A Semantic Version of Russell's Paradox

"The mother of all the logical and semantic paradoxes was Russell’s paradox, named for its author, twentieth-century English philosopher Bertrand Russell. It goes like this: “Is the set of all sets that are not members of themselves a member of itself?” This one is a real screamer—that is, if you happen to have an advanced degree in mathematics. But hang on. Fortunately, two other twentieth-century logicians named Grelling and Nelson came along with a more accessible version of Russell’s paradox. It’s a semantic paradox that operates on the concept of words that refer to themselves.

Here goes: There are two kinds of words, those that refer to themselves (autological) and those that don’t (heterological). Some examples of autological words are “short” (which is a short word), “polysyllabic” (which has several syllables), and our favorite, “seventeen-lettered” (which has seventeen letters). Examples of heterological words are “knockkneed” (a word that has no knees, touching or otherwise) and “monosyllabic” (a word that has more than one syllable). The question is: Is the word “heterological” autological or heterological? If it’s autological, then it’s heterological. If it’s heterological, then it’s autological. Ha! Ha!"

Thomas Catchcart & Daniel Klein, Plato and a Platypus Walk Into A Bar... Understanding Philosophy Through Jokes


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