Which Alice?
Which Alice?
Which Alice?
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ALICE IN PUZZLE-LAND<br />
<strong>Alice</strong> thought this over. Somehow, she didn't find this explanation<br />
very helpful.<br />
"You see," he continued, "there are certain people here called<br />
Looking-Glass logicians. Their statements seem a bit bizarre until<br />
you understand the key—which is really quite simple. Once the key<br />
is understood, the whole business makes perfect sense."<br />
"And what is the key?" asked <strong>Alice</strong>, more curious than ever.<br />
"Oh, it would never do to tell you the key! However, I will give<br />
you some clues. In fact, I will give you the five basic conditions<br />
about Looking-Glass logicians from which you can deduce the key.<br />
Here are the conditions:<br />
"Condition One—A Looking-Glass logician is completely honest.<br />
He will claim those and only those statements which he actually<br />
believes.<br />
"Condition Two—Whenever a Looking-Glass logician claims a<br />
statement to be true, then he also claims that he doesn't believe the<br />
statement."<br />
"Just a minute," interrupted <strong>Alice</strong>. "Are you not contradicting<br />
yourself? According to the first condition, a Looking-Glass logician<br />
is always truthful. If, then, he claims a statement to be true, he must<br />
really believe that it is true. How then, without lying, can he claim<br />
that he doesn't believe the statement?"<br />
"Good question," replied Humpty Dumpty. "However, I never<br />
said that a Looking-Glass logician is always accurate! Just because he<br />
believes something doesn't mean that he necessarily knows that he<br />
believes it, nor even that he necessarily believes that he believes it.<br />
Indeed, it could happen that he erroneously believes that he doesn't<br />
believe it."<br />
"You mean," replied <strong>Alice</strong>, utterly astonished, "that a person<br />
can actually believe something, and yet believe that he doesn't<br />
believe it?"<br />
"With Looking-Glass logicians, yes," replied Humpty Dumpty, "in<br />
fact with Looking-Glass logicians this always happens—this is a<br />
direct consequence of the first two conditions."<br />
"How is that?" asked <strong>Alice</strong>.<br />
"Well," replied Humpty Dumpty, "suppose he believes a statement<br />
to be true. Then, by Condition One, he claims the statement is<br />
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