Information Sheet #7

January 19, 1988

SELF-REFERENTIAL SENTENCES

A recent issue of Omni advertises a contest for self-referential sentences, sentences that somehow refer to themselves as sentences. The classic example is one we have printed on a card hanging from the ceiling of the Writing Center. On one side the card announces: "The statement on the on the other side of the card is true." On the reverse side is printed: "The statement on the other side of this card is false."

One of the finest collections of self-referential sentences can be found in Douglas Hofstadter's Metamagical Themas. Hofstadter's book provides a fascinating introduction into our language's capabilities for commenting on its own processes of symbolic meaning-making. He also demonstrates how ubiquitous and powerful the self-referential element is, not only in language but in all human behavior. Hofstadter quotes from George Brabner at the University of Delaware, suggesting how fundamental self-referencing is to our conceptions of self:

Part of our 'verbal behavior' deliberately, often playfully, explores the boundaries between conceptual levels of systems. All of this has its root in the struggle to survive, in the fact that our brains have become so flexible that much of their time is spent in dealing with their own activities, consciously or unconsciously. It is simply a consequence of representational poweras Kurt Godel showedthat systems of increasing complexity become increasingly self-referential.

But enough pontificating. Relax and have some fun reading and thinking about the following sample of self-referential sentences.

This sentence contains exactly threee erors.

The reader of this sentence exists only while reading me.

When you are not looking at it, this sentence is in Spanish.

This sentence has cabbage six words.

This is to be or actually not two sentences to be, that is the question, combined.

Does this sentence remind you of the Coe Writing Center?

This sentence is a !!!! premature punctuator

I used to think I was indecisive, but now I'm not so sure.

You have, of course, just begun reading the sentence that you have just finished reading.

If (pi) were 3, this sentence wuld l●●k smething like this.

Here are two longer examples of self-referential writing. The first item is particularly appropriate for anyone teaching Nature of Science and reconsidering Gale's stories about scientific theories being accepted despite incomplete evidence.

Only the fool would take trouble to verify that his sentence was composed of ten a's, three b's, four c's, four d's, forty-six e's, sixteen f's, four g's, thirteen h's, fifteen i's, two k's, nine l's, four m's, twenty-five n's, twenty-four o's, five p's, sixteen r's, forty-one s's, thirty-seven t's, ten u's, eight v's, eight w's, four x's, eleven y's, twenty-seven commas, twenty-three apostrophes, seven hyphens, and, last but not least, a single !

Hofstadter comments: "I (perhaps the fool) did take trouble to verify the whole thing. First, though, I carried out some spot checks. And I must say that when the first random spot check worked (I think I checked the number of g's), this has a strong psychological effect: all of a sudden, the credibility rating of the whole sentence shot way up for me. It strikes me as a weird (and wonderful) how, in certain situations, the verification of a tiny percentage of a theory can serve to powerfully strengthen your belief in the full theory. And perhaps that's the whole point of the sentence!" Hofstadter also reprints a great story of the Liars Bridge, a self-referential anecdote sent to him by a Dutch mathematician Hans Freudenthal:

There is a story by the eighteenth-century German Christian Gellert called "Der Bauer und sein Sohn." One day during a walk, when the son tells a big lie, his father direly warns him about the "Liars' Bridge," which they are approaching. This bridge always collapses when a liar walks across it. After hearing this frightening warning, the boy admits his lies and confesses the truth.

When I [Freudenthal] told a ten-year-old boy this story, he asked me what happened when they eventually came to the bridge. I replied, "It collapsed under the father, who had lied, since in fact there is no Liars' Bridge." (Or did it?)

A variation on the game of self-referential sentences is finding instances of unintentional self-reference. Here are two examples from the current leader of the free world. The examples are taken from The New York and Harper's.

From a transcript of a press conference given by President Reagan:

Q: That wasn't my question. You answered a question I didn't ask.

A: I'm answering the question because the question you asked isthe answer is so obvious. That, obviously, after these years of out-of-control and built up to the level they have, there's no one that pretended that you couldthis would then have to go to the states for ratification. There would be a period of time before it was actually put in place. And in that period of time, you have an opportunity to work out a budget which would not have to penalize people who are dependent now, because, on the Government for help.


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