Shadow's Form

“No one ever looks out a window and sees a tree.” This bit of wisdom came to me from Donald Davis by way of Jim May. It’s not that trees are invisible. That’s just silly. It’s that “tree” is simply the word we assign to the thing we see. Someone who studies trees looks out the window and sees an oak or a pine or a redwood. Someone looking out the window of their childhood home sees the old swing or the tree fort wherein many summers were spent pretending to be pirates or cowboys. Sometimes, too, the person looking out the window sees the tree as the shade over the burial spot for a beloved family pet or happy afternoons resting against its sturdy trunk while reading a book or talking to friends and family. Sometimes, too, we see the intricate patterns in the bark, the leaves, the giant scar from a long ago lightning strike that could not destroy the great plant. Carpenters may see the tree in board feet, carvers a grain that would be perfect for making a bowl. We don’t see a “tree.” What we see is the sum of our experiences. We see ourselves in the tree when we look out the window. It came up in my Friday intensive session with Jim May and Megan Wells. The storyteller has a story, but the reason for picking that story comes from the storyteller’s own experience. There’s a screen playing out images in the teller’s mind. The audience has screens, too. The goal is to put a screen between the teller and the audience, to create a shared experience, a shared understanding. The goal is to, just for a moment, show everyone the tree as the teller sees it. Plato would tell you that there’s an ideal “Form” of a tree somewhere in the firmament and that the trees we see out the window are nothing but pale reflections of that one, perfect tree. We carry this teleology with us in Western civilization. There’s the world, we believe, and then there’s the world as it ought to be. Every time we look at the world and see something that’s just not right is a disappointment. This fuels Millennialism. See, the religions that are interested in such things tell us that there is the world that is and the world that ought. There are the people that are and the people that ought. We do not live in the world that ought and are not the people who ought. So we’re on the clock. Either we take that single, homogenous Platonic form or the heavens will take it upon themselves to make it happen. But what happens to that wonderful tree in the front yard where squirrels chase and chatter? What happens to that old one in the back with the tire swing? Why do they need to be destroyed and replaced with perfection simply because they don’t live up to a Platonic ideal? What matters more? That the tree is perfect or that it has provided shade and sustenance for hundreds or thousands of creatures great and small throughout its long life. Imagine the stories a tree could tell. Some could tell of the rise and fall of nations. Some could tell of the passage of great migrations of animals. Some could tell of children running around, laughing, and growing up. Some could tell of the encroachment of civilization and the great forests lost to logging and progress. The stories those trees could tell would put the lie to our own pathetic decades strutting about and acting like human industry and endeavor is all that matters. What happens to that tree with the arrival of the new heavens and the new Earth? What happens to its stories? What happens to your stories when that happens? What happens to mine? Don’t we need the struggle and the pain to appreciate the good times, anyway? Isn’t it the imperfections, the variations from the Platonic ideal that make life worth living? I took a workshop on Saturday morning called “Befriending the Jitters.” Not “Overcoming the Jitters” or “Avoiding the Jitters,” but “Befriending.” Andre, the storyteller who developed it, was in the same intensive I was the day before and was able to continue on Jim May’s theme of Carl Jung’s “shadow.” He told us that we weren’t going to unpack all of the reasons why we were afraid to tell stories. Instead, he told us we were going to play to our skills. We were going to tell a story about our jitters. We built a character around our fears. We stood up and told everyone else about that character while using our bodies and words to take the shape of those things that we feared. We acted out our fears, gave them a name and a face and a story. Then we created another character. This character was exactly the opposite of the first. It wasn’t who we felt we were, but who we felt we wanted to be on stage. We acted out that story, too. Neither character was to be given our name or our face. One of the other people in the workshop tried to give the second one her name. I'd given the first mine before scratching it out. It was hard to separate the exercise from reality. But it was necessary. Then, and this is crucial, we wrote a story. In the story we wrote those two characters met, interacted, and learned from each other. The self and the shadow met, interacted, merged. It’s okay to be afraid. It’s okay to have doubts. It’s okay to have imperfections. The awareness of fear and imperfection is what drives us forever onward to bigger and better things, to higher heights. The trick is to work with them, not to cover them up or run from them. When that happens our shadow drives us, makes us do work we don’t want to do in order to go places we’d rather not go. I suppose it’s inevitable that I thought about this in conjunction with my own musings about past experiences going on church retreats. I spent many weekends going to woodland lodges in Wisconsin and trying to rid myself of my shadow, my sin. One year we wrote our sins on sheets of paper and symbolically nailed them to a cross. Another year we wrote them on flower pots and broke them. It was, I suppose, cathartic. But it wasn’t cleansing. The sins I nailed to that cross were probably the exact same ones I wrote on that flower pot. When I drove back down the byways of Wisconsin afterwards I’m sure that my thoughts were more around all the ways I needed to work harder when I got home to be good and cleansed and holy. In the back of my mind I’m sure I was thinking of the inevitable fall off the mountain. Mostly, I think the only thing I ever learned on a church retreat was that simple truth from Razor’s Edge: It’s easy to be a holy man on top of a mountain. I also learned time and again that I did not live up to that Platonic ideal of human form given apotheosis by the weird strain of Christianity to which I’d unfortunately dedicated my life. I could never live up, only learn to grovel and promise to try harder in the future. It was a burden I carried with me and rarely managed to put down for more than a moment or two. My shadow, however, is me. I cannot cut the chain that binds me to my shadow and cast off. The lie of the Christianity I have cast off is that I should and that I should want to. The lie is that I cannot be me until I have sent my shadow away. I cannot take on my preferred form until I've gotten rid of a part of myself. The simple fact is that I shouldn’t cut that chain, anyway. My shadow makes me what I am just as much as the self I’d rather the world see, know, and love. When I got on the road on Sunday afternoon I didn’t feel as though I’d been cleansed. I did, however, feel that I’d taken one halting step towards being whole. This was a feeling I’d never gotten from sermons. It seems to happen all the time when I encounter stories.


