Monday, August 31, 2009

Vagueness is not what you think it is

I am forcing myself to start writing in this blog again, because I thought of a brilliant format change: each day there is a Dinosaur Comic, I am going to write about that comic and post as soon as I can. Some days will be more philosophical than others, naturally, but I will try to make the writing as interesting as possible. All other writings will be, um, posted as I write them. I have some things I'm working on right now that I will post just as soon as I get to it.

Now let's talk about comics, because, dudes, have I got a comic for you. I took a whole class on this goddamn subject. Philosophers call this problem "vagueness," which is not what it sounds like, so I sometimes call it "metaphysical vagueness" to clear up any confusion.

The paradox that God and T-Rex are discussing is called the Sorites paradox. It is not named after a person, but literally means "heaper." My favorite such paradox is this one: you get a bucket of green paint, and a bucket of red paint, okay? And you get a giant stack of tiles. You paint a tile with paint from the green bucket, and then you add a few drops of red paint to the green bucket. Repeat for every single tile until the very last tile is made with pure red paint. Each of these tiles is going to look virtually identical to its neighbor, but look very different from, say, a tile ten spaces away.

Now, you set these up in a big room, maybe a warehouse, snaking around the room so that they start out green, and gradually become red, and come around to have the pure red tile meet the pure green tile. (I sometimes imagine doing this as an installation art project, where you walk in the door and have green on your left, and red on your right. But I digress.) The question is now, where do the tiles stop being green, and where do they start being red?

The problem with answering that question is that, no matter where you decide the point is, you can hold up two neighboring tiles, tiles that look virtually identical, and say, "One of these is green, and the other is not." Which seems ridiculous.

Okay, you look confused. You're saying, "I still don't see how this is a problem. Why don't we use T-Rex's solution?" So let me explain to you something about how philosophers think. For them, truth and logic are part of the very fabric of the universe. For any question that statement that makes grammatical sense (e.g., "This tile is red"), there will be a corresponding truth value of either "true" or "false." You don't get to say, "Eh, well, it's kind of true..."

This is why some philosophers have made logical systems that have multiple possible answers. Fuzzy logic, for instance, assigns a truth value that ranges between 0 (completely false) and 1 (completely true). Another logical system goes for trivalence instead of bivalence, adding an answer like "indeterminate" in addition to "true" and "false". The problem with these alternative logics, though, is that when you start using logical operators with them, you start getting strange results that are a departure from traditional logic.

This class was one of the reasons that I had a falling out with analytical philosophy. Much of the literature seems to have, in its background, the premise that our language can precisely describe the world as it is, all of the time. But our world precedes language. Whatever color each of those tiles is, they will be that color no matter what words we have for those colors. The universe doesn't care how many grains of sand make a heap. Furthermore, no matter what a tongue-clucking grammarian says, language is all about how people use it, and whether the way that they use it successfully communicates what it is they want to say.

This is why my favorite answer to the Sorites paradox comes from Timothy Williamson: "there is an answer, and we cannot know it."* Imagine that you are looking at a crowd of people in a stadium, trying to determine how many people there are, and let's say that the precise number of people in the stadium at that moment is m. You know that m must be at least 10,000, maybe as high as 20,000, but you do not have the ability to count the number of people accurately. No matter which method you use to count the people, you have no way to tell whether you have arrived at m, or if this is actually m + 1, or m - 1. You could just guess the number of people, but if you were correct, you would not actually know the number of people, you would merely have a lucky guess. (That sort of thing only works when you when a prize for guessing things like how many jelly beans are in a fish bowl.)

My personal answer is a trivalent logic where the third option is "mu," preferably pronounced to sound like a cow. (Someone with more knowledge of Japanese or Buddhism is probably going to object to what I am about to say next, and to you, I respond: shut your trap.) Literally, "mu" means something like "no," "nothing," and "no-thing." It is an answer that is beyond affirmation or negation, and kind of negates a question by saying that the question itself is wrong. The most well-known example in the Western world is, "Have you stopped beating your wife?" But some other examples in philosophy include, "Is the set of all sets which are not members of themselves a member of itself?"

Try giving this answer in your next philosophy class. When your teacher asks, "How can you be sure that you have knowledge of the outside world?" just say, "Moooo." I guarantee that you will get positive results.**


* - If you're really interested in this subject, this comes from Williamson's book. Guess what it's called? That's right. "Vagueness."
** - This is not a guarantee.

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