The Surprise Examination, Part Two

When discussing hard questions, or philosophizing, as it were, I find it's best to break the ice by being a total prigger and showing everyone just how smart you are. It's a great way to break the ice [Edit: which I just said in the very first line, jesus CHRIST I need to stop posting at 3AM], and regardless of whatever happens afterwards, everyone will remember that you're the guy who's clever, as opposed to merely "smart."

So, without further ado:

The Smartass Solution to the Surprise Examination Paradox: Stipulating for the sake of argument that Scott's general logic is sound, Scott's conclusion is nevertheless flawed. Professor X is perfectly capable of giving his class a surprise examination, because he is not precluded by anything he told the class from giving more than one.

The rebuttal to this, of course, is, what if Professor X gives an exam on Thursday? Then, in order to have a surprise exam, he would have to give it on Friday, which of course would no longer be a surprise.

But what if he doesn't give an exam Friday? That means the Thursday exam was the surprise exam. The mere possibility that Professor X could give more than one exam puts the surprise/not surprise property of the first exam in an undetermined state until the week is at a close.

So now, to put an end to the cuteness, let's assume Professor X told the class he's giving one and only one exam the next week.

First Proposed Solution: Inclusion of the Paradox within the operative definition of "surprise": thinksinpictures was good enough to propose this solution. Simply put, the term "surprise" is wide enough to encompass the very logic that Scott puts forth, meaning that no matter how many iterations of this paradox Scott formulates, the term "surprise" continues to encompass them. There will always be the possibility of a real surprise, because the very logic that renders the giving of an exam "impossible" makes the surprise once again possible.

Other, more serious philosophers probably approach this solution from another angle, namely, parsing the term surprise and breaking it down into constituent parts. One may be surprised either by ignorance or by error. I remember reading something like this somewhere.

Other serious philosophers, those whose strong academic credentials give them license to be flippant, will simply resolve the paradox by pointing to the end result: clearly, it was not impossible for Professor X to give a surprise examination, because, well, he did it. I believe this to be part and parcel with the first proposed solution.

Second Proposed Solution: Scott's basic argument goes like this: If Professor X does not give the exam by Thursday, he must give it Friday, therefore he cannot give it Friday. However, if he cannot give it Friday, then if by Wednesday... yadda yadda. Notice what has happened here. Professor X being unable to give the exam Friday relies upon him having to give it Friday, which in turn relies upon him not having given it a previous day. The apparent paradox is created because Scotty is choosing to contemplate only one out of five possible futures. In four of those futures, Hypo-Scotty in fact knows that there will be no exam Friday because it's already happened. Therefore, Professor X is not obligated to give the exam Friday, and therefore still can.

To put it glibly, Professor X is only enjoined from giving the exam Friday on Thursday night, because only then will all the relevant superpositional states have been resolved such that he cannot give the exam, either because he already has, or because it will no longer be a surprise. Although it may not make sense, Professor X on, say, Tuesday night, can still give the exam on Friday, because he doesn't yet have to.