Say a teacher says he’s going to give a pop quiz next week, and the day he’s giving the quiz will be a surprise. Here are the options:
Mon Tue Wed Thur Fri
Right off the bat we can say that the quiz must be given at the latest by Thursday, because if the quiz isnt given by Thursday you’ll know it MUST be on Friday because that’s the only day left, hence ruining the surprise. So we’re left with:
Mon Tue Wed Thur Fri
The same thing can be said about Wednesday. If the quiz isn’t given by Wednesday, then you’ll know its on Thursday. So you must be getting it by Wednesday.
Mon Tue Wed Thur Fri
So now if the quiz isn’t given by Tuesday, then you’ll know the quiz is going to be on Wednesday because you also can’t have it on Friday or Thursday. So it must be on Tuesday.
Mon Tue Wed Thur Fri
If the quiz isn’t given by Monday, then you’ll know it must be on Tuesday. But it can’t be on Tuesday, or any other day!
Mon Tue Wed Thur Fri
With only one day left to give the quiz you know it must be on Monday. But this means that its impossible to have a pop quiz truly ever be a surprise.
Remember the criterion for this “pop quiz” was that it must be a true surprise, but through a little logic it can be shown that it is impossible to make it a surprise.
wait, maybe i do get it, ha. This is how i perceive this, so i hear i can get a test this week, if i dont get it monday, well i could still get it t, w, t, f. Logically that would imply that it “could” be tomorrow, not that it “is”. Right? I do see where your coming from in saying that if not “now” then it must be the next closest “now” in which it could reside, which ruins the “suprise.” But before that time arrives it is unkown, and a suprise, i dont see to big of a paradox here, but i dont perceive as you do.
This is the same or similar to the prisoner’s paradox, correct? Your argument only holds true IF the quiz isn’t given by the end of class on Thursday. However, the quiz could be given on Tuesday. Then it would be a surprise, wouldn’t it?
The argument is based on the premise “IF it hasn’t happened by the end of class on Thursday,” though, right? Why would it not be a surprise if it happened on Tuesday?
I understand how the argument is structured, I had this in a logic class but it was the prisoner’s paradox (can’t recall the exact name). I still say that it is faulty, because it could occur on Tuesday and be a surprise.
But the student doesn’t know on Monday or on Tuesday that it must be Tuesday, therefore…[size=150]surprise[/size]! [size=85]
(sorry, two beers it all it takes to get me a little loopy…)[/size]
Right off the cuff, it seems that the ‘logic’ is bass ackwards. You have to know the end of the week to be not surprised Mon or Tues. It is reversed logic which doesn’t hold.
The quiz can be a surprise Mon, Tues, Wed, less on Thurs, and not a surprise on Fri.
This is how and why ‘logic’ is a very limited tool to determine ‘truth’ at any level.
Logic can make the most ridiculous nonsense, such as the above, seem like a rational ‘proof’ rather than the irrational ‘poof’ that it so often is.
This shows how ‘formal logic’ can produce the same category of ‘lie’ that it so rigorously tries to ‘expose’!
Logic has its occassional pragmatic uses, granted, but it is no ‘god’ or ‘universal law’!
The problem is the revelation of the surprise, not surprise itself. If the test is going to be on Friday, then the surprise is revealed/discovered at the end of Thursday. You don’t know until that instant which it will be.
Of course you could also argue that any foreknowledge eliminates the possibility of surprise in the first place. That’s why they call it a pop quiz instead of a surprise quiz. If you were warned to be prepared for a pop quiz on any day it can’t be a surprise or unexpected.
If none of the days can be a surprise, then what ever day the quiz does take place on, it WILL be a surprise, because, as you’ve reasoned the quiz can’t be on that day.
The minute you’re told there is a quiz next week, bang goes the surprise. A real surprise would be if the teacher then did the quiz the following Monday.
I think the problem here is that we’re assume both students and teacher have thought the logic of the OP through and are counting on it to predict when the test will be given. I don’t think we have the right to assume this.
If the teacher says there’s going to be a pop quiz some day this week, that’s all we can assume. We can assume that if the test is given on Friday, it won’t be a surprise (the students aren’t that stupid), but before the end of Thurseday, no student knows whether it will be today (Thurseday) or tomorrow (Friday) and are therefore in a state of suspense and would be surprised if it was given today (Thurseday).
If we make it a mandatory part of the problem that the students WILL be surprised - no exceptions - then indeed the test couldn’t be given on Friday, but it doesn’t follow that the same logic applies to Thurseday, and if this doesn’t follow, it doesn’t follow for any of the other days of the week. It doesn’t follow because we’re not justified in assuming the students and teacher have followed the logic in the OP (and somehow know the other has also followed this logic). In other words, the only way it would NOT be a surprise on Thurseday is if the students KNEW the teacher had planned ahead and decided not to give the test on Friday, but we don’t have the right to assume this - even if the teacher indeed chose not to give the test on Friday for the sake of preserving the element of surprise.
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