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other adjectives and see how they relate to themselves: polysyllabic is polysyllabic. Monosyllabic is not monosyllabic. Pentasyllabic (made of five syllables) is pentasyllabic. Misspelled is not misspelled. Adjectival is adjectival. Female is not female. Awkwardnessfull is awkwardnessfull. Unpronounceable is not unpronounceable. In effect, we have two groups of adjectives: those that describe themselves and those that do not. All adjectives that describe themselves are called autological (from the Greek auto meaning “self” or “one’s own” and logos meaning “word,” “speech,” or “reason”) or homological . In contrast, all adjectives that do not describe themselves are called heterological (from the Greek heteros meaning “other” or “different”). So we have that English , polysyllabic , adjectival , and so on are all autological. In contrast, French , monosyllabic , unpronounceable , and so forth are all heterological. With these two categories set up, we now pose the following question:
    Is heterological heterological?
    Let us say that heterological is heterological. Just as
    English is English ⇒ English is autological,
    so too
    heterological is heterological ⇒ heterological is autological
    and hence heterological is not heterological. In contrast, if we take the opposite view and say that heterological is not heterological, then just as we saw that
    French is not French ⇒ French is heterological,
    so too
    heterological is not heterological ⇒ heterological is heterological.
    We have come to the conclusion that heterological is heterological if and only if it is not heterological. Buzz! This is a contradiction and troublesome.
    We can again envision this self-referential paradox as figure 2.2 .
    Figure 2.2
    Which subset does heterological belong to?
    This paradox also seems to have a simple solution: there is no word heterological , or if the word does exist, it has no meaning. We saw that if one defines heterological , then we come to a contradiction. This is similar to saying that the village in the barber paradox does not exist.
    However, we cannot simply solve all problems by waving our hand and declaring that the word heterological does not exist or has no meaning. The problem is too deeply rooted in the very nature of language. Rather than dealing with the word heterological , consider the related adjective phrase “not true of itself.” Simply ask if the phrase “not true of itself” is true of itself. It is true if and only if it is not true. Are we simply to posit that “not true of itself” is not a legitimate adjectival phrase? There are no problems with any of the words in the phrase. There is nothing about the phrase that is weird like the word heterological . Nevertheless, we come to a contradiction if we use it.
    The reference-book paradox is very similar to the heterological paradox. A reference book is a book that lists books in different categories. There are many reference books that list books of many different types. There are reference books that list antique books, anthropology books, books about Norwegian fauna, and so on. Certain reference books list themselves. For example, if one were to publish a reference book of all books published, that reference book would contain itself. There are also certain reference books that would not list themselves. For example, a reference book on Norwegian fauna would not list itself. Consider the reference book that lists all reference books that do not list themselves. Now ask yourself the following simple question: Does this book list itself? With a little thought, it is easy to see that this book lists itself if and only if it does not list itself. We conclude that no such reference book with such a rule for its content can exist. (I leave to the reader the task of drawing a diagram similar to figures 2.1 and 2.2 for this paradox.)
    Bertrand Russell