Which Alice?

Looking-Glass Logic
true. Then, by Condition Two, he claims that he doesn't believe the
statement. Hence, again by Condition One, he must believe that he
doesn't believe the statement.
"Anyhow," continued Humpty Dumpty, "I'm giving you too
many hints! Let me finish my list of conditions, and then you should
deduce the key to the entire mystery.
"Condition Three—Given any true statement, he (the Looking-
Glass logician) always claims that he believes the statement.
"Condition Four—If a Looking-Glass logician believes something,
then he cannot also believe its opposite.
"Condition Five—Given any statement, a Looking-Glass logician
either believes the statement or he believes its opposite.
"And that," concluded Humpty Dumpty proudly, "is the entire
list of conditions. From these you should be able to infer just which
statements a Looking-Glass logician believes to be true and just
which ones he believes to be false. I will now ask you some questions
to test your understanding.
"Question One—Suppose a Looking-Glass logician believes that the
Red King is asleep. Does he believe that the Red King is dreaming
of you, or doesn't he?"
"Now, how could I possibly know that?" cried Alice.
"You should," replied Humpty Dumpty. "The answer follows
directly from the conditions, but I won't tell you how until later.
Meanwhile, let me ask you this:
"Question Two—Suppose a Looking-Glass logician believes that
either the Red King or the Red Queen is asleep. Does it follow that
he believes that the Red Queen is asleep?"
"Why should it?" replied Alice.
"It does," said Humpty Dumpty, "but I won't tell you why till
later. Meanwhile, try this:
"Question Three—Suppose he (the Looking-Glass logician) believes
that the Red King is asleep. Does he necessarily believe that the Red
Queen is asleep?"
"Now, why in the world should he?" asked Alice, more bewildered
than ever.
"Good question," replied Humpty Dumpty, "and we'll discuss it
later. Meanwhile, try this:
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