Re: Smullyan's Quiz Problem

From: Roger Bagula (tftn_at_earthlink.net)
Date: 12/03/04 

Date: Fri, 03 Dec 2004 22:31:34 GMT

http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Smullyan.html
Looking at his history the exam question isn't paradoxical at all,
but expected.
"unexpected" has the connotation of Random:
If you substitute "at random" for "unexpected , it becomes an
probability problem with an "expectation" distribution , and not a paradox
or logical question anymore. It becomes equally probable that he will
give the exam
on the class days that week ( including the day he announces it).

Here's an alternative:
The professor comes in and writes :
The Swedish civil defense paradox
on the chalk board.
He, then, announces he with give an unexpected exam at some time that week.
The week passes and he gives no exam.
At the first day of the next week when no one has responded to the
phrase which he has left on the chalkboard,
he announces that they all failed the exam:
no one has told him what the "The Swedish civil defense paradox"
is about.
Dirty trick?
Or a clever way to make the students pay better attention?
William Hughes wrote:

>Roger Bagula <tftn@earthlink.net> wrote in message news:<41AF374F.1060107@earthlink.net>...
>
>
>>This is the Swedish civil defense paradox:
>>page 34Mathematical Fallacies and Paradoxes, Bryan Bunch, Dover books,1982
>>It was analyed by Williard Van Orman Quine in 1953
>>
>>The analysis was that the 4th logical possiblity is best :
>>The test will occur this week but it will be unexpected
>>
>>Martin Gardner also has a version of this in an Scientific American
>> article.
>>
>>Bunch concludes that reasoning isn't enough to solve the paradox.
>>Randy Yates wrote:
>>
>>
>>
>>>Raymond Smullyan presents the following (paraphrased) riddle in his
>>>book, "Forever Undecided":
>>>
>>> On Monday a professor says to his class, "I will give you a surprise
>>> examination some day this week. You will not know that there is an
>>> examination when the class begins." A student then reasoned, "I
>>> can't get the quiz on Friday because if I haven't gotten it by
>>> Friday I will know the quiz must be that day." Similarly he reasoned
>>> for Thursday all the way to Monday. Where is the error in his logic?
>>>
>>>My question is this: Why is there any inconsistency in the professor
>>>giving the quiz to the class on Monday?
>>>
>>>Now if the professor had stated to his class on Friday, "I will give
>>>you a surprise examiniation some day next week," then there would be
>>>inconsistency problems for all days of the week, but that's not the
>>>way the problem is stated.
>>>
>>>Comments anyone?
>>>
>>>
>>>
>>>
>
>
>Agreed, the professor can give the exam on Monday and
>it will indeed be unexpected. However, that really doesn't
>deal with the paradox.
>
>This paradox has been presented under many names:
>the Swedish civil defense paradox, the prediction paradox,
>the unexpected exam, the unexpected egg
>to name a few. It gets my vote as the best paradox.
>I have not seen a resoltuion that I find satisfactory.
>
>My own analysis is that the error is the insistance that the
>students must have a rational basis for believing
>that there is or is not going to be an exam.
>
>In essence the professor is saying to the students:
>"you have a rational basis for believing there
>will be an exam if and only if you do not have a rational
>basis for believing there will be an exam". If the
>students believe the professor, they must conclude
>that they do not have a rational reason to either
>to believe that there will be an exam or to believe that
>there will not be an exam. The best resolution is that
>the students should not believe the professor.
>
>In real life, of course, the professor can only
>say "There is a very high probability that you
>will have an unexpected exam next week". This statement
>does not lead to a paradox, so the impression that
>a professor can make this kind of statement and
>communicate information is justified.
>
>In other forms of the paradox, where there
>is no prediction element and hence no probablity,
>the statement (e.g. there is an unexpected egg)
>cannot be believably made.
>
> -William Hughes
>
> 

-- 
Respectfully, Roger L. Bagula
tftn@earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn@netscape.net
URL :  http://home.earthlink.net/~tftn

Relevant Pages

  • Re: Smullyans Quiz Problem
    ... >students must have a rational basis for believing ... >that there is or is not going to be an exam. ... >In essence the professor is saying to the students: ...
    (sci.math)
  • Re: Smullyans Quiz Problem
    ... > Bunch concludes that reasoning isn't enough to solve the paradox. ... the unexpected exam, the unexpected egg ... students must have a rational basis for believing ...
    (sci.math)
  • Re: Updated unexpected hanging paradox bibliography
    ... > the surprise examination or unexpected hanging paradox. ... The claim from the logical school ... an exam tomorrow, but you do not know that"). ... the students hold inconsistent beliefs about how knowledge ...
    (sci.logic)
  • Re: Indias Killer School Exams.
    ... a sizeable chunk of which are students - ... education system and a society in intense transition and it's all too ... March is the year's most dreaded month for Indian students: it's exam ...
    (soc.culture.china)
  • Re: High School Dropout Rate
    ... not a one swell swoop exam at the end. ... Passage Rates on High School Exit Exam Exceeding Projections ... students in the class of 2006 is exceeding projections. ... initially took the CAHSEE as tenth graders in 2003-04. ...
    (soc.retirement)