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Which Alice?

Which Alice?

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And That's the Beautiful Part of It!<br />

"I can't think of everything!" replied <strong>Alice</strong>.<br />

"I never said you could," replied Humpty Dumpty. "I merely said<br />

you should."<br />

"But is it reasonable to say that I should do something that I<br />

cannot do?" asked <strong>Alice</strong>.<br />

"That is an interesting problem in Moral Philosophy," he replied,<br />

"but that would take us too far afield. Coming back to this problem,<br />

since my baby loves himself and also loves only me, it would follow<br />

that I am my own baby! Therefore, not everything I told you can be<br />

true."<br />

"That was a funny one!" said <strong>Alice</strong>.<br />

"True," replied Humpty Dumpty, "and now I would like to tell<br />

you a rather special puzzle. It's one I invented myself, but I'm not<br />

sure I know the answer to it! It seems like a paradox, but I'm not<br />

absolutely sure it is."<br />

<strong>Alice</strong> was very curious as to what sort of puzzle could possibly<br />

confound Humpty Dumpty himself!<br />

"Well, it's like this," he began. "You know puzzles about knights<br />

who always tell the truth and knaves who always lie?"<br />

"Oh, many indeed!" replied <strong>Alice</strong>.<br />

"Well, then, suppose you are in a land inhabited entirely by<br />

knights who always tell the truth and knaves who always lie. You<br />

meet one inhabitant about whom you know nothing—all you know<br />

is that he is either a knight or a knave, but you have no idea which.<br />

He makes but one statement: You do not and never will know that I am a<br />

knight. What would you conclude?"<br />

"Well, let's see," said <strong>Alice</strong>. "Suppose he is a knave. Then his<br />

statement is false, which means that I do or will know that he's a<br />

knight. But if I know that he is a knight, then he must in fact be one<br />

(because whatever is known must be true). Therefore, if he is a<br />

knave, then he must be a knight, which is a contradiction. So he<br />

can't be a knave; so he must be a knight."<br />

"Then you know he is a knight," said Humpty Dumpty.<br />

"Yes," said <strong>Alice</strong>, "but that makes further trouble! Since I know<br />

he is a knight, then his statement that I do not and never will know<br />

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