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Path: utzoo!linus!decvax!cca!ima!ism780!jim
From: jim@ism780.UUCP (Jim Balter)
Newsgroups: net.math
Subject: Re(2): surprize quiz
Message-ID: <32@ism780.UUCP>
Date: Sun, 11-Sep-83 10:13:00 EDT
Article-I.D.: ism780.32
Posted: Sun Sep 11 10:13:00 1983
Date-Received: Mon, 12-Sep-83 01:06:35 EDT
Lines: 28

re:

I am going to give a quiz, subject to two conditions:

	1) It will be given during class one day this term.

	2) At no time prior to the quiz will it be possible
	   to infer from these conditions that the quiz will
	   be given on a certain day.

I say that the paradox is now genuine. That is, it is impossible
for the teacher to fulfill these conditions.
---
Sorry, but no.  If the teacher gives the test on the first day,
(1) is certainly true, and on what basis could anyone have inferred
that the test would have been given on that day?  If the test is given
on the last day, you can infer that, so the test cannot be given on the
last day *if* the above conditions are satisfied.  But if the test
has not been given prior to the next to last day, you can infer that *either*
the test will be given on the next to last day *or* the conditions will be
violated.  You cannot infer either alone.  So, the test can be given on the
next to last day (or any previous) without violating the conditions.
The problem is that the student is treating the inviolatability
of the conditions as an axiom in his induction, which isn't valid because
such an axiom can only be part of the metalanguage, and so is not available
to the student's logical calculus.

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