From: IN%"jheap who-is-at oise.on.ca" "James L. Heap" 28-MAY-1996 23:34
To: IN%"wdarrou who-is-at calstatela.edu", IN%"green@edstar.gse.ucsb.edu", IN%"peglin@mach2.wlu.ca", IN%"colsen@oise.on.ca" "Chris Olsen", IN%"enangel@cityu.edu.hk", IN%"wilson@sscf.ucsb.edu", IN%"dzimmerman@descarte.ucsb.edu", IN%"rdheyman@acs.ucalgary.ca", IN%"j
CC:
Subj: (Fwd) ANALYST May (Preprint #22)
Greetings,
A bit of amusement, forwarded to me by Peter Weeks of St. Thomas
University in Fredericton, New Brunswick.
James
------- Forwarded Message Follows -------
Date: Sun, 26 May 1996 11:29:19 BST
Reply-to: Analyst-Admin who-is-at sheffield.ac.uk
From: analyst admin <Analyst-Admin who-is-at sheffield.ac.uk>
To: Multiple recipients of list <analyst who-is-at sheffield.ac.uk>
Subject: ANALYST May (Preprint #22)
Volume 2 Number 16
__________________________________________________________________________
ANALYST -- 26 MAY 1996
__________________________________________________________________________
Preprint #22
The Paradox of the Question
Ned Markosian
Once upon a time, during a large and international conference of the
world's leading philosophers, an angel miraculously appeared and said, "I
come to you as a messenger from God. You will be permitted to ask any one
question you want - but only one! - and I will answer that question
truthfully. What would you like to ask?" The philosophers were
understandably excited, and immediately began a discussion of what would
be the best question to ask. But it quickly became obvious that they
needed more time to discuss the matter, so they asked the angel if he
could get back to them. The angel was obliging, and said that he would
return at the same time the next day. "But be prepared then," he warned
them, "for you will only get this one chance."
All of the philosophers gathered at the convention worked at a frenzied
pace for the next twenty-four hours, proposing and weighing the merits of
various questions. Other philosophers from around the world became
involved as well, faxing and emailing their suggestions. Some were in
favor of asking the kind of practical question that lots of people might
like to know the answer to, such as this one:
Q1 Is it better to check your oil when the car is hot or when it is
cold?
But others said they should not squander this rare opportunity, which gave
them a chance to learn something about a truly important and intrinsically
interesting topic, and after some discussion it was generally agreed that
this was right.
The philosophers were puzzled, however, about which truly important and
intrinsically interesting topic they should address in their question. The
problem was that they really needed to know in advance what would be the
best question to ask, in order to make the most of their marvelous
opportunity. One proposal was to try to sneak in two questions, by asking
something like this:
Q2 What would be the best question for us to ask, and what is the
answer to that question?
But this proposal was quickly voted down when it was pointed out that the
angel had explicitly said that they would get just one question.
Another proposal was simply to ask the first of the questions in Q2, in
the hopes that some day they would have another opportunity similar to
this one, when they could then ask the question they knew to be the best.
This proposal was ruled out, however, on the grounds that if they adopted
it then they would probably never get a chance to ask the best question
once they knew what it was.
For a while there was a growing consensus that they should ask this
question:
Q3 What is the answer to the question that would be the best question
for us to ask?
That way, it was argued, they would at least have the all-important
information contained in the relevant answer. But eventually concerns were
raised about the possibility of receiving, in response to Q3, an answer
such as 'seven', or 'yes', which would mean nothing to them unless they
knew which question was being answered.
Finally, just as the philosophers were running out of time, a bright young
logician made a proposal that was quickly and overwhelmingly approved.
Here was her question:
Q4 What is the ordered pair whose first member is the question that
would be the best one for us to ask you, and whose second member is
the answer to that question?
Nearly everyone (remember, these are philosophers we're talking about)
agreed that this was the ideal way to solve their little puzzle. By asking
Q4 the philosophers could ensure that they would learn both what the best
question was, and also what the answer to that question was. There was a
great deal of celebrating and back-clapping, and as the minutes ticked
down to the time when the angel had promised to return, the mood among
philosophers throughout the world was one of nearly feverish anticipation.
Everyone was excited about the prospect of learning some wonderful and
important truth. They were also more than a little pleased with themselves
for hitting upon such a clever way to solve the problem of how to find out
what the best question was, and also get the answer to that question, when
they had only one question to work with.
Then the angel returned. The philosophers solemnly asked their question -
Q4 - and the angel listened carefully. Then he gave this reply:
A4 It is the ordered pair whose first member is the question you just
asked me, and whose second member is this answer I am giving you.
As soon as he had given his answer, the angel disappeared, leaving the
philosophers to pull out their hair in frustration.
The above story leaves us with another little puzzle to solve. At the time
the philosophers asked Q4, it seemed like that question was the ideal one
for their peculiar situation. But as it turned out, Q4 was obviously not
at all the right thing to ask. (They would have been better off asking
whether one should check one's oil when the car is hot or when it is
cold.) The puzzle, then, is this: What went wrong? <1>
Copyright Ned Markosian
nmarkos who-is-at wvnvms.wvnet.edu
1. I am grateful to Mark Aronszajn and Donald Turner for dicussions of
this topic, and to Donald Turner for telling me the joke that the puzzle
is based on.
Peter Weeks
St.Thomas University
Fredericton, N.B., Canada
Email PWEEKS who-is-at StThomasU.ca
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