Re: The world's first readable calculus

[Ludwik Kowalski <kowalskiL@MAIL.MONTCLAIR.EDU>]

On December 3, 1998 Jack Uretsky gave us the URL for the draft of
his calculus textbook for engineering students. My comment has
to do with a puzzle, not the main part of the content.

> You are in a land where everyone is either a liar or a truthteller.
> You desperately need a truthteller for a business deal. You have
> lunch with 3 people, A, B, and C and ask if any of them is a
> truthteller.
>
> They answer as follows:
>
>      A: "There are 3 truthtellers here".
>       B: "No, only 1 of us is a truthteller."
>       C: "The second person is telling the truth."
>
> Which, if any, are the truthtellers?
>
> ANSWER TO THE CHAPTER I PUZZLE
>
> All are liars:
>
> (a) If A's statement is true, then B's denial is false, and B is a
> liar. But if B is a liar, then A's statement is false. Therefore A's
> statement cannot be true and A is a liar.
>
> (b) If B's statement is true then either B or C must be the truth
> teller, since we know that A is not. But if C is the truth teller,
then
> B cannot be, making B's statement false. Thus, either B is the only
> truth teller, or B is a liar.
>
> (c) If B is a truth teller, then C's statement is true. But If B is a
> truth teller, then B must be the ONLY truth teller, so C's
> statement must be false. Thus C is a liar, and C's statement must
> be a lie, making B's statement false and C's statement must be a
> lie, making B's statement false.

It seems to me that something is missing in this logic, unless one
can assume that "A, B and C know each other in terms being or
not being liars". This is implied in their answers. But how can the
answers of possible liars be taken seriously? I think the assumption
should be clearly stated at the beginning.