PersonalFailure said...

Joy is in the imperfections. It is our weaknesses and foibles that make us human, that make us capable of sympathy, and in the end, love.

Too many people seem to want a world without love.

Trevor Morgan said...

It’s okay to be afraid. It’s okay to have doubts. It’s okay to have imperfections. Thanks for posting this. I need to be reminded that it's ok to attempt things that I'm not already perfect at. I've been reading a lot recently about the impact of Plato on christian thought - it's interesting to hear your take on it.

hapax said...

Uh, Geds -- nice smackdown of a straw-Plato, there.

(Yeah, you had to know that was coming, didn't you?)

I mean, you CAN use Platonism that way -- just as you can use any philosophy as a club and an excuse.

You get out things what you bring to them. If you are insistent on being an asshole, you're not going to produce anything but shit.

But this weird demand for oppressive homogeneity certainly isn't inherent in the forms of Platonism I was taught or practice.

The Woeful Budgie said...

Hey, someone smart once told me that "beauty is beauty in spite of perfection". :)

The exercise you describe reminds me of something I did a while back, where I tried to paint my shadow. Colors opposite to my favorites, traits I found annoying in other people, whatever. After it dried a bit, I ended up painting the person I present over it, and before that quite dried, I took a spray bottle to it so that some of the persona ran off in drips and patches, letting the shadow through. I'm not sure how I felt about the final product---it feels a bit forced and silly---but it was kind of a fun process.

The problem with trying to get rid of your shadow, is you push down a lot of good things along with it. Perhaps some of the best things.

Geds said...

I'm not talking Platonism itself. I know a bit about Forms and all.

I use it as a jumping-off point to a discussion of fundamentalist Christianity and it's belief that there is exactly one and only one way to be.

You never seem to want to give me credit for poetic license...

Geds said...

Also, Budgie, I didn't know you learned all your important life lessons from Roger Clyne, too...


Geds said...

Besides, hapax, you have to know that I'm not going to agree with the Platonic Forms, anyway.

There is no innate "treeness" to the tree outside my window. There is a tree and we call it that because that's the term we give to leafy, trunked things. That tree neither contains nor is built around a blueprint for treeness.

The evolutionary process simply dictated that the tree would grow in the way it grows because that gives it the best chance to survive and pass itself on. We later came along and said, "Hmm, I think I'll call that a tree." It was then decided that there is an inherent tree-ness to that tree.

But the trees themselves are constantly changing. If the conditions change enough, the trees in future generations may well cease being trees and instead become something else.

Evolution itself refutes the Platonic ideal of the form. Life isn't interested in making trees. Life is interested in making life. If you can say "life" is something which has agency at all. And, technically, you can't.

It is in the combination of Plato and Genesis that I take my original issue, anyway. Christianity inherited the story of Adam naming the animals. Western civilization inherited the concept of the form.

