The ol' pop quiz paradox:
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<br>On the first day of class, a professor announces that there will be a surprise quiz at some point during semester. Now, imagine some student on the evening before the last lecture. He realizes there has not yet been a quiz, so he knows the quiz must be the next day. But in that case, this quiz will not be a surprise. So, this student knows the test cannot be on the last day. But, if the quiz was to be given the next-to-last lecture, then again the night before this lecture, the student would know that it must be the next day (since there are only two days left, and if the quiz were given on the last day it would not be a surprise). But now the very same reasoning seems to rule out the second-to-last lecture, the third-to-last lecture, and so on. Therefore, the promised &quot;surprise&quot; quiz is not possible!
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<br>Not convinced? Here's a little demo: <!-- BBCode Start --><A HREF="web.mit.edu/adam/www/quiz/" TARGET="_blank">Surprise Quiz Simulator</A><!-- BBCode End -->
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Does anyone know Quine's solution to this paradox?

&gt;&gt;Does anyone know Quine's solution to this paradox?
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<br>I think Quine tries to argue that the students cannot claim they will know on the eve of the last day, that the quiz will occur on the last day. So, the whole argument never gets started....
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<br>But I'm not sure about the details. The two references I know of are,
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<br>W. V. O. Quine, On a so-called paradox, Mind 62 (1953), 65-67. and
<br>W. V. O. Quine, The Ways of Paradox, and Other Essays, Harvard University Press, Cambridge, MA
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ok...i'll bite.
<br>the 'paradox' seems to rest on the shrinking sample set, but that places the professor's statement in a different context. the statement is merely that there will be a pop quiz during the semester - at that point, the statement is true. that the quiz could be scheduled on a date (the last day) that would enable the students to know in advance (by one day) the location of the quiz does not negate the truth of the statement at the time it was made.
<br>taylor wagen
<br><!-- BBCode auto-link start --><a href="www.breadandcircuses.com" target="_blank">www.breadandcircuses.com</a><!-- BBCode auto-link end -->
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This paradox is flawed in that it involves both logical AND psychological expectation, which clouds the issue. But the latter can be removed, and this can most easily be done in the paradox's more colorful incarnation, known as &quot;The Unexpected Hanging&quot;. Thus --
<br>A prisoner is brought before a judge on a Sunday, and the judge says &quot;You have been sentenced to hang, but your hanging must satisfy two conditions: One, you must be hanged on one of the five days following today, and two, you cannot be hanged on any day on which your hanging would be necessary to satisfy the first condition&quot;.
<br>The prisoner goes back to his cell and thinks, &quot;Wait a minute. Friday is the last day he can hang me, and thus it's a day on which my hanging would be necessary to satisfy the first condition. Therefore I can't be hanged on Friday. But that makes Thursday the last day he can hang me, and thus the reasoning that was just applied to Friday can now be applied to Thursday, which makes Wednesday the last day, and this can be repeated right through Monday, and so he can't hang me at all!&quot;
<br>But the judge orders the prisoner hanged on Wednesday (or Friday or Monday or Thursday or Tuesday), and feels himself to be entirely within his rights, since Wednesday was one of any five days on which he could have hanged him, and therefore had no necessity attached to it.
<br>Put in this way, the root of the paradox becomes fairly clear. Anyone care to give it a shot?

The difference between the two paradoxes is partially one of inevitability. In the pop quiz problem the statement that there will be a quiz and that it will be a surprise seems to make a statement that the professor can know to be true or false at the time the statement is made, plus a prediction that when the quiz is given it will be a surprise. The predictive element turns out, under certain circumstances, to be false. This is not logically paradoxical, it just casts the original statement in error. In other words, the professor can be right or wrong about the truth or his own statement and the accurracy of his prediction. For the student to be able to perform the shrinking set regressive analysis in a futile effort to escape the quiz through his wits, he must BELIEVE that the surprise element MUST be true. It turns out that the surprise part can turn out to be false under certain circumstances (i.e. the professors procrastination, or the professors failure to see that he will falsify his own statement by scheduling the quiz on the last day). Since the quiz is certain, but the truth of the &quot;surprise&quot; is not, the student's logic falls to the harsh reality that the quiz can be given on any day, even the last.
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<br>The unexpected hanging does remove the psychological element of &quot;belief&quot; as Marnasin points out. Here though the element of the future event (hanging) NOT being inevitable changes the equation. A friday hanging can still occur consistent with the judges orders because the order allows for the possibility that no hanging will occur. If you insist that the judge is ordering a certain hanging, then you must accept that the order may simply turn out to be impossible to comply with if thursday comes and goes. Because a hanging is not certain, either by the judges instructions or by &quot;reality&quot;, the prisoners hope is misplaced.
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<br>Ken