Hofstadter on Detachment

Now we can do a more advanced exercise, based on a Zen kōan called “Gantō's Ax”. Here is how it begins:

One day Tokusan told his student Gantō, “I have two monks who have been here for many years. Go and examine them.” Gantō picked up an ax and went to the hut where the two monks were meditating. He raised the ax, saying, “If you say a word I will cut off your heads; and if you do not say a word, I will also cut off your heads.”

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The power of the Propositional Calculus is shown in this example. Why, in but two dozen steps, we have deduced Q: that the heads will be cut off! (Ominously, the rule last invoked was “detachment” … )

It also reminds me of the Queen in Alice in Wonderland, who was always saying “Off with her head!”. I always thought there was some connection between the two, but apparently there isn't.

Speaking of quotations within quotations, or of stories within stories, one of my favorite examples is the Tale of the Three Storytelling Machines of King Genius from The Cyberiad.