Which Alice?
Which Alice?
Which Alice?
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ALICE IN PUZZLE-LAND<br />
grant that the theory is highly improbable, but that does not mean<br />
that the theory is logically impossible.<br />
"And there is something about the King's argument worth<br />
observing," I added, "namely that if the King himself were of either<br />
Type A or Type B, then his believing those three things would make<br />
them true! The King's argument would be valid if we added the<br />
premiss that the King is of Type A or Type B; if the King is of one<br />
of those two types, it really follows that everyone else is—in other<br />
words that the theory must be correct."<br />
"I still think it's the stupidest theory I ever heard," said Michael,<br />
and that appeared to be the end of the matter.<br />
But it was not quite the end of the matter! That night <strong>Alice</strong> had a<br />
remarkable dream. When she went to bed, her mind was filled with<br />
all the strange puzzles she had heard that day—particularly the<br />
inversion of truth and falsity of the Looking-Glass logicians, and the<br />
Red King's theory.<br />
Is it really possible that the Red King's theory could be correct?<br />
thought <strong>Alice</strong>. And if so, I wonder which type I would be, Type A<br />
or Type B?<br />
Then <strong>Alice</strong> had the dream. She dreamed that she was the other<br />
<strong>Alice</strong>—the <strong>Alice</strong> in the Looking-Glass. She dreamed that she met<br />
the Red King and explained to him the gap in his proof. He then<br />
filled in the gap by giving her another proof that he really was<br />
either of Type A or Type B. (Unfortunately, <strong>Alice</strong> couldn't<br />
remember the proof the next morning, so I can't tell you what it<br />
was!) Anyway, <strong>Alice</strong> was thoroughly convinced in her sleep that the<br />
King really was of Type A or Type B, and hence (by the King's first<br />
argument) that everybody was of Type A or Type B. Then they had<br />
the following conversation:<br />
"There is another <strong>Alice</strong>," said the King, "who right now is asleep<br />
and who is dreaming she is you."<br />
"How extraordinary!" exclaimed <strong>Alice</strong>. "Isn't it possible that it is I<br />
who am now asleep and dreaming I am she?"<br />
"It comes to the same thing," replied the King.<br />
This remark puzzled <strong>Alice</strong> dreadfully! She could not see at all why<br />
it was the same thing.<br />
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