Those two things, I would argue, intertwined. They become apparent in the one size fits all evangelism approach taken by your average evangelical. They culminate in the hope for an orgy of destruction that ends with Earth being wiped away and replaced by New Earth in the End Times.

For what are the Buck and Rayford of Glorious Appearing if not corrupted, Christianized versions of Plato's form? Christianity of this variety says that there is exactly one correct form of human and all who make it to the New Earth will take it on.

That's the specific variety of the form I rail against. I don't so much care about Plato's, since he was trying to be descriptive and not prescriptive.

I don't think Plato believed any single plant or animal or object had a Form that was any better than any other plant or animal object. He simply believed there was a teleological reason things appeared the way they did. Every table had the essence of tableness because the table was a form and to truly understand the table in front of you you had to understand the tableness.

The table in front of me has the shape it does because it's a convenient way of holding things. If I instead called it a book it would still have the same shape, size, and purpose it currently holds. I call it a table and my kitchen table a table because they serve similar functions. The overall term "table" then serves to facilitate communication.

Moreover, as with the tree I introduced the entry with, no two people look at something and see it in quite the same way. And if there's no way for our perceptions to line up 100% when looking at the same object, does that not negate the idea that there is an idealized Form of that object? Do a billion unique perspectives that vary in difference from inconsequential to huge add up to a single Form of anything?

And if we had no observers with words to describe the Form of the tree or dog or stream would not the tree or dog or stream still exist? If we called that tree a telephone would it suddenly not be a tree as we know it?

PersonalFailure said...

Christianity of this variety says that there is exactly one correct form of human and all who make it to the New Earth will take it on.
Can you imagine the horror of that?

I think that's what scares me most about people who celebrate that type of belief. There will be no room in their brave new world for you or me or anyone like us. The quirky, the eccentric, the neurotic, the flawed: we will all disappear. We have no place in their perfection, nor excuses nor reasons.

Success is boring, come fail with me. ;)

hapax said...

Geds, I'm willing to take at face value that you were using the idea of Platonic forms as a jumping off point. Sorry if I missed the metaphor; I'm usually better at things like that.

Unless you want to turn this comment thread into a forum on Platonic philosophy, though, I'll just leave it at saying that I would answer practically every assertion you made about Platonic philosophy in your follow up comment with "Umm. No. That's not how it works at all."

Very very short version: Plato (and those who follow him) wasn't the least bit interested in "Why are things the way that they are?"

What interested him (in this respect) was "How do we know the things that we think we know?"

It isn't very surprising that certain extreme variants of Christianity may have mangled this into a prescription for "How Things Should Be". But I think the blame should lie on those who misinterpret, not the victims of their ignorance.

Geds said...

But if your question is, "How do we know what we think we know?" how is that fundamentally different from, "Why are things the way they are?"

If you're going to create an ineffable Form of table-ness, does that not make an implication of how things are compared to some form of how we think things should be?

hapax said...

Geds, my allergies must be making me really stupid today, because I've read your last questions three times and they make no sense whatsoever to me.

You can't seriously be equating epistemology with ontology. One is inherently subjective, the other (depending on your worldview) generally objective.

And neither has much to do with "the way things ought to be" -- I'm not even sure what sphere that is. Ethics? Theology? Politics?

Or has this all wandered so far off topic that we should just give it up as a bad job?

Geds said...

We may well have to. I think we have a fundamentally different response to Platonism.

I also think I'm rather less of a fan than you are.

See, in general I like the Simile of the Cave for its illustration. However, I see the Simile as offering the basis of the Forms and creating a false dichotomy wherein the basic claim is that there is the enlightened one who sees the source of all light and everyone else who is trapped. I don't believe there is a single, metaphysical source, therefore I reject the notion of the Form itself.

I do believe that there are those who are endarkened and those who are enlightened, so I like to overall narrative. But my response to anyone who claims a single source is, "This is my truth, tell me yours."

And you may well tell me that I'm drawing a false parallel between the Simile and the Form, but I've always seen the two notions as deeply interconnected. It's also been a good ten years since I've given any of it much deep thought. I never really liked the Greek philosophers that much.

Fiat Lex said...

I'd like to jump into the forms debate for a bit.

Good post, by the way. Sounds like that workshop was an awesome time!

But if your question is, "How do we know what we think we know?" how is that fundamentally different from, "Why are things the way they are?"The first question is about epistemology. Epistemology asks how it is we come to know things. It tries to unpack and explicate the process by which things outside the self are brought into the mind, and transformed from sensory data into experiential knowledge.

