Re: Smullyan's Quiz Problem

From: ray (ray_sitf_at_yahoo.co.uk)
Date: 12/04/04 

Date: 4 Dec 2004 14:38:07 -0800

>
> I think that if someone says "there will be a surprise test sometime
> in the next week", he usually only means that there is no way *now*
> to figure out what day it will occur on. People don't usually mean
> the stronger claim that, even on the day of the test, you won't be
> able to figure out that there will be a test. Obviously, on the last
> day of the week, you can reason that if you haven't had a test yet,
> you're going to have it today.
>
> > As someone pointed out, the strong interpretation is not actually
> paradoxical, once you realize that just because somebody says something
> doesn't make it true. So, if the teacher announces that there will
> be a surprise test, one possibility is that he is lying---either
> there won't be a test, or it won't be a surprise. If you consider
> the *possibility* that the teacher is lying, then you can't logically
> deduce anything from the fact that he said there will be a surprise
> test, and so on the day of the test, it *will* be a surprise.

I think that you have given the "solution" to the "unexpected exam"
problem.

By Thursday morning, the students will know that either (1) the test
will be on that day and it will be a surprise, or that (2) the test
will be on Friday and it will not be a surprise, in which case the
teacher will have said something that is false when he said that the
test will be a surprise.

However, there is the possibility that the test will not be given on
Friday after all, the teacher might forget, or he might have been
lying, or be taken ill, or he might decide on Thursday night to give
the test the following week. (Put yourself in the shoes of a student
sitting in the class on Friday morning – you don't know for certain
that the test will go ahead that day, its happening is a contingent
event, not a logical consequence of what the teacher said last week.)
Thus the class does not know for certain that the test will be on
Friday. So the test is still a surprise when it is on Friday, although
less of a surprise.

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