Twin Peaks Usenet Archive
Subject: Re: Calm speculation (was Re: Wild Speculation)
From: email@example.com (David E Hollingsworth)
Date: 1990-10-09, 12:02
In article , firstname.lastname@example.org (Brian L. Kahn) writes:
|> All things considered (more or less) I think the biggest clue we have
|> so far is Jennifer Lynch (author of Laura's Diary) being quoted
|> somewhere that she thinks people will be really surprised when they
|> find out who the killer is. Ben Horne is NOT surprising. Neither is
|> Leo. Neither Ben nor Leo did it, guaranteed.
|> B< Brian Kahn email@example.com "may the farce be with you"
Isn't there a logic problem called something like the "hangman's paradox"?
I think it goes like this:
The guilty party is told by the judge that he will be executed at dawn
some day within the next week, but that he [the guilty party] will not know when
this will occur until that very day.
After thinking about this for some time, the guilty party recognizes
something: he cannot be executed on the last day of the week. After all, if the
first 6 mornings pass without incident, then he will know late into the 6th day
that he execution must happen "tommorrow". However, the judge told him that he
would not know until the day it is going to happen.
Likewise, once the first 5 mornings pass by, the prisoner will know that,
because he cannot be executed on the 7th day, the only day left is the 6th. But
then again, he would have the foreknowledge that the judge's statement claimed
that he would not have.
The same argument continues until we discover that his execution must occur
on the very next day, but that it cannot, because he has just concluded so, and
therefore "knows" that it must be the day.
Therefore the prisoner is content the knowing that the sentence cannot be
carried out, because it is paradoxical.
Now here's the neat part. Because the prisoner has "proved" that none
of the days may be "the big one", they are all fair game. The prisoner will be
equally surprised no matter which day it occurs because he believes that the event
cannot happen at all. By logically analyzing the situation, he has reduced it to
the original scenerio.
So if you assume that neither Ben nor Leo did it, "guaranteed", then you
will definitely be surprised if either one DOES turn out to be the killer...thus
making Jennifer's statement true. So much for the "biggest clue we have so far"...
David E. Hollingsworth