The second question is about teleology. Teleology is the study of purposes and goals. Teleology only asks "what is it?" in the context of trying to answer the question "what is it for?" It is a wonderful discipline for analyzing the actions and motives of human beings. Humans have purposes, goals and motives which other humans can understand. And in some cases, such understanding can help create a framework within which we can negotiate with one another. But it is a shitty, useless thing to apply to the study of nature. Or anything else that may, in fact, lack the kinds of purposes and intentions that render questions of teleology meaningful.

Allowing epistemological exploration to be supplanted by teleological isogesis is my principal complaint against modern-day Christianity.

Geds said...

Fiat Lex:

I totally agree with your final point.

And I think that you helped work around to the point I was trying to make. You need epistemology to study nature and teleology to study manufactured goods. The purpose of a table or chair or 2009 Hyundai Genesis is part and parcel with what it is. I do not build a table if I don't need to put something down on it.

Teleology was, for all intents and purposes, the default way of looking at the natural work, too, for the vast majority of human history. The assumption was that the universe was there for a reason and that the creator or the universe itself had some sort of end goal in mind. We don't have to make that assumption any more.

To bend the Simile of the Cave to (and, possibly, past) the point of breaking, if Plato's philosopher and I walked out of the cave at the same time, we'd see two different things when we looked at the sun. He would see the source of all truth which makes all else but reflection and shadow. I would see a giant fusion reactor built from millions or billions of years of chemical reactions.

To pull back to the Forms, then, that difference in the way we see the sun renders the concept moot.

As long as you're only looking at the initial stages of the Simile it works quite well. When you go from the shadows cast on the wall by the people parading back and forth in front of the fire to the objects being used to cast the shadow there is a leap of understanding.

However, looking at the fire tells you nothing more about the objects being carried. They would have the qualities they have whether they were out in sunlight or in a pitch-black room. Deciding that the fire contains any further revelation, then, is a mistake. To then make the final leap and say, "Ah ha! The sun must be the ultimate fire!" is a further mistake.

Now, of course, the "fire" and "sun" are stand-ins for other things. I'll leave it up to you whether you want to say human logic and reason or the creator or whatever. But it should now go without saying that I don't think a tree gives a flying crap what I think its purpose is. I may rest under its shade, but it doesn't exist to keep me from getting a sunburn...

Fiat Lex said...

And, as my dad would have enjoyed pointing out, "what is it again that makes you think you're native to this planet?" We get sunburned in the sun, frostbitten in the winter, need salt vitamins to keep our bodies healthy, etc...

I'm not sure that my point is. Kind of drunk right now. Yay tequila.

As I was discussing with Pearl earlier today, Plato was a bit like Freud. His ideas may have been crude, but they were the first hacks in the sheer cliff of our boundless ignorance about ourselves and our relationship with the larger world. Maybe Aristotle did things with philosophy that never occurred to Plato, and maybe Jung did things with psychology that never occurred to Freud. But the later thinkers dug a little bit deeper into the veins of wisdom exposed by the earlier ones. And if modern people, in our self-centeredness, want to go back to those rough-hewn thoughts, it is understandable. Even if it is not something you and I wish, upon sober reflection, to condone.

hapax said...

Geds: "He would see the source of all truth which makes all else but reflection and shadow. I would see a giant fusion reactor built from millions or billions of years of chemical reactions."

Well, I'm sure you're familiar with this passage from HOGFATHER: (link because I think the whole passage is worth reading, not just the best-known snippet)

This, I think is why epistemology is important to our understanding of ontology (if not necessary teleology, which is is a profound misuse of Platonism, and is a product of Original Sin in my opinion)

To the best of my knowledge, Pratchett is neither a Platonist nor a theist. But his writings are probably at least as central to my world view as Augustine's.

Honestly, though, I think that you are reacting to an excessively literalist reading of Plato, and Platonic interpretations of Christianity.

It is possible, you know, for more than one understanding of a sun, a tree, or a story to be true at the same time.

(Neither "fact" nor even "not a lie" an isagoge for "truth", for that matter.)

But now I'm going off into the airy-fairy realms where philosophy starts to blur into poetry, and people who just want to chop some firewood, dammit, start throwing heavy objects at people like me.

Geds said...

Would this be a bad time to point out that the only Pratchett I've ever read is Good Omens?

