Danny Uncanny7 wrote:The paradox is a lot easier to see if you narrow it down to just one day.
The professor says, I will give you an exam tomorrow, and it will be on an unexpected day. The students realize that this is impossible, so if it is to be unexpected, it can't be tomorrow. Then they are happy and think the evil professor made a promise he couldn't hold, and don't prepare for the test. However, the next day, they have the exam. And all are surprised.
I agree that's an element of the paradox. But certain expressions like commands for example aren't truth functional and our linguistic conventions regarding such expressions reflect this. If the teacher said, "I will give you the test, and you will love it." The former he can do; the latter he can command, or hope for, but it's not a truth functional claim.
Similarly, surprise can not be commanded, or if it is , it is a wish or hope, but not fact that can be reliably averred. If I told you there is a cupcake in the fridge, and when you see find it, you will be surprised. You ask, "Why, is a special cupcake? I say, "if you like Hostess, it is, but otherwise no." "You will be surprised that there is a cupcake there at all." You would not be surprised.
Now, maybe you know me to be a glutton, or a liar, or both, but assuming I'm truthful and not a glutton, and you believe these things about me, you just won't be surprised. I haven't lied, because it was a hope, a naive, stupid hope that you would be. It's not a hard fact the way the cupcake in the fridge is.
So if the teach says" You will take the test tomorrow, and you will be surprised" I would say you can make me take the test, but I'm sorry, if I know I'm taking the test, you can't surprise me by giving it. You can hope or command that I be surprised, I'm sure bad magicians hope they will amaze and astound, but they don't.
Of course, add an element of real unpredictability, and a use of surprise where it actual applies, and you get the paradox. But if the test occurs on Friday, you will know on Thursday, even if surprise is predicted, it just won't happen given the convention of surprise, Otherwise, you will really have no certainty ( there will be probabily -- see three card monty issue) when the test will be given, and no idea at all, on Monday.
phlip wrote:skullturf wrote:This has already been mentioned in this thread, but isn't one relatively common interpretation of the surprise exam paradox is that it's a proof by contradiction that a certain set of premises is inconsistent?
That was my favoured interpretation for a while, but I realised it doesn't fit... if the premises were inconsistent, it would be impossible for them to all be true at once (by definition), and yet at the end of the story, there was an exam, during the specified time period, and the class was surprised.
The claim that the premises are inconsistent are at the heart of the paradox. Specifically: 1) The exam will be given on one of the five days of a week running consecutively from Mon to Fri ; 2) The students will be necessarily be surprised on the day of the exam; 3) Enthymatic premise, if one knows one will be tested on a particular day, one is not surprised. Say, the test is given of Friday, via disjunctive syllogism, the student knows the test will be given on Thursday, which based on 2 and 3, means he's not surprised, call this 4. 4 and 2 are inconsistent and you have a contraction S and not S.
I argue above that the definition and context of the term "surprise" creates this problem and will for any defined set where one knows only a limited number of events can take place within the subsets. That definition of surprise can not be met, provided the enthymeme 3, which is a basic convention of our language use.
If the set up is too confusing for George and the others, the paradox is just a case of misunderstanding, and there is no paradox, just one of those " What the hell was I thinking?" moments. People who don't grasp rules are bound to be surprised on a regular non-paradoxical basis.
Or in the alternative, the on the day of the exam part, which wasn't defined in the version I originally read, but was covertly assumed, is discharged, even if George and his class, follow the rules they will still be surprised ,even on the day of the exam, except Friday.
Or the teach is just violating 2, and again no paradox, just a teacher who screws up the rules and causes confusion/surprise in so doing.