| Superstitionblogging 31-39: Platonic Forms |
[Nov. 8th, 2012|11:29 pm]
Scott
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Epistemic Status: Hastily written and confusing, for which I apologize, but I think mostly right. Almost all taken from the Less Wrong sequence on words, which I keep trying to convince people to read because it contains like half the secrets of the universe, and people keep on not reading it. But then they keep on thinking I'm super-smart when I shamelessly plagiarize some of its insights, so I guess it all works out.
Theory of Forms is the first interesting and controversial philosophical argument in Last Superstition. Feser tries to defend Plato's Theory of Forms, even though in the end he's going to say Aristotle's somewhat-different Theory of Forms is better.
The argument goes sort of like this:
There are various instances of triangles in the world, for example the triangle that might be on the third page of my geometry textbook, or the triangle on...hmmm, this attempt at example generation is actually making me realize how few triangular things there are in the world. I'm looking around my hotel room for triangular objects and not coming up with anything. Now I'm giving up and googling "what sorts of things are triangular?". It's suggesting the "MEN" sign on bathrooms. You know, until this moment, I never realized that the "MEN" sign was usually triangular and the "WOMEN" sign usually circular. I wonder if this derives from a stylized representation of the sexual organs.
Uh, moving on. There are various instances of triangles in the world, for example the triangle on the third page of my geometry textbook, the triangle on the men's room of the hotel. These triangles are all somewhat different: some are white, some are blue, some have a stylized picture of a man on them, some don't. They aren't even perfectly triangular either; the men's room sign may have a little chip, and even the geometry textbook can't be perfect at the atomic level. But we recognize they both have some quality called triangularity.
What is this triangularity? There are two possibilities: either it's an abstraction in the mind, or it's a real entity. It's not an abstraction in the mind, because it's objectively real. Things were triangular before there were any humans, and if a massive pandemic kills all humans tomorrow (except of course the Madagascarans) there will still be triangles then. And as Feser puts it, with his characteristic uh-let's-call-it-wit:"If the Canadian parliament, say, should declare that in light of evolving social mores, triangles should be regarded as sometimes having four sides, and decrees that anyone who expresses disagreement with this judgment shall be deemed guilty of disciminiatory hate speech against four-sided triangles, none of this would change the geometrical facts in the least, but merely cast doubt on the sanity of Canadian parliamentarians."
Therefore, triangularity is not just an abstraction in the mind. Therefore, it must be a real entity. Therefore Platonic forms exist. I think this is the main thrust of the book's support for Platonism.
(this might be more interesting if at this point you try to find a flaw in this argument yourself so that I can either get independent confirmation of my analysis or else hear other interesting methods of attack; my thoughts are below)
I think triangularity is in fact something in the human mind. In particular, it is the human mind's tendency to lump a bunch of approximate shapes into the category called "triangle".
If all humans were to die tomorrow, there would be no one to set the boundaries of the category "triangle". There would still be the men's room sign on my hotel bathroom. It would still have certain characteristics, like having three sides, being blue, and having a chip in it. And there would still be the picture on page 3 of my geometry book, which would also still have all its characteristics. There would be no one pointing out that these things are related in any way. There would be no one saying "You know, even though that men's room sign has a chip in it, it's still rounds off to being pretty much a triangle." There would still be the island of Greenland, with all its fjords and rugged coasts, but there would be no one to say "You know, if all those fjords were filled in it could abstract into a pretty decent isoceles triangle."
So "triangle" is the human tendency to draw a boundary around a certain collection of objects and say "These are triangular", even though they may be different and may not be perfectly triangular.
A counterargument would be "Well yes, obviously that's the origin of the word 'triangle'. But why does pretty much everyone draw that particular boundary? Don't they draw it exactly because triangle is a natural kind, one that existed even before we started making words?"
A lot of Plato (and Feser's) discussion of forms centers on mathematical objects, animals, and artifacts. These three things are extra confusing because they are sorta natural kinds.
For example, "triangle" as defined in mathematics is always perfect and has no extraneous qualities, by definition. We call real things "triangles" insofar as they approximate this mathematical definition, since we can (to some degree) apply mathematical results about triangles to them. In that sense, "triangle" is a natural kind to anyone who understands mathematics on any level.
Animals tend to come in nicely-defined categories, like "squirrel" or "giraffe" with specific squirrel or giraffe DNA rather than being randomly scattered across the space of possible genomes. This is for two reasons: first, evolution tailors an organism to its environment, and second population genetics keeps animals within mutually reproducing groups. This makes it easy to pick out cluster structures in thingspace.
