Today In Epistemology: More Daggone Puzzles

I don’t know, do you guys ever wonder why we always learn about PHILOSOPHY with puzzles? I mean, it’s always phrased as a sort of a problem — how can this thing that seems to be true also not be true? SUCH IS THE NATURE OF THE UNIVERSE. Anyway, I don’t know. Today, I’ve got some puzzles to look at, as usual they come from MIT’s Open Courseware thing, which I think I’m supposed to credit or something. Here are the notes.

THE FIRST CASE:

??? How is this even a paradox?

First of all, look, “surprise exam” can mean a lot of things. It can mean that I don’t know what day it comes, it can mean I don’t know what minute it comes, it can mean the content is about something I wasn’t expecting (maybe it’s on Anselm even though we did Anselm like a week ago), it could be in a form I wasn’t expecting. So if I get to Thursday and there’s been no exam, but then the professor wakes me up at 12:01 on Friday morning, that would still come as a surprise; similarly, even if I knew to expect the exam on Friday but then I got to class and there were a bunch of ninjas and the exam was actually about how well I learned how to dodge ninja stars, that would also be a surprise.

But SECOND OF ALL, if I get to Thursday and there’s been no exam, I can’t reason that there won’t be an exam on Friday, only that it won’t be a surprise because I was expecting it. Well, so? At the end of class on Thursday, necessarily the professor has made a liar of himself by permitting me enough information to predict the day of the exam, which is well within the realm of possibility.

So, at the end of class on Wednesday, we certainly do NOT know that the exam can’t be on Friday, because we don’t know for sure that the professor wasn’t just fucking lying about it, which means we similarly do not know that the exam must be on Thursday, but even if we did, the fact that we know it’s on Thursday doesn’t mean there won’t be an exam, just that we won’t be surprised by it.

(Contrarywise, if a bunch of MIT students rationally conclude after their Thursday class that it’s impossible for them to have a surprise exam on Friday because of Logic, then if you gave them an exam anyway it’d come as a huge surprise. Good job, smart guys.)

(Does this fit with my distinguishability criteria? I don’t know; this seems like a paradox that hinges on a semantic argument — “what does it mean for something to be a surprise?” — but also makes heavy use of the fact that a person just saying something doesn’t necessarily have anything to do with the truth. Especially because our knowledge here is sequential: I hear the professor telling me one thing on Monday, and then I make conclusions about experiences I have on subsequent days. So, when I say I “know” that there will be a surprise exam, what distinguishes a world in which the professor told me there will be a surprise exam but actually there won’t be from a world in which there will be a surprise exam but actually there will be? If there’s no distinguishability, then it’s outside the scope of knowing, and I’d be wrong to say I knew one way or the other.)

“Surely that’s wrong!” Yes…I think so? Let’s assume for the sake of argument that this is one of those lotteries where there are a billion numbers and everyone gets a unique one (after all, lotteries go by every day where no one wins, even though millions and millions of people play them), so that if a billion people play, someone has to win.

The problem here isn’t that Jones is wrong to believe that no one will win, it’s that he’s wrong to believe that he won’t win. I mean, he probably won’t win, the odds are a billion to one after all. And those are extremely bad odds! He can conduct his life as though he won’t win with a relatively high degree of security that this is true. Nevertheless, if he wants to believe something accurately about the universe, he’d be better served instead of saying, “I definitely won’t win,” by saying, “The odds of my winning are a billion to one.”

Because if he says that, then when a billion people play the lottery the odds of someone winning are one, which is what we should expect to happen in a situation like this.

So, what’s the deal here? Is this just an exercise in semantics? Well, on the one hand I think there’s a useful distinction to be made between “circumstances in which it makes sense to conduct my life” and “extreme circumstances”. In the case of the lottery, the numbers are specific, known, and very high — it’s perfectly rational to conduct your life as though you won’t win the lottery, despite it being technically untrue that you can’t win the lottery, but the rules change when you add a billion minus one more people in to it.

On the other hand, this also seems just like an exercise in pointing out how you can create a linguistic phrase that makes sense in a certain way, but not in another — that is, we can mean a lot of different things by “won’t win.” We can mean, “it’s literally impossible for me to win,” but we can also mean, “the odds of my winning are astronomically bad.” When I substitute “won’t win” for “bad odds”, the sentence still makes both logical and intuitive sense, but when I exploit the ambiguity in “won’t win” and put “impossible” back in there instead, it stops making logical sense.

(You might have guessed that “if, by whiskey…” is my favorite logical fallacy, and it’s because I think it’s surprisingly appropriate sometimes. “if, by won’t win…” et cetera.)

Okay, last one.

I guess this is a great paradox to keep in mind whenever I run into something that’s unquestionably true, but since it presupposes the existence of something that can be definitively known despite evidence both for and against it, I’m not gonna hold my breath.

(There are solutions to all these problems but I am not reading them; anyone else wants to read them and tell me how close I got, feel free.)