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Russell's Paradox

In the middle of the night I got such a fright that woke me with a start,
For I dreamed of a set that contained itself, in toto, not in part.
If sets can thus contain themselves, then they might also fail
To hold themselves as members, and this leads me to my tale.

Now Frege thought he finally had the world inside a box,
So he wrote a lengthy tome, but up popped paradox.
Russell asked, ``You know that Epimenides said oft
A Cretan who tells a lie does tell the truth, nicht war, dumkopf?

And here's a poser you must face if continue thus you do,
What make you of the following thought, tell me, do tell true.
The set of all sets that contain themselves might cause a soul to frown,
But the set of all sets that don't contain themselves will bring you down!''

Now Gottlob Frege was no fool, he knew his proof was fried.
He published his tome, but in defeat, while in his beer he cried.
And Bertrand Russell told about, in books upon our shelves,
The barber in town who shaves all those who do not shave themselves.

Harry Mairson
Thu Oct 9 11:06:29 EDT 1997