Friday, October 25, 2002

Experience Mathematics #18 - All about itself

Russel’s Paradox shows that considering sets that contain themselves (or even asking whether they contain themselves or not) can lead to contradictory situations. But Real Life has many such self-referential situations. In this column, we will collect together many amusing (and not!) statements, such as this one.

“All Cretans are Liars”, said the Cretan Epimenides. Did Epimenides tell the truth? How can he, since he is a Cretan, and hence a liar? But if he lied, maybe he is telling the truth!

What about: This sentence is false. Is it true or false? Go through each sentence in this column and evaluate whether it is true or false.

This sentence has four words. This one, however, has six words. This one has one too too many words.

This sentence has no comma. This sentence does not describe itself.

This article is written by the author of this article. In other words, the author of Experience Mathematics writes Experience Mathematics. It is self-referential, since it refers to itself. In fact, the article refers to itself several times—but only once does the article refer to itself twice in one sentence. The author of this article is careful not to write self-referential statements.

Is this a question or not. How about this statement?

The above two statements beg the question. But what is the question? Was that the question? Does this answer the question?

The sentence below is false. The above sentence is true.

Lets not say any more, and end.

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