The surprise quiz next week

[hellokeith]

Teacher - "Students, there will be a surprise quiz next week."

Erudite Student, thinking to him/herself - "'Surprise' dictates I will not know the day of the quiz. If by the end of Thursday we have not been quizzed, then I would know the quiz will be on Friday, thus it is not a surprise, so the quiz cannot be on Friday. Knowing it cannot be on Friday, then if by the end of Wednesday we have not been quizzed, the quiz would have to be on Thursday, but again I would know the day and therefore it is not a surprise, so the quiz can neither be on Friday nor Thursday. If I continue this logic, then it is impossible for the teacher to surprise us, so this means we are not having a quiz!"

I have a theory on this. It's not a solution, but I believe it solves one of the problems in the paradox.

 

[Cattlegod]

What exactly are we trying to solve?

 

[TuxDave]

Care to share your theory before we all start chiming in?

 

[Pulsar]

It's not a paradox. True, the quiz cannot be on Friday for the stated reason. However, the logic from there is faulty. The student could have the test Monday and it would be a complete surprise. The only issues comes from the assumption that he will make it to Thursday without a quiz - which is obviously faulty.

 

[hellokeith]

Incorrect. It is impossible for the quiz to happen on Friday and be a surprise. Knowing it can't happen on Friday, that rules out Thursday as well, because if it hasn't happened by the end of Wednesday, then it would have to be on Thursday (since Friday is already ruled out), and knowing it will happen on Thursday means it isn't a surprise on that day either. Keep going with this logic, and you are left with Monday as the only day, but since it's the only day remaining for the quiz, then it isn't a surprise on that day as well.

A surprise means you are not expecting it. Foiling the surprise does not require perfect knowledge of the future, just some knowledge.. in this case, only a prior day.

 

[BrownTown]

The reasoning seems pretty sound to me given that you assume the teacher is actually telling the truth. In reality they would simply choose one of the 5 days and every fifth time you would in fact know the date of the exam

 

[PowerEngineer]

It seems to me that the key here is "when" the student is supposed to be surprised. I may be wrong, but the assumption here is that the student has to be "surprised" at the moment the teacher starts passing out the quiz.

I'll suggest that the student can be equally "surprised" on those days in class when the teacher does NOT pass out the quiz.

If the quiz doesn't occur before Friday, then the student is not surprised on Friday -- but the student has been surprised on Monday, Tuesday, Wednesday, and Thursday when the quiz didn't occur.

If the quiz occurs on Monday, then the student is surprised on Monday -- but there are no surprises for the rest of the week.

So, on that basis, I think the student is still "surprised" when the quiz is on Friday.

 

[BrownTown]

Yeah, thats a good way to think about it. I think most people (including myself) assume that he must be surprised on the day as the test is being passed out. The reason for this assumption however is likely due to the fact that in reality the reason for trying to anticipate a pop quiz is to procrastinate studying for as long as possible. In the case that the test is on friday if the student learns this on Thursday then he knows to prepare that night and has suceeeded in playing the system by minimizing the amount of study time he needs to prepare (since studying on Sunday like he probably should would mean forgetting some of what he had learned by Friday). Therefore most people assume the surprise should come at the time of handing out the test.

 

[CSMR]

Originally posted by: hellokeith
Teacher - "Students, there will be a surprise quiz next week."

I was told this by a philosopher. I don't understand why it is paradoxical. Perhaps philosophers are a gullible sort and always believe their teachers.

 

[CSMR]

The non-paradox is this:
the teacher tells the student something that may be true but cannot be believed.
Another example is:
"You believe in ghosts but you are wrong."
I think why some people find the original statement paradoxical is they get caught up in the logic and have only a little brain-power left with which they see the non-paradox as a paradox.

 

[Cattlegod]

I don't think your argument holds up. I mean, I can simply say that you will have a surprise in your future. Going by your logic, you will never have a surprise again because you will be expecting it when in reality, you know that you will be surprised at some point.

 

[PhatoseAlpha]

The logic only seems to work by limiting the suprise to being the day of the week it's on. If you allow smaller amounts of time, I'd expect that you wouldn't be able to get back to monday from friday - each attempt to move would have to be subdivided into smaller lumps of time, then those into smaller, and smaller, etc, etc.

