Resolving The Surprise Test Paradox

Why I think I've found a solution

In this post, I’m going to resolve the surprise test paradox.

The surprise test paradox is as follows:

A teacher tells a student that he’s going to have a test this week, but that he will not know when the test is coming.

Upon hearing this, the student realizes that he will not have a test on Friday, since, if the test were on Friday, he would know that morning that the test was going to occur.

But, since he knows that the test won’t occur on Friday, he realizes that he also won’t have a test on Thursday because, on Thursday morning, he would expect for the test to occur since he would already know that it’s not going to occur on Friday.

Then, using similar logic, he also deduces that the test also won’t occur on Wednesday, Tuesday, or Monday, and that, as such, he shouldn’t expect for the test to occur at all.

Glad that he isn’t going to have a test, he walks into class on Wednesday and is, of course, handed a test.

I used to think this was a paradox since it seems like the student’s logic is correct and, yet, it leads to a conclusion that guarantees that he will not know when the test is coming by causing him to expect for no test to come at all.

I now no longer think that it is a paradox.

When the student concludes that the test is not going to occur on Friday, he, in fact, makes it possible for the test to occur that day since he, now, no longer expects it. As such, the student made a reasoning error by failing to take into account the fact that his expectations determine whether or not a test occurs. If the student were instead reasoning properly, he should have realized that, each morning, he should expect a test to occur that day, since, if he expects it to occur, it will not.

So, in reality, the surprise test paradox is not a paradox at all. If each morning the student expects to have a test, he will never receive one and the teacher’s statement will be false. If the student doesn’t expect to have a test on a given morning and then receives a test later that day, the teacher’s statement is true.

What makes the situation strange is that, each morning, the student should expect to have a test despite the fact that, if he expects to get a test, he “should” also expect not to get a test since expecting to get a test guarantees that he will not get a test. Although this is a strange state of affairs, it is not paradoxical because the first “should” and the second “should” are two different kinds of “shoulds.” The first “should” is a should based on what he ought to do to avoid being executed. The second “should” is a should based on what he ought to do to be logically consistent. This is only a paradox if one believes that individuals ought to be logically consistent in all situations, which this “paradox” clearly reveals is not the case.

I’m not sure whether the paradox has been resolved in this way by others in the past, but I thought I’d share it with you guys since it’s quite an interesting philosophical conundrum.