Yakk wrote:By (1), we can prove trivially that (exam friday).
By (2), this implies ~(exam friday).
Thus (exam friday) and ~(exam friday), contradiction.
silverhammermba wrote:The problem isn't quite so simple.
silverhammermba wrote:The first claim is valid. That is, "The test can't be on Friday because if we haven't gotten the test by Thursday we'll know it's on Friday."
However, there is no way to phrase that without that crucial "if". That is if the test has not been given Monday-Thursday then it can't be on Friday.
silverhammermba wrote:But, Drostie, we know that the student's argument ends up being wrong in the end. So either logic is inherently paradoxical or the student made a mistake. I am much more in favor of the latter.
Fonkey wrote:An interesting thought... what if the prof says "you MAY have an exam next week" instead of "you WILL have an exam next week"?
Drostie wrote:If the students had expected the test every day, then there is obviously no day the professor could give the test such that it would be unexpected.
adlaiff6 wrote:The professor's logic is inherently flawed. He cannot hope to create the scenario he dictates.
Vi wrote:I think one of the problems is that "surprise" is not a very quantifiable term. "Surprise" does not equal "logically it could be a different day besides today." Expectation is a human quality and not a logical one.
T T T T X
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Drostie wrote:So, when you say that, on Thursday, "the test could come tomorrow," what do you really mean? Could it, if all the kids are expecting it?
Fonkey wrote:Yakk wrote:PS: Fonkey -- damn, I've never seen a spambot who detects discussions about surprise exams, and posts in them, before!
What are you saying? That I'm not contributing anything worthwhile to the discussion?
Let us first examine what the schoolmaster actually said. He made two statements: (a) that there would be an examination on one of the five afternoons of the following week; and (b) that the examination would be unexpected. We may define 'unexpected' in this context as meaning that by no process of valid logical argument can the boys at any time predict without contradiction the day of the examination....
...The argument eliminating the last day itself contains two arguments:
(i) The examination must be held on the last day because on the morning of the last day it is the only day left.
(ii) Because of (i) the examination is expected on the morning of the last day and therefore, by (b), cannot be held on that day.
Note that both arguments place the arguer hypothetically on the morning of the last day.
What has been proved by these two arguments is that, for a boy arguing on the morning of the last day, it is necessarily the case that the examination both is and is not held on that day. The conclusion that the examination must be held on the last day is just as warranted as the conclusion that it cannot then be held. Therefore the boys cannot predict, by a valid process of logical argument and without laying themselves open to contradiction, that the examination will be held on the last day. Therefore the examination, even if it is held on the last day, will be unexpected in the required sense.
lazydrumhead wrote:this is my attempt to make everything incredibly simple:
can't we say that our conclusion about friday follows the same rules as the result of the 'paradox' ?
can we not say, "on friday, the teacher cannot give us the exam, because it is the last day of the week (which would not surprise us, therefore not following what he said about the exam occuring during this week). however, he might use this tactic against us and surprise us by giving it to us on friday if we thought we could not have the exam on friday"
therefore friday could possibly be a surprise
therefore any day could possibly be a surprise
Drostie wrote:It is worth asking, if your professor said, "There will be an unexpected test tomorrow," does the same issue occur? (Quine would say it could. Consider what happens if everyone says, "Well, we're going to expect it tomorrow; so it's impossible" and then fails to expect it. Chapman and Butler would extend this by saying that the students cannot come to the desired conclusion by any logical manner. And Nerlich would argue that the primary paradox, here, is that the students' argument doesn't specify a day -- whereas on the Friday-only version, it can.)
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