Artifacts tend to be built for specific purposes and tailored to those purposes. And artisans tend to copy one another's work. So most cars have four wheels both because four wheels is an unusually useful number for the purpose of transportation, and because having four wheels is a car-making tradition. Again, this produces cluster-structures that it's easy to mistake for natural categories.
If every human died tomorrow, there would still be cars, in that there would still be four-wheeled objects with engines and so on. But there would be no one to set the boundaries of the category "car" or care that these things had an unusual level of commonality.
One more counterargument. Suppose someone says "I'm not talking about how humans come to recognize triangles. I'm talking about how triangles become triangular in the first place, or how they stay triangular!"
First of all, this objection fails in the case of animals and artifacts. We have excellent non-metaphysical causal histories of how animals and artifacts gain and maintain their shapes from the fields of genetics, developmental biological, and manufacturing. At the extreme, we even know the physics behind why cats stay together instead of collapsing into a pile of formless dust. The importance of this can't be overstated, because Plato had no idea. It must have seemed to him a minor miracles that cats consistently stayed cat-shaped and gave birth to cat-shaped kittens.
But triangles are a slightly thornier case. I think pixels are an instructive metaphor here. We can imagine six pixels arranged like so:
OXO
XXX
The Xs here are roughly in a triangle shape. It's not a perfect triangle, but neither is anything else in the real world. But it's come from a completely reductionist system. We can just as well describe the system as 1: O, 2: X, 3:O, 4: X, 5: X, 6: X. This was another piece of the puzzle Plato was missing: the idea that things are made of component parts. Once we've got that, the mystery of what makes something triangular becomes much less mysterious: it's just a certain arrangement of parts in space.
Once we know this, we don't have to accept the next step in Plato's formulation, which is to pretend we have an objective standard of goodness by how well things approximate the Form. For example, Plato says that my hotel's Men's Room sign with a chip in it is a worse triangle than one that didn't have a chip in it. To him, it is failing at instantiating the Form of the Triangular.
But if Forms are just our attempts to pattern-match things to cluster-structures in thingspace, then all we can say is that my men's room sign pattern-matches my category of triangularity less well than a nonchipped sign was. And although this is an objective statement (and in this case, because triangularity is mathematical, even the statement that it is a less perfect triangle than a nonchipped sign is objectively true) it is subjective for me to hold triangularity as the standard it should be trying to attain. It's not an object trying to instantiate the Form of Triangularity and failing, it's an object that I'm trying to pattern-match to a triangle and finding it to not be a very good match.
I think both Plato and Feser accept that my decision to judge the men's room sign as a triangle is sort of arbitrary, but they lose that understanding when they start talking about people and animals:"A squirrel will be a better squirrel the more perfectly it participates or instantiates the form of a squirrel. A squirrel who likes to scamper up trees and gather nuts for the winter (or whatever) is going to be a more perfect approximation of the squirrel essence than one which, through habituation or genetic defect, prefers to eat toothpaste spread on Ritz crackers and to lay out "spread eagled" on the freeway. This entails a standard of goodness, and a perfectly objective one. It is not a matter of opinion whether the carefully drawn triangle is a better triangle than the hastily drawn one, nor a matter of opinion whether the toothpaste-eating squirrel is deficient as a squirrel. If a squirrel could be conditioned to eat nothing but toothpaste, it wouldn't follow that this is good for him."
There are a few factors going on here. First, squirrels are pretty well-evolved. Most squirrels that deviate from normal are going to be worse than normal, for the same reason most mutations are bad. This makes it tempting to conflate "squirrel who is good at pattern matching to the category of squirrel" with "squirrel who is successful at being a squirrel" and (to throw in a dash of naturalistic fallacy) "squirrel who is doing things the proper natural squirrel way" and lump them into one big idea of "good squirrel".
This is the way almost every bad philosophical theory starts. Take A and B which co-occur 99% of the time. Say "Therefore, let's lump A and B together as a single thing." Then accidentally stumble across the case where they don't co-occur. Then say either "This case seems to have A and not B, but that doesn't make sense, so we can safely assume it has B".
(For example, things that are natural (A) are usually safe and nontoxic (B), and chemicals manufactured in factories (~A) are usually dangerous and toxic (~B). So people conflate "natural" and "healthy" as basically the same thing, and then say "Medicines are synthetic chemicals, so they can't possibly be good for me. Herbs are natural, so I'm sure they'll cure my illness.")
The next chapter of Superstition has more to say about Forms, as well as some stronger arguments in their favor that need to be addressed. |
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