Meaning? — Srap Tasmaner

Really?


Also make sure we don't confuse proportion with the sample space.

There is another sample space you are not even considering.

{H,T}

And when I see the word "just" used as it is here — Srap Tasmaner

Or perhaps that is just innocent word usage. Just is kind of a hard word to avoid, there are not a lot of options that fill its role so concisely.

If ever a coin flip wasn't "just" a coin a flip, surely it's Sleeping Beauty. — Srap Tasmaner

Why? There was one coin, it was flipped once, it was fair and only had two sides. Seems to have all the characteristics of being just a coin flip.

This is a common failing of human perception, people tend to overthink things until they can no longer see the simple. It is still just a coin flip; let's not think our way out of that practical aspect. Probability is not about pushing numbers around on a page, it is about making a reliable model.

I don't think we should assume, for instance, that Beauty is informed by being awakened. — Srap Tasmaner

I didn't say she was being informed by being awakened, I said she was being informed by the interview.

One more point I want to press.

You can slice up probability up whichever way you like, and argue all types of samples space that pay no mind to relevant temporal location or Occam's razor; however, when you get right down to it: it is still just a coin flip. Pushing numbers around on a page will not change that.

If we are to argue temporal location as relevant to update the probability model, and our task is to do so as if we are Beauty, then sleeping periods are irrelevant, Beauty has no temporal awareness while asleep. Also the moment she wakes up is also irrelevant sure she might be thinking about the probability already, but she could also be thinking about apple pie; we'd be speculating on her thoughts and we can't ground a reliable probability model in speculation.

Our task is to formulate Beauty's response to the interview; that means the relevant temporal locations, are not when she is awakened, but immediately after the interview. By the nature of the experiment the interview itself conveys information, which eliminates all days not contained in the three awakened days of the experiment. This means by the time Beauty is ready to response she already knows the relevant possible awakened states.

Beauty can either consider the probability based on the three possible awakenings that include an interview, or she could consider the coin flip, because regardless of any other considerations, a coin flip is still just a coin flip. Those are the only two relevant sample spaces.

Which context is relevant depends on the perspective one is taking - the perspective of the independent observer or the awakened Beauty. — Andrew M

The relevant context is the awakened Beauty after the interview, as she is asked the question when awakened; it is right in the OP, which would mean you don't consider periods of sleep in the sample space. They effectively do not exist to Beauty. I mean you are arguing against yourself here.

As long as Beauty is uncertain of her temporal location, then Beauty only has two relevant sample spaces to choose from: awakenings and the coin flip.

Don't forget to include the possibility she is on the Moon when she awakes. I mean as long as we are adding unnecessary entities.

It is the notion we start with a prior then update that prior. You don't update priors in a Classical apporach, as there are no priors. In a Classical frame they should be viewed as two different sample spaces, and the probability is dependent on the event, which is the randomly selected subset from the sample space. How they are selected would depend on the conditions of the subset.

We thirders think halfers are looking at the wrong event — Srap Tasmaner

Why should I even consider the Bayesian approach in the first place?

When considering probability, which is the measurement of uncertainty, then we consider the domain of uncertain possible outcomes. Certain outcomes bring no value to that domain, unless they are confounding and even still they don't show up in the domain themselves. Otherwise you skew your measurement by adding extra irrelevant information. If you like consider this under the scope of Occam's Razor.

Hey look at that. He saw the Wednesday argument and slipped in a defeater! — Srap Tasmaner

Speculation on Beauty's possible speculation was never a good foundation for reallocation.

Elga's argument is:

The answer is that you have gone from a situation in which you count your own temporal location as irrelevant to the truth of H, to one in which you count your own
temporal location as relevant to the truth of H.

If that is so then when Beauty considers the actual question that is when temporal location is relevant and at that time Wednesday is already off the table, as the asking of the question eliminates it. And speculation that Beauty was considering Wednesday as a possibility before the interview is speculation and is outside the relevant temporal location which is in consideration.

If you don't buy that argument, then you still have not explained how this supposed new information is relevant to the uncertainty of temporal location when considering if it is Tuesday or Monday. That uncertainty still remains, and probability is the measure of uncertainty. Wednesday is certainly off the table, at this point.

If your position is that it's just a prior and you can pick whatever you want — Srap Tasmaner

That was never my point. My point is that you don't update priors with priors. Priors can be subjective but the "new information" needs to be objective. Priors on the other hand need solid reasoning to be used, and I have said many time both are valid positions; as such, you could justify either one as a prior.

You are too fast for my ninja edits, so you end catching my typos. I don't want to review any more Lewis tonight, maybe tomorrow I'll take another look at the end.