Bear in mind, my original reaction was to the Christian/Plato interface. I get the point that there's a difference between epistemology/ontology/teleology. I also get that the Christian use of Plato is flawed (look at today's After the Flood entry).

Even so, I reserve my right to reject Plato's Forms. I don't think that we're living in a shadow universe which is a simple reflection of the perfect universe of Forms. Thereby I can find Plato's discussion of Form interesting. I can find his attempts to find a perfect form of governance based on them a worthwhile topic of conversation.

But we hit a point where I have to point out that I don't believe in the philosophical underpinnings of the Forms.

And the fact is that I see a great deal of danger in pointing out that there is a perfected or perfectable form of this, that, or the other. It is those arguments that invite teleological follow-up.

Overall, too, it's not at all apparent that Plato believed in the Forms until his dying day. Aristotle's Metaphysics certainly indicated that the pupil didn't fully agree with the master. Given that it wasn't a perfect, unassailable philosophy, I see no reason why I can't critique it based on the negative implications I can see coming out of the philosophy and use the way others have looked at it as evidence.

Does that mean it was Plato's intent to see his Forms fused with Christianity? No. I can't hold that against him, then.

But I'm still fully allowed to see it as a flawed way of looking at the world. I'm basically a naturalist who sees no teleology in nature beyond the simple idea that life is ever attempting to propogate itself. That, at least as I see it, limits the use of Form in discussing the natural world.

hapax said...

Geds: "But we hit a point where I have to point out that I don't believe in the philosophical underpinnings of the Forms.

And the fact is that I see a great deal of danger in pointing out that there is a perfected or perfectable form of this, that, or the other. It is those arguments that invite teleological follow-up."



I don't really care whether you believe in "The Forms" or not. I don't care whether Plato did.

I'm not entirely sure that *I* do, depending what you mean by "believe in."

I am merely arguing about a very limited topic -- that you are misrepresenting what the concept means.

I don't doubt that the concept of the forms can be MADE to be teleological -- that it is the PURPOSE of this particular tree to attain Perfect Treeness, and the PURPOSE of every human being to achieve Perfect Humanity.

But *that isn't what Plato said.*

That *isn't how he has been generally understood in Christianity* (or any of the other religions very heavily influenced by Platonism, including Judaism, Islam, Gnosticism, Manicheanism, and some Western interpretations (or bastardizations, take your pick) of Buddhism.

The metaphor of the forms isn't teleological. It just isn't. If you've got problems with teleology, then make that your villain.

The metaphor of the forms is ontological, partially, but primarily epistemological.

Aristotle rejected it unequivocally on both grounds.

I think that Aristotelian ontology is even more problematic from a naturalistic point of view, but there's no question that his epistemology is much more useful. In fact, modern Western science is almost certainly impossible dependent on a Platonic epistemology.

If your definition of "the Real World" is "the world I can see and touch and measure", why yes, the doctrine of the Forms is highly irrelevant, and probably counter-productive.

But I thought that this was about story-telling, not about writing up research results.

And (for me, at least) the whole point of storytelling is to invest each individual detail, and the narrative as a whole, with a significance beyond itself.

(Honestly, I'm not being quarrelsome here. This is a topic of immense interest to me, personally. A great deal of my personal life journey can be summed up in Pilate's heedless question "What is truth?" and *the fact that he never receives an answer.*)

Geds said...

See, that's why it's worthwhile to keep these sorts of conversations going some time.

I'd literally never thought of the idea of the Forms as related to the archetypes of myth and story. I don't know that I would actually say that Plato had stories in mind when he formulated the idea, but it's an interesting way of looking at the whole storytelling thing I do.

Of course, you then have to contend with my way of looking at storytelling. It's my firm belief that the archetypes of the story hold a great deal of power, but the stories themselves must be updated again and again, lest we remain trapped in outmoded ways of thinking. It's why I tend to go back to Big Fish when I discuss storytelling. Because inasmuch as it was a wonderful story, it had a huge, gaping flaw: the wife's job was to remain at home and wait for the husband to return from his adventures.

I decided long ago that if I ever got married (and, dagnabit, I'm nearly 28 and I'm still saying "if" there) it wouldn't be to someone whose sole ambition was to housewifery. Now, the weird thing is that I don't see anything wrong with someone becoming a house wife (or a house husband), at least for a time if that is a necessary or desirable option. But I knew a lot of girls who simply wanted to get their Mrs. degrees and let the ring on their finger define who they were. Not only did I never see the appeal in that, I never saw the appeal in entering in to a relationship with someone who saw the world that way.

