Adam Elga

And if we have that in that case, then we can work backwards from the verdict in that case, 50-50, that the corner of the land heads once I'm sure that it's Monday or conditional on it being Monday, using an assumption about how your beliefs should change upon hearing the news that it's Monday and

to get a verdict about what you should believe before you heard that news.

And the crucial assumption that's needed is that the news doesn't change or shouldn't change the ratio of your probability in the scenario heads Monday and the scenario tails Monday.

So those are two scenarios.

They're both compatible with the news.

And the idea is when you get that news that narrows it down to just those two, you don't monkey with the ratio between them.

If you have that assumption linking your pre-Learning It's Monday beliefs to your post-Learning It's Monday beliefs, you end up forced to the conclusion that in the case where you don't learn that it's Monday, you should be two-thirds confident in Monday.

tails and one third in heads.

And that's being a thirder.

Correct.

Well, I shouldn't say the other option because there are two other options.

Because in this story where you learn that it's Monday, there's the question of what you should believe about the coin before learning that it's Monday.

And the question about what you should believe about the coin after learning it's Monday, there's this other view, a little bit less well-known, but I think also worth thinking about, the so-called half-halfers, who in the stage of the experiment before learning that it's Monday, think it's 50-50 about the coin.

And then after learning that it's Monday, think it's still 50-50.

In other words, those people deny the premise I just mentioned about keeping the ratios the same when you learn that piece of news.

Exactly.

Although that's somewhat of an accident of the way the combination of the fair coin and the other assumptions hold.

The crucial thing that's happening in the third position really is that the world that involves more awakenings gets a kind of boost associated with the fact that there are more instances of that.

state of mind being instantiated.

And I think that's going to be a crucial thing when it comes to thinking about bolts and brains, as when we talk about them later, is do those worlds deserve a boost?