"Mohammad and I are both liars."

What are each?

In the real world anyone can say anything, even as paradoxical as "I am lying". In the real world we are always kept guessing as to whether a person is lying or telling the truth. There are even cases where people tell the truth with the hope that people will think they're lying and so be misled.

However, here we are on the island of Liars and Knights (liars and truth-tellers). Here no one would say "I am lying." as that is neither a lie nor the truth. Likewise, only a liar, not a knight, would say "2+2=5", and indeed his saying it would not make it true. Then, as "Mohammad and I are both liars" cannot be true if spoken by either a liar or a knight, it has to be false, and furthermore, made false by the falsity of its first component, about Mohammad, as, since it is false it is spoken by a liar. On this island of liars and knights, unlike the real world, if Mohammad were a liar, absolutely no one on the island would (or even could) say "Mohammad and I are both liars".

Admittedly it's a fictitious world, one invented just to flex abstract logical muscles, to see how well we can divorce ourselves from considerations outside what is presented in the problem. Consider it getting rid of preconceived notions.

Posted by Charlie on 2003-04-09 04:54:50