 

[Howard]

Originally posted by: hellokeith
Incorrect. It is impossible for the quiz to happen on Friday and be a surprise. Knowing it can't happen on Friday, that rules out Thursday as well, because if it hasn't happened by the end of Wednesday, then it would have to be on Thursday (since Friday is already ruled out), and knowing it will happen on Thursday means it isn't a surprise on that day either. Keep going with this logic, and you are left with Monday as the only day, but since it's the only day remaining for the quiz, then it isn't a surprise on that day as well.

This does not refute Pulsar's argument.

 

[Peter]

Dude, just revise your stuff and let the test hit you whenever

 

[blahblah99]

Originally posted by: hellokeith
Incorrect. It is impossible for the quiz to happen on Friday and be a surprise. Knowing it can't happen on Friday, that rules out Thursday as well, because if it hasn't happened by the end of Wednesday, then it would have to be on Thursday (since Friday is already ruled out), and knowing it will happen on Thursday means it isn't a surprise on that day either. Keep going with this logic, and you are left with Monday as the only day, but since it's the only day remaining for the quiz, then it isn't a surprise on that day as well.

A surprise means you are not expecting it. Foiling the surprise does not require perfect knowledge of the future, just some knowledge.. in this case, only a prior day.

It's only seems paradoxical because you're assuming that the quiz will not happen prior to the assumed event, in which case is perfectly valid. But the event CAN occur at ANY time prior to the assumed event, so the paradox falls out of place and your reasoning is no longer valid.

 

[Ipno]

Its a quiz about surprises.

 

[Pulsar]

I'll say it once more in a different way.

The logic that it cannot hold Friday holds.

The logic that says it cannot happen Thursday does NOT.

Thursday, in school, you do not know if it will happen today or tomorrow.

The flaw is in how it's presented. You are reasoning backwards, with knowledge from Friday. A normal person passes through time the other way.

It clearly falls apart when looking at it from the start of the week. The only truth is that if you haven't had it on Thursday, you'll know it's on Friday. Otherwise, a quiz given Monday, Tuesday, Wednesday, or Thursday will surprise the students.

I'm not a philosophy major so I don't know the big words to use. But clearly the flaw in the reasoning is trying to move backward through time presupposing knowledge that you wouldn't otherwise have doesn't work.

 

[QuantumPion]

This is a variation of the classic http://en.wikipedia.org/wiki/Unexpected_hanging_paradox.

Formulation of the judge's announcement into mathematical logic is made difficult by the vague meaning of the word "surprise". A first stab at formulation might be:

* The prisoner will be hanged next week and its date will not be deducible from the assumption that the hanging will occur sometime during the week (A)

Given this announcement the prisoner can deduce that the hanging will not occur on the last day of the week. However, in order to reproduce the next stage of the argument, which eliminates the penultimate day of the week, the prisoner must argue that his ability to deduce, from statement (A), that the hanging will not occur on the last day, implies a last-day hanging will not be surprising. But since the meaning of "surprising" has been restricted to not deducible from the assumption that the hanging will occur during the week instead of not deducible from statement (A), the argument is blocked.

This suggests that a better formulation would in fact be:

* The prisoner will be hanged next week and its date will not be deducible in advance using this statement as an axiom (B)

Some authors have claimed that the self-referential nature of this statement is the source of the paradox. However, Fitch[4] has shown that this statement can still be composed in mathematical logic. Using an equivalent form of the paradox which reduces the length of the week to just two days, he proved that although self-reference is not illegitimate in all circumstances, it is in this case because the statement is self-contradictory.

 

[Steve]

Now, a clever man would put the poison into his own goblet because he would know that only a great fool would reach or what he is given. I am not a great fool, so I can clearly not choose the wine in front of you. But you must have known that I am not a great fool, so I can clearly not choose the wine in front of me....so you could have put the poison in your own cup, depending on your strength to save you, so clearly I cannot choose the wine in front of you. But you've also bested my Spaniard, which means you must have studied and in studying you must have learned that man is mortal, so you wouldhave put the poison as far from yourself as possible, so I can clearly not choose the wine in front of me.

 

[QuantumPion]

Never go in against a sicilian, when death is on the line.

 

[JSSheridan]

If you believe everything a professor says, you'll just make a B.

You won't make an A until you find their mistakes.

 

[weflyhigh]

Originally posted by: Ipno
Its a quiz about surprises.

Hahahaha

 

[CSMR]

Originally posted by: QuantumPionhttp://en.wikipedia.org/wiki/Unexpected_hanging_paradox.

Wow! Philosophers must be real morons to consider this a "problem".

 

[Leros]

The surprise is that the test is actually this week.

 

[yh125d]

The teacher comes to your house on Saturday and quizzes you.


/thread