Prediction Paradox

[Hannibal]

The teacher and the class know that the last day of term is Friday. A week before, the teacher tells the class that before the end of term there will be an unexpected examination: the pupils will not know, the evening before, that the examination will occur on the following day. It seems plain that the teacher can set such an examination. But the bright pupil argues as follows. The examination cannont be on the final Friday. For then we would know, on the Thursday evening, that it had to be on that day. So the teacher's effective period, within which the examination must be set, ends on Thursday. But then we know, on the Wednesday evening, that (since Friday is already excluded) it must be on Thursday. This contradicts the condition again. So the teacher cannot wait until Thursday. By similar reasoning we can show that there is no day on which the examination can be set.


This is half of the total points of my midterm exam... My teacher included his personal take on the article (which makes it very hard to come up with ideas that don't sound like his words re-hashed, but i have done it), which I will post later if you guys would like, and I have come up with my conclusion, which I would also post later, but I'm interested in how you guys take this....
For this?
Against this?
Could this be truth?

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As miserable as life may be I hold it pretty precious...

If I lose the light of the sun, I will write by candlelight, moonlight, no light. If I lose paper and ink, I wil write in blood on forgotten walls. I will write always, I will capture nights all over the world and bring them to you.
Word And Voice
Motocross Fanatics
General Philosophy

[This message has been edited by Hannibal (edited March 08, 2002).]

[zelazny]

well, considerin the teacher is usually a smart person, he would only tell you that it's an unexpected exam, but secretly, it's an expected exam

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Sure the universe is a great place, but if it wasn't here, no-one would miss it.

[TastinGood]

Why couldnt it be on Monday.

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[Hannibal]

Because.. the teacher just told us about it...
and he said we wouldn't know the night before...
which would be sunday, but we'll be charitable and consider it, the "school night" before.

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As miserable as life may be I hold it pretty precious...

If I lose the light of the sun, I will write by candlelight, moonlight, no light. If I lose paper and ink, I wil write in blood on forgotten walls. I will write always, I will capture nights all over the world and bring them to you.
Word And Voice
Motocross Fanatics
General Philosophy

[Hannibal]

This was what I turned in on it...

II. I chose to analyze the ?prediction paradox? from the philosophy folder. I have never

taken on a task such as trying to explain how something can be, or how something cannot

be, however over the course of the past week, this has seemingly become a common task.

I wanted to get other opinions and ideas on the paradox, although I had my own notes

already written out, so I showed it to some unexpecting parties. None of the parties to

whom I showed the paradox could quite grasp the concept of how the bright student could

eliminate days in such a fashion as the paradox describes. They were as I was when I first

attempted to tackle the subject at hand, perplexed. Upon closer examination of the

paradox however, along with the help of your notes, I came across a few interesting ideas

that I think might be able to disprove how this is possible. At the beginning of the

description, we are told that the teacher has told the class there will be an ?unexpected

examination?. Since he just told the class, it is no longer unexpected. We now have a

time frame to expect the test within, so at any moment, it is expected that the test could

be given, the teacher has already given himself away and proven himself wrong. But this

is not the matter at hand.

The key to this paradox I think lies within the idea of assumptions and fact. We

are given certain facts in the first read of the paradox. When the pupil speaks his theory

we are given both fact and assumption, but it is made to look very much like all fact. I

think this is where people get hung up, is that the pupil expects his assumption to act as if

it were a fact. ?The examination cannot be on the final Friday. For then we would know,

on the Thursday evening, that it had to be on that day.? says the bright pupil. This is fact

for the reasoning he employs here, there is no refuting that. But this assumption follows

later in the statement by the pupil, ?...but then we would know, on the Wednesday

evening, that (since Friday is already excluded) it must be on the Thursday.?. This

assumption, is made thinking that the teacher had not sprung the test on Tuesday before

Wednesday, thus shattering any idea the children might have the night before. But seeing

how earlier in the paradox, the children were made aware of the quiz, they are then

expecting the quiz every day. The students paradox only works if we assume the students

cannot know, but since they already have been made aware of the coming quiz, they can,

and do ?technically? know the night before that there will be a quiz. The assumption that

they must not know is one that is implied, but we cannot take assumption as fact because

it is not so. The fact is that the teacher told them about it, so the students will always be

aware of the quiz. Every night they are aware of it. After letting them know there will be

a quiz, there is no effective way of ?suprising? them with a quiz, thus allowing the quiz to

be given on any day of the following week. This is a rough hypothesis, and some parts

could probably be disproved, but some parts stand on firm logic. My goal with this was

to attempt to come up with a viable answer without ?re-hashing? the notes you provided

with the paradox, and I think I?ve done just that

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As miserable as life may be I hold it pretty precious...

If I lose the light of the sun, I will write by candlelight, moonlight, no light. If I lose paper and ink, I wil write in blood on forgotten walls. I will write always, I will capture nights all over the world and bring them to you.
Word And Voice
Motocross Fanatics
General Philosophy