Which Alice?
Which Alice? Which Alice?
And That's the Beautiful Part of It! "I can't think of everything!" replied Alice. "I never said you could," replied Humpty Dumpty. "I merely said you should." "But is it reasonable to say that I should do something that I cannot do?" asked Alice. "That is an interesting problem in Moral Philosophy," he replied, "but that would take us too far afield. Coming back to this problem, since my baby loves himself and also loves only me, it would follow that I am my own baby! Therefore, not everything I told you can be true." "That was a funny one!" said Alice. "True," replied Humpty Dumpty, "and now I would like to tell you a rather special puzzle. It's one I invented myself, but I'm not sure I know the answer to it! It seems like a paradox, but I'm not absolutely sure it is." Alice was very curious as to what sort of puzzle could possibly confound Humpty Dumpty himself! "Well, it's like this," he began. "You know puzzles about knights who always tell the truth and knaves who always lie?" "Oh, many indeed!" replied Alice. "Well, then, suppose you are in a land inhabited entirely by knights who always tell the truth and knaves who always lie. You meet one inhabitant about whom you know nothing—all you know is that he is either a knight or a knave, but you have no idea which. He makes but one statement: You do not and never will know that I am a knight. What would you conclude?" "Well, let's see," said Alice. "Suppose he is a knave. Then his statement is false, which means that I do or will know that he's a knight. But if I know that he is a knight, then he must in fact be one (because whatever is known must be true). Therefore, if he is a knave, then he must be a knight, which is a contradiction. So he can't be a knave; so he must be a knight." "Then you know he is a knight," said Humpty Dumpty. "Yes," said Alice, "but that makes further trouble! Since I know he is a knight, then his statement that I do not and never will know 99
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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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