Ron Barnette's Zeno's Coffeehouse Challenge #44 Result
Dear Zeno's patrons: Here are the results....very creative suggestions...over 500!
First the challenge, as written, then some replies.....
After their successful St. Patrick's Day celebration at the Coffeehouse, Charles and Maggie have been busy working on an appropriate sign to be posted above the entrance to Zeno's Coffeehouse. Each wanted to display a sign, but only one sign could be displayed. Here's some important background information to think about: Whenever Charles makes a sign, he (impishly) inscribes a false statement on it, and whenever Maggie makes a sign, she inscribes a true statement on it...being the truthful woman she is! Being the only signmakers who hang signs at the Coffeehouse, I want you to reflect upon the following sign that was placed directly above the entrance to Zeno's:
THIS SIGN WAS MADE BY CHARLES
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An odd sign to see upon entering the good Coffeehouse, indeed! "Why would Charles make such an odd sign for the Coffeehouse entrance?," a puzzled Candy, a loyal patron, asked. However, as Candy and others realized, if Charles made the sign, then he wrote a true statement on it, which is impossible, since he always incribes false statements on his signs! So it looks as if Maggie made the sign, since the two of them are the only signmakers for the Coffeehouse. But wait! If Maggie made the sign, then the statement on the sign is false, which is again impossible, since Maggie only inscribes truthful statements on her signs! What's going on??? The sign makes perfect sense, if only odd to see above the entrance. If it was made by Charles then it's true, and if it wasn't, the sign is false...right? So what's the solution?????
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The many creative relies were most appreciated, as I read and replied to those who responded. My original intent was with Lauri's first possibility below, but I have been taken immensely by others' most creative responses! Good work all!!! And thank you:) Barnette
Daniel writes:
comments: An airtight version of this story, produced by stating explicitly various
things that are hinted at here, would contradict itself and therefore could not be true.
This version, on the other hand, has an assortment of interesting loopholes. A selection
of possibilities:
1. Charles made the sign and inscribed a false statement on it; then someone, perhaps even
Charles himself, erased that statement, or painted over it, or hid it by turning it toward
the wall, and put the true statement "This sign was made by Charles" on it.
2. Maggie made the sign and inscribed a true statement on it; then someone erased or hid
that statement and put the false statement "This sign was made by Charles" on
it.
3. (personal favorite:) Maggie made the sign and inscribed the true statement "This
sign was made" on it. Then Charles impishly added the sentence fragment "by
Charles".
4. Some unknown person made the sign; then some unknown person put "This sign was
made by Charles" on it; then:
A. It was placed over the entrance without being hung.
B. It was hung by Charles or Maggie.
C. It was hung by someone who was not a signmaker.
5. Maggie made the sign, and inscribed the true statement "This sign was made by
Charles" on it; the statement is true because:
A. the phrase "this sign" refers to the previous sign over the entrance, which
is almost completely covered up by this new sign.
B. 'Charles' is Maggie's last name.
C. The statement "This sign was made by Charles" is the Zlabonian translation of
"This is Zeno's Coffeehouse"; the Zlabonian language bears a coincidental
resemblance to English.
Mathieu writes:
comments: This is the essence of the self-referrential paradox. Barring any tricky
solutions (such as "Charles wrote the inscription and therefore did not technically
'make' the sign." or "Charles and Maggie each wrote one line."), there is
very little logical room for maneuvering. To me it must be Charles. Maggie tells the
truth, and I understand the truth to be an absolute form of correctness and
straight-shooting. Therefore, it is unthinkable for her to make this sign. However,
Charles "impishly incscribes false statements." He wants to lead us astray. So,
he makes the sign above, which leads us to impossible conclusions.
Lauri writes:
comments: I think there really are three possibilities.
1. The premisses of the problem are inconsistent. So, somebody (Ron?) is trying to bluff
us. This is perhaps the only purely logical answer to this problem (and to liar's paradox
type problems on the whole).
2. More philosophical way to try to answer the problem requires endless - and usually
fruitless - speculations about "truth", "false", "metalanguage
vs. object language", etc. Trying to answer the problem within this philosophical
category is far out of my reach.
3. There remains (at least) one possibility which in fact requires more detective work.
Maybe someone else than Ron has done the bluffing. The sign is really made by Charles or
Maggie. BUT SOME PRACTICAL JOKER HAS TURNED THE SIGN AROUND. The original sentence (by
Charles or Maggie) is now unseen, facing the wall. The joker has written the sentence we
see now. And all the background information given is consistent with this solution.
Eric writes:
comments: well there are many reasonable conclusions. one of which is that the sign
itself( the wood or whatever the signs material was) was made(as in built) by charles. if
that is the case then maggie was right, charles did make the sign. That was one point of
view that although doesn't count, I felt like sharing anyways. Now for what i think the
answer realy is. I find it hard to believe that an establishment does not have an entrance
sign, giving the customer an idea to where he/she is. So in light of that, charles had
crafted the "Zeno's coffeehouse" sign. Maggie had posted a sign describing who
had made the sign above. She is obviously not good with details as to which sign was made.
Shack writes:
comments: Perhaps Maggie inscribed "THIS SIGN WAS MADE".
Then Charles (impishly) inscribed "BY CHARLES".
Mark writes:
comments: Let us (in the Zeno tradition) make a random assumption (provisionally of
course), then to derive our impossible conclusions from it.
Assume Charles made the sign.
When you compare the assumption with the information on the sign "THIS SIGN WAS MADE
BY CHARLES", no false information can be found. This violates the first
constraint. So we must nullify this assumption and conclude that Charles did not make this
sign.
Using similar logic we can determine that Maggie did not make the sign either.
Given the final constraint, must we conclude that only Charles or Maggie made this sign?
No! Assuming the scope of sign makers is limited to 'only' Maggie or Charles is a
false dilemma. Take a closer look at the final constraint
"Being the only signmakers who hang signs at the Coffeehouse, I want you to reflect
upon the following sign . . ."
The subject of the sentence is 'I' and that 'I' is Ron Barnette. Maggie and Charles
are not explicitly mentioned in the final requirement. You can therefore interpret
the last requirement as
Maggie, Charles or Ron being only sign makers who hang signs at the Coffeehouse
Assume now that Ron hung the sign
The problem places no limitations on Ron for truthfulness of his signs.
Ron, Zeno's Proprietor, can place a sign at the coffee house without violating any
constrains given in the problem.
The sign maker was Ron.