keesan@bbncc5.UUCP (Morris M. Keesan) (02/19/86)
One must be careful when devising answers to the truth-tellers vs. liars puzzles
to examine what the definition of a liar is. In order to have the puzzles be
meaningful at all, we must assume that any truth-teller or liar will always give
an answer which has some relation to the question, i.e. is either true or false
but not nonsensical, but if a liar is simply defined as one who never tells the
truth, or equivalently as someone who always tells untruths, we have no
guarantee that the liar's answers will be what we want. Many of the posted
solutions have relied on the assumption that the liar will tell us the exact
opposite (in some sense) of the truth. Given the minimalist definition of a
liar, a question like "If I were to ask you which of these two roads leads to
the hospital, what would you say?" could be answered by the liar, "A fish."
This is certainly untrue, as under our basic assumption the liar would have to
answer the question about the roads with an answer about the roads, and it is
not nonsensical, since it makes sense as an answer to "what would you say". A
better question to ask, i.e. one which makes fewer assumptions, would be, "If I
were to ask you if that road [pointing] leads to the hospital, would you say
'yes'?"
--
Morris M. Keesan
keesan@bbn-unix.ARPA
{decvax,ihnp4,etc.}!bbncca!keesanags@pucc-h (Dave Seaman) (02/21/86)
In article <1763@bbncc5.UUCP> keesan@bbncc5.UUCP (Morris M. Keesan) writes: >One must be careful when devising answers to the truth-tellers vs. liars puzzles >to examine what the definition of a liar is. . . . >A >better question to ask, i.e. one which makes fewer assumptions, would be, "If I >were to ask you if that road [pointing] leads to the hospital, would you say >'yes'?" And what can you conclude if he answers this question by saying "certainly!" [Think about it.] -- Dave Seaman pur-ee!pucc-h!ags