Jeff Jo

Sleeping Beauty (SB) volunteers for this experiment, and is told all these details by a Lab Assistant (LA):

• I will put you to sleep tonight (Sunday) with a drug that lasts 12 hours. After you are asleep, I will flip two coins - a Dime and a Nickel. I will lock them in an opaque box that has a sensor which can tell if at least one coin inside is showing Tails.
• I will then administer a drug to myself, that erases my memory of the last 12 hours, and go to sleep in the next room.
• Until I am stopped (which will happen on Wednesday morning), when I wake up in the morning I

Here is yet another variation of the problem that I think perfectly identifies the source of the controversy. The experiment's methodology is the same as the original, except in these four details:

(1) Two coins, a Nickel and a Quarter, are flipped on Sunday Night.

(2) On either day of the experiment, Beauty is wakened if either of the two coins is showing Tails.

(3) On Monday Night, while Beauty is asleep, the Nickel is flipped over to show its opposite face.

(4) Beauty is asked the same question, but about the Quarter.

The only functional difference is that there is a 50% chance that the "optional" waking occurs on Monday instead of Tuesday. Since Beauty does... (read more)

Well, I never checked back to see replies, and just tripped back across this.

The error made by halfers is in thinking "the entire analysis" spans four days. Beauty is asked for her assessment, based on her current state of knowledge, that the coin landed Heads. In this state of knowledge, the truth value of the proposition "it is Monday" does not change.

But there is another easy way to find the answer, that satisfies your criterion. Use four Beauties to create an isomorphic problem. Each will be told all of the details on Sunday; that each will be wakened at least once, and maybe twice, over the next two days based on the... (read more)

You said: "The standard textbook definition of a proposition is a sentence that has a truth value of either true or false.

This is correct. And when a well-defined truth value is not known to an observer, the standard textbook definition of a probability (or confidence) for the proposition, is that there is a probability P that it is "true" and a probability 1-P that it is "false."

For example, if I flip a coin but keep it hidden from you, the statement "The coin shows Heads on the face-up side" fits your definition of a proposition. But since you do not know whether it is true or false, you can assign a 50%... (read more)

"You're failing to distinguish between though experiments that are only mildly-fantastic, like ones assuming perfectly fair coins, when real ones have (say) a 50.01% chance of landing heads, versus highly-fantastic thought experiments, such as ones assuming that on Sunday you know exactly, in complete detail, what all your experiences will be on Monday."

I'm not failing to distinguish anything. I'm intentionally not bothering to distinguish what the problem statement says we should treat as indistinguishable. "While awake she obtains no information that would help her infer the day of the week." Whether or not you think it is more realistic, the problem you are solving is not... (read more)

"[Elga and Lewis] don't realize that that is relevant information. They're mistaken." They are not. The very premise of the problem is that it cannot be relevant. The same reasoning suggests we don't need to accept that the coin is fair, or that Beauty might wake on Tuesday after Heads.

"Surely you would agree that a thought experiment is uninteresting if the conditions for it are actually impossible?" I absolutely would not. There is no coin, or a methodology for flipping one, that produces exactly 50%. In fact, if we could achieve the level of detail you try to with Beauty, a coin flip is deterministic.

And the conditions that we assume for nearly... (read 468 more words →)

It is consensus on how one uses experiences as evidence, not the usage itself, that is only possible if the method is uncontroversial. Controversy just means that two people see its applicability differently. Not that it is impossible to use, or that either is correct or incorrect.

But neither Lewis, nor Elga, say anything about using Beauty's experiences during the day of an awakening as evidence. Elga's footnote is defining what he means by "new information," which we are calling "evidence." He never relates it to experiences during the day, only to experiences inherited from Sunday at the start of a day. So while Beauty's nose may itch, she has no idea why... (read more)

Lewis says that the evidence that it is Monday or Tuesday is identical, not the totality of her thoughts and experiences is identical. A window and rain on only one of the days constitutes different experiences, but requires knowledge of the weather forecast to extrapolate that difference into evidence.

The context you omitted from the Elga quote was comparing Sunday's knowledge to Monday's, with no mention of Tuesday. He even added a footnote: "To say that an agent receives new information (as I shall use that expression) is to say that the agent receives evidence that rules out possible worlds not already ruled out by her previous evidence." His point was that she... (read more)