What is a Liar? Does It Matter?

Constructing puzzles and decision theory problems is easy if you define an artificial world. For instance, the classic case of the truth-tellers and liars who live on an island. A castaway wants to get to the village on the island for food and help. He meets an islander and knows that such people only answer one question and depending on whether the islander is a truth-teller or liar, will answer accordingly. Two paths lead into the forest. One goes to the village and the other is guaranteed to get the castaway thoroughly lost. What can he ask to be assured of getting the right direction?

Note that several unrealistic assumptions are made to construct the virtual world. We can easily accept the isolation, the branching path, and a logical truth-teller. Then the obvious solution to the castaway’s dilemma is to ask, “If I were to ask you which way to the village, what would you say?” Simple analysis shows that either brand of islander will give the right answer.

However, we have made an implicit assumption about what constitutes a liar. Is a liar someone who logically responds with a lie, or is a liar one who deliberately tries to fool? The classic solution assumes a logical liar, which in not the usual type of liar one meets, on an island or elsewhere. A true liar would answer the classic question by pointing to the wrong branch of the path regardless of the logic. A true liar is difficult to overcome.

One solution is to ask, “Do you know there is free beer in the village?”, and then simply follow the islander as he runs off. This might not work for a die-hard true liar who might be willing to run the wrong way to perpetuate the lie, but that would cause him to miss out on the free beer (which, ironically, the castaway lied about).

Decision theory problems in real space are constantly before us, but not always as obvious. For instance, in our local paper, the letters to the editor section has been the scene of a vigorous argument about whether same-sex marriage should be allowed. Today (January 22) an anti-same-sex marriage regular writer submitted this in response to a criticism of his previous letter:

…I strongly suggest Mr.______ contact his local high school about a remedial reading comprehension program. If he would read my letter again, he will see that I never said that I “hated” anything. Period. I said, “I do not have to accept them” as equal (homosexual marriage). If their lifestyle is normal, then all others are abnormal…

[Note: I left the minor grammatical errors intact.]

This is the last paragraph of letter. I am most interested in the last sentence. It is related distantly to the bifurcation of the islanders into two logical groups, and just as artificial–and plainly wrong, but so plausible that a casual reader could easily agree.

Obviously the writer assumes a definition of “normal” which excludes alternatives he opposes. He does this with no justification other than he can get away with it. Even more insidiously, he obviously brands “abnormal” as bad (immoral) and “normal” as good (moral). He packs a lot into a short sentence. The danger here is not that the writer is being clever in his use of English to fool readers. The real danger is that is exactly what he believes.