Which Alice?

ALICE IN PUZZLE-LAND
eleventh pages, which were still blank. Then he wrote the following
on the tenth page and handed it back to Alice.
—10—
THE SENTENCE
ON PAGE 10 Is
FALSE.
"Now," said Humpty Dumpty, "is the statement on page ten of
your book true or false?"
"I see no way to tell," replied Alice, after thinking it over for a bit.
"It could be either."
"Wrong!" exclaimed Humpty Dumpty. "It's not that it could be
either—it's that it couldn't be either!"
"Why not?" asked Alice.
"Now look, child; could the sentence possibly be true?"
"Why not?" asked Alice.
"Well, suppose it were true. Then what it says must be the case.
But what it says is that it is false. Therefore, it must be the case that it
is false. So if it is true, it is also false. But it is impossible that it can
be both true and false; therefore it is impossible that it is true."
"Of course," said Alice, "and since it cannot possibly be true, then
it must be false."
"Wrong again!" said Humpty Dumpty triumphantly. "It can't be
false either!"
"Why not?" asked Alice.
"Well, suppose it were false. Then what it says is not the case. Now,
what it says is that it is false. Since what it says is not the case, then it
is not the case that it is false—in other words, it is true. So if it is
false, then it is true, and we again have a contradiction. Therefore,
it can't be false. That's glory for you!"
"Oh, dear," said Alice disconsolately. "I seem to be in the same
predicament as with your first puzzle!"
"Exactly!" replied Humpty Dumpty, "and that's the beautiful part
of it!"
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