Which Alice?

ALICE IN PUZZLE-LAND
Alice did not quite know what to say to this; Humpty Dumpty's
logic sessions were certainly most instructive. Yet, she thought, he
does seem to be a little on the boastful side!
"You said this puts the old barber puzzle in a new light," said
Alice. "What is the relationship between the two puzzles?"
"Oh, I'm glad you asked that," he replied. "Well, you see, there
could be a barber like Barber A, and such a barber must shave
himself. Also there could be a barber like Barber B, only such a
barber could not shave himself. However, you can't have Barber A
and Barber B being the same person! Now, in the original problem,
you were given one person who had both the properties of Barber A
and of Barber B, and that is impossible!"
"Oh, I see!" said Alice, "that is interesting!"
"Here's another puzzle for you," said Humpty Dumpty, "and this
one does have a definite answer. You know the one about the
Hearts Club?"
"No," replied Alice, "I've never heard that one before."
"Good," he replied, "you got that one right!"
"I got what right?" asked Alice.
"The question I asked you! I asked you whether you know the
puzzle about the Hearts Club, and you said you never heard it
before, and you were right!"
"Well, yes," said Alice, "of course I was right, only how could you
have known it?"
"Because I invented the puzzle myself, and I've never told it to
anyone before, so you must have been right!"
"Oh!" said Alice. "But what is the puzzle of the Hearts Club?"
"Well," he replied, "in a certain community, the inhabitants have
formed various clubs. One particular club is called the Hearts Club.
We are given the following facts:
"(One) Given any lady in the community, if she does not belong
to every club, then she belongs to the Hearts Club.
"(Two) No man can be a member of the Hearts Club unless there
is at least one other club of which he is not a member.
"(Three) Given any club, every man outside the club loves every
lady in the Hearts Club.
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