I POSTED THIS ON TUESDAY BUT IT APPARENTLY GOT LOST IN WEBSPACE. IGNORE IF
IT IS A DUPLICATION.
Colleagues:
OK, OK! I am calling time because I don't have the energy to respond to
every proposed solution.
Here is my take on the "King's Knights' Beanies Problem." The answers (see
below) of John Norwood and, later, Kent Schenkel (and one received off list
from Leo Moersen) all seem to state what is generally considered to be the
"correct" answer. But I think they are suspect deductions. In fact, I think
Clinton has a stronger argument that he didn't have sexual relations than
the knight has that he deduced! Here is my thinking. Challenges invited.
As I stated in one of my responses, if a factual inference (assumption) is
required to justify the conclusion then the conclusion has not been arrived
at by deduction, but by induction. It seems to me that all of these
answers, as well as the official solution, infuse an inferred fact not in
evidence, to-wit, that the other knights would have declared within 10
seconds if they had seen a white beanie on our "hero." The conclusion of
RED depends entirely upon the hero's assumption about the other knight's
likely behavior. The RED conclusion is not a deduced one because it is not
necessarily true--the knights might not act that quickly, or at all. Maybe
they throw the game when they realize the daughter is no grat catch! And we
know what Michael O'Hara says about fathers-in-law.) It seems to me that
this is analogous to Bertrand Russell's chicken who assumed that the farmer
would continue to feed it for the rest of its natural life, albiet perhaps
a highly probable conclusion because of the farmer's perfect record up to
the fatal moment. It might be highly _plausible_, but it cannot be arrived
at by the syllogistic logic of deduction.
Now, you might think I am picking nits here, and the chicken example trite,
but consider the tragedy of the Challenger explosion where the NASA and
Morton Thiokol engineers assumed that the risk of launching in sub freezing
weather was negligible because of a 19 out of 19 successful launches up to
that point.
THE GENERAL TEACHING POINT: The lesson I try to teach my law students is
that "99.4%" of our everyday reasoning is inductive in nature. We cannot
assume that our conclusions (decisions, beliefs, judgments) are necessarily
true because there is always some likelihood that a fact exists which is
contrary to our assumption. But we delude ourselves into unwarranted
certainty because we tend to construct our arguments in a deductive form
(and thus believe our conclusions are _necessarily true_) and we forget
about the probabilities.
The better our research the more facts we have, and the more probable our
conclusion. That is what the scientific method of inductive reasoning is
all about--getting the best possible version of the facts so that we can so
that we can use them deductively with confidence. (The major premise
leading to the deduction that Socrates is mortal, "All human-beings are
mortal" is really an inductive conclusion, but it is so highly unlikely
that it will be disproved with contradictory facts we are confident of its
"absolute" truth. But with cloning, who knows?)
THE TEACHING POINT FOR LAW STUDENTS: Inductive reasoning is also the
predominant reasoning leading to a jury verdict (conclusion). That is why
the trial advocate attempts to persuade the jurors that their particular
version of the facts is the most probable. ("Beyond a reasonable doubt, or
"by a preponderance..."). It is more clearly featured in the
"circumstantial" case than in one based on direct evidence, but even the
latter requires induction. Appellate decisions, on the other hand, are
predominately deductive in order to convince the parties of their
undeniable truth--but don't be deluded!
>>>>>>>>>>>>>>>>>>>>>>>>>>> APPENDIX <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
The Norwood Solution:
"WELL, I HAVE SEEN A PROBLEM LIKE THIS BEFORE, SO MAYBE I HAVE AN UNFAIR
ADVANTAGE.. NONETHELESS, HERE IS THE EXPLANATION...
OUR HERO OBSERVES THAT PERSON NUMBER ONE HAS HIS HAND IN THE AIR... THIS
MEANS THAT EITHER OUR HERO IS WEARING A RED HAT, OR THE THIRD PERSON IN
THE GROUP IS WEARING A RED HAT. OBVIOUSLY, THE THIRD PERSON SEES PERSON
ONE WITH HIS HAND IN THE AIR, AND ALSO KNOWS THAT EITHER HE OR THE HERO
MUST BE WEARING A RED HAT. IF THIS THIRD PERSON SEES A WHITE HAT ON THE
HEAD OF THE HERO, THEN HE KNOWS THAT HIS HAT IS RED. HOWEVER, THE THIRD
PERSON DOES NOT ATTEMPT TO ANNOUNCE THAT HIS HAT IS RED... THEREFORE, THE
HERO DOES NOT HAVE ON A WHITE HAT... CONCLUSION: HERO HAS ON RED HAT!"
The Moersen Solution (Received off-list):
"The knight knew his beanie was red because after 10 seconds he was able
to conclude that the failure of the other knights to solve the riddle
meant that his beanie could not have been white. Had his been white,
then the other knights would each have seen one red and one white. They
each then would have concluded that had their own beanie been white, the
the third knight would not have raised his hand (because the third
knight would be looking at 2 white beanies). They each would have
instantly recognized then that their beanie was red and so declared.
But since neither of the other 2 did so declare within 10 seconds, the
winning knight concluded the others' did not have the advantage of
looking at one red and one white beanie, but rather at 2 red beanies.
Therefore his must have been red."
Kent Schenkel's Confirmation:
"John Norwood got it right:
Knight #3 (hero) reasons as follows:
1. If any knight sees two hands raised and at least one white beanie,
he will stand.
2. Neither knight stands.
Neither knight sees a white beanie. (10 second delay is to see if any other
knight stands)"
"It's impossible that everything
that is possible is happening"
- Richard Feynman
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Professor Keith A. Maxwell |
Legal and Ethical Studies| | Voice: 253 756 3703
School of Business | Fax: 253 756 3500
University of Puget Sound | Internet: [log in to unmask]
Tacoma, WA 98416 |
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