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Does English Have an Infinite Number of Words?
Following up on yesterday's post about the size of the English lexicon, we think that an argument could be made that English has an infinite number of words. Well, this depends of course on how you define word, but it's not as crazy as it may sound. Or it's crazy enough to demonstrate that the whole word-counting affair can easily get to an absurd point. Languages are characterized by something called recursion. Recursion is a process by which elements recur in a given structure. The thing about recursion in language is that it can, in principle, be infinite. Think of the old nursery rhyme This is the House that Jack Built. It basically goes on and on by simply adding that clause after that clause, resulting in the end in a really, really long sentence. But that sentence could go on and on, ad infinitum. Recursion can happen in words, too. Take great, as in great-grandmother. Language doesn't care about the fact that you can only go back so many generations before that distant female relative isn't homo sapiens any more, so, you could in principle construct an infinite number of words, just by recursion of the element great. The prefix re- could be used this way, too. If you never quite get a job done right, you may have to re-re-re-re-re-(∞)-do it. You'll die at some point, and your hopeless efforts will cease, but again, language doesn't care about that. Another obvious example of infinite recursion in words is numbers. Is one a word? Sure. Is nineteen a word? Yup. So, how about one million five hundred sixty thousand nine hundred and three? You can see where this is going... Recursion isn't the only problem with word-counting. One intuitive definition of a word is that it's an object that means something. By meaning something, you could say that a word refers to something. That begs the question, how many things are there to refer to? Even if proper names can't be used in Scrabble, they still refer to things, namely individual, unique people. Right there that gives us about six billion words (and counting). They're not all English names, but to refer to those people we'd use their actual names, so in a sense we'd borrow a foreign name into English. Similarly, how many place names are there? How many cities, towns, streets, parks, squares, etc., are there on Earth? Those are all things you'd refer to, so you'd use a unique word. And if a word is unique if it refers to a unique thing, then it doesn't matter how many Springfields there are; they're all different words, and there are a heck of a lot of them. Absurd? Probably, but depending on how you count words, the logical conclusion is that English (and every other language for that matter) has an infinite number of words. So, it may be best to stop counting them. (Chris) Tags: English, Global Language Monitor, meaning, recursion, words
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