# Why would modal realist Lewis believe that the answer to the Sleeping Beauty problem is 1/2?

Why is Lewis, of all people, the champion of the halfer position, when modal realism seems to imply the thirder position?

The main argument he seems to make for the halfer position is that, although she does acquire centered information when she wakes up ("I'm awake today and therefore today is not Tuesday if the coin landed Heads"), she doesn't acquire any uncentered information, which Lewis seems to treat as the only legitimate kind of information. She should therefore keep her 1/2 credence unchanged.

But if I understand correctly, one of the virtues of modal realism is that it removes the distinction between centered and uncentered facts. When stating facts about the real world we're really just stating facts about our own location in the set of possible worlds. If so, all 3 awakenings are equally real and no relevant distinction can be made between any two of them. This becomes even more clear on the clones version of the problem, which uses space instead of time:

Instead of waking up twice on Tails, the scientist makes an identical copy of her (including all her memories), such that there are two versions of her when the coin lands Tails and one when the coin lands Heads. If modal realism is true, then there will be 3 actual copies of her, and two of them will exist in the Tails world. This is equivalent to not tossing any coin and making two copies of her, and then asking them for the probability of being the original sleeping beauty. Since there is only 1 original out of 3, the probability assigned should be 1/3.

So it seems to me that the belief on the 1/3 solution should be even stronger on a modal realist than on a non modal realist, which makes me wonder if there are any contradictions between modal realism and the thirder solution that I'm ignoring given that Lewis argued so strongly for the halfer position.

No, there are is no contradiction between Lewis's view on modality and him being halfer.

1. Remember that Lewis was a counterpart theorist! This means that there are only counterparts to sleeping beauty in other possible worlds so they aren't identical to her– they're only related by similarity. It's hard to see why the going ons in those possible worlds should influence my credence in the probabilities in my world.

2. Lewis would probably say that ur argument presupposes a uniform probability distribution over possible worlds. But this can't be correct– there is no good empirical grounds for assuming this at all. Lewis believedthat objective probabilities supervene on facts in our universe (see Lewis' subjectivist guide to objective probability), not on possible worlds.

3. In terms of the space analogy you drew. I think it's hard to see how being a modal realist implies there are three actual copies of her... It sounds like you're merely using the space case to motivate being 3rder and not connecting it to modal realism.

• Thanks! this clarifies things a bit. Regarding your 3rd point, the idea is that according to modal realism there would be (in the clones version of the experiment) two real worlds where one contain 1 copy and another 2 copies of her, and when she wakes up she'd be uncertain about which of there 3 copies is actually her. Is this not how modal realism works? I guess not given your 2nd point; I'll take a look at that guide since I find it weird why we couldn't apply probabilities across multiple possible words when we're uncertain about which world we're in.
– Juan
Commented Jan 21 at 11:47
• @Juan Well, it’s hard to see how to make sense of probabilities on possible worlds. There’s going to be worlds where sleeping beauty doesn’t wake up, there’s worlds where she turns into a butterfly. For Lewis, all these worlds will be equally real! So, it would be hard to justify to limit the scope to just 3 worlds.
– zzz
Commented Jan 21 at 23:07