I'd prefer someone who doesn't want to just sit at home to listen with rapt attention to her husband's tales of adventure. I'd prefer someone who has her own goals and desires. I'd prefer someone who doesn't to a certain extent make me her entire world.

So when I tell stories, one of the archetypes I look to shatter is that of Sleeping Beauty, whose only task is to wait for Prince Charming to come along.

And I've totally forgotten what that has to do with the Forms...

Sniffnoy said...

Huh, I've generally just considered Plato's forms as a precursor to (and basically obsoleted by) our modern notion of equivalence classes; certainly nothing teleological about those. But then I don't actually know very much about Plato; is that just really off-base?

Geds said...

Y'know, something tells me this is the wrong place to ask that question...

hapax said...

Sniffnoy, I don't know from mathematics (as a cursory glance at my tax forms would reveal) but after trying to slog through the Wikipedia article on equivalence classes, I don't think so.

Plato (and those who follow his ideas) use the forms to answer two related questions:

1. When I look at a particular tree, how do I know that it a tree and not a zebra?

2. What makes trees tree-ish, and zebras zebra-ish, anyways?

Plato postulated that there is a Real-er than real "Form" (or Idea or Archetype) out there of "Tree", and all individual trees get their tree-ish-ness by "participating" in some way in that Form. We know that it is a tree because in some way we apprehend the Tree inside the individual tree.

(Also, a tree is more tree-ish the more it corresponds, or participates in the Idea of Tree -- thus an oak tree is more tree-like than a banana-tree, which is actually an herb, although we apprehend a certain tree-ishness in it as well. This particular notion *can* be twisted to become prescriptive and teleological, as Geds rightly points out, but it isn't inherent in the teaching)

Also, later thinkers realized that each individual has to participate in a multiplicity of forms: Being, Vegetable, Tree, Oak, White Oak, all the way down to "Haeccitas" or "Thisness" (the Form of particular individuality) at which point William of Ockham threw his hands up in the air and took a razor to the lot of 'em.

Forms take on a spiritual dimension when the realm of Ideas becomes identified (in Neo-Platonism) with the Logos, the Word / Mind / Plan of God. This is also where you get into the issues of, say, semiotics and the intentionality of narrative archetypes and other fluffy-type concepts that make me go all snarky on other people's blogs.

Aristotle, for what its worth, used "form" as well, but it means something very different in his ontology. As for his epistemology, classes (genera and specie) are in a technical sense imaginary, "abstracted" by the observer from perceived similarities among the individual members of a group.

I think that the equivalence classes (if I understand them aright) are more similar to this Aristotelian sense, although mathemeticians do sometimes get very Platonic (even mystical) about the transcendent reality of mathematical concepts (see, e.g., Bertrand Russell)

Is that at all helpful?

Sniffnoy said...

Well I'm not sure I understand all that but it does help, thank you. The example I had in mind was something like evenness and oddness. We want to treat the abstract ideas of "evenness" and "oddness" as concrete objects, how do we do it? Just take the set of all even numbers, and the set of all odd numbers! Bam, sledgehammer abstraction! :) But really I think I may have been a bit too narrow - really this (pretty much) what the whole notion of "set" does, as a set pretty much *is* a property - or at least was back in the days before axiomatic set theory, but not going to get into such issues here. The point is that they're extensional. And if you want to take an abstraction and make it concrete, it's a simple and yet complete; it has all the information.

But I guess the matter is complicated by the categories under consideration; the examples you give are all fuzzy and not necessarily well-defined, and so probably better represented [mathematically, of course :) ] in other ways; you can't just take the set of all red things because not everyone agrees what "red" is. So quite possibly you can't accurately represent such an abstraction at all until you understand the data structures of the human mind, which we are quite far from! Are Aristotle's "forms" meant to be universal or per-observer? It's not clear from your description...

Also I guess the problem with what I'm saying is that for all I know, forms, in Plato's conception, are intensional? (If they had such a concept as extensional vs. intensional.) Probably are offhand. Though I mean intensional notions of such things as "function" preceded our modern extensional one, and after all it led to Aristotle's, so...

I guess really the main problem with that idea is that I was thinking of simple things which we know how to represent mathematically, and they're thinking of complicated things that we don't. Still, when we figure that all out, I don't see any reason not to abstract with the metaphorical sledgehammer. They're just a precursor to something we don't have yet. :)

...yeah, I'm not really sure what my point there was.