Saturday, February 19, 2011

Is "pretty" pretty?


Are any words pretty? Maybe not (outside of calligraphy or song). But I’m reluctant to say that “pretty” isn’t pretty because it is not too odd-looking (as words go) and it does make us think of prettiness. Still, I am reluctant to say that it is pretty, and so it seems to me that “pretty” is about as pretty as not. Perhaps you think that “pretty” is pretty. Or perhaps you think that “pretty” is not pretty. But if about as many people think it is as think it is not, and lots of people have no strong opinion either way, then a good case could be made for “pretty” being about as pretty as not.
...... Descriptive accuracy is, in general, a matter of degree. E.g. “is long” is not a long English predicate, while “is so far from being short that, not only is it not short, it is rather long for a predicate written in ordinary English” is quite a long English predicate, and so it seems fairly plausible that there might be some predicate that means the same as “is long” and which is about as long as not. For just one more example, “is boring” seems a little interesting, now that I come to think about it, although it does not hold my interest for long.
...... Words are heterological if they do not describe themselves, and so it seems to me that “pretty” is about as heterological as not. And if words are heterological insofar as they don’t describe themselves very well, then the fact that if “heterological” is heterological then it is not heterological, and the fact that if it is not then it is, those facts show that “heterological” is about as heterological as not. Those two facts are called the Grelling-Nelson paradox, and they are a version of Russell’s paradox.
The most significant version of Russell’s paradox concerned collections. When we refer to some things collectively, we are referring to their collection. E.g. “all the words in this post” refers us to all of the words in this post (including those words). Some collections include themselves (e.g. the collection of all the collections would include itself), but most do not (e.g. the collection of all the words in this post is not itself a word in this post). Russell’s paradox is that the collection of all the collections that do not include themselves would include itself if it did not include itself, and would not include itself if it did. Mathematicians tend to think that Russell’s paradox shows that we should only use well-defined kinds of collections. But if we could not talk about things that we were finding it hard to talk about, we would never learn anything.
A similar resolution of the Grelling-Nelson paradox would be that it shows that the word heterological is not a well-defined word. Perhaps Grelling and Nelson (who were mathematicians) should not have introduced that word. But what is wrong with saying that “heterological” is about as heterological as not?

1 comment:

  1. I enjoyed your explication of this paradox. On a semi-related note, the word "mellifluous" describes itself very well! I would love to see it used a philosophical example more often.

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