Is there any argument for not reporting both the 1/2 and 1/3? Seems like a perfectly valid solution to me and if I ever had a similar dilemma in the real world that is exactly what I would do.

He is trying to show Elga's argument leads to a contradiction, the same contradiction you posted here: https://thephilosophyforum.com/discussion/comment/184884

But I have already said several times, I think they are both wrong.

The simulation proves that both views are valid ways to look that the possible outcomes. All this nonsense about to reallocate or not to reallocate is just that nonsense, both proportions can be used to represent the problem accurately. There is no mistake in the math on either side, there is no mistake in the theory on either side and people are grasping at straws over this idea of new information just to argue their point of view. The reasons being given for why it should be 1/3 over 1/2 would never be a practical reason to give for application.

The problem is that wagering confirms the odds are 2-1, which, duh, there are 2 tails interviews for every heads interview. If it's all about getting to give the right answer most often, there's no way to go but tails. — Srap Tasmaner

She is asked about if the coin landed on heads, we can't go tails. The short and dry of it is all, is that a coin flip is still a coin flip. I posted my simulation up above, if you are considering the 1/2 argument then the odds are not 2:1 in favor of tails, they are 1:1 and those are better odds.

I think one of the best ways to envision probability is to imagine what would happen if you did the event 10,00 times, so that is what I have done


Here is the output:

[1] 5037 - Number of Tails
[1] 4963 - Number of Heads

[1] 4963 - Number of Monday and Heads
[1] 5037 - Number of Monday and Tails
[1] 5037 - Number of Tuesday and Tails

You can see that the 1/3 argument does in fact lead to a 33% split and the 1/2 argument does lead to a 50% split; however, you should go with the 1/2 argument, as 4963/10000 is better odds than 4963/15037, therefore you have a better chance of being correct.

One might argue that all else being equal Beauty should go with the 50% credence, since 50 is greater than 33, which gives her a higher chance of being right. If both arguments are equal that is.

Speculative claims about what Beauty might be thinking before the interview is speculative, and you can't update your probability model on that. The nature of the problem is to give Beauty's response to the question itself. So she already knows it is not Wednesday when trying to determine the credence and even if you do see that as "new" information, that still does not justify additional reallocation of credibility, you need to justify them all.

When you are first awakened, you are here: — Srap Tasmaner

We are already there and no one has been put to sleep yet.

you don't know if it's Monday or Tuesday or Wednesday, but you know you've been awakened. — Srap Tasmaner

Sorry, I actually misread a few words in your post, however. . .

Wednesday is irrelevant. The interview is what triggers the response, before then you are merely speculating. Also the probability if it being Wednesday would drop to 0% as soon as the interview happened, and her response to the interview is what we are concerned with. And one more point, Wednesday is not new information. Everything we know, she knows.

Never-mind misread.

The problem with Elga's argument is that you can't count your temporal location relevant if you don't know what it is.

That is P(HEADS | you told me it's Monday) = P(HEADS | you asked me) + 1/6 — Srap Tasmaner

I already know this. It is a statement showing P+(Heads) does not equal P(Heads). Elga's argument is that her credence in H, because she knew she would be awaken on Monday, should shift when she is awakened on Monday. Lewis is merely showing that the two are not the same thing.

Let H be the proposition that the outcome of the coin toss is Heads. Before being put
to sleep, your credence in H was 1/2. I’ve just argued that when you are awakened
on Monday, that credence ought to change to 1/3. This belief change is unusual. It is
not the result of your receiving new information — you were already certain that you
would be awakened on Monday.3 (We may even suppose that you knew at the start of the
experiment exactly what sensory experiences you would have upon being awakened on
Monday.) Neither is this belief change the result of your suffering any cognitive mishaps
during the intervening time — recall that the forgetting drug isn’t administered until well
after you are first awakened. So what justifies it?
The answer is that you have gone from a situation in which you count your own
temporal location as irrelevant to the truth of H, to one in which you count your own
temporal location as relevant to the truth of H. - Elga

https://www.princeton.edu/~adame/papers/sleeping/sleeping.pdf

I think several of you are way overthinking this, but to be honest, I think philosophers and the like tend to do that. This whole problem was summed up pages ago.

so that's not the explanation for the magic 1/6. — Srap Tasmaner

1/2+1/6 = 2/3

P+(Heads) = P(Heads)+1/6

1/6 is the differences between P+(Heads) and P(Heads)

I think it is just a statement noting the difference, to show they are not the same thing.

It is a possible outcome; she just won't be asked about it. — Srap Tasmaner

And Tuesday first week of April in the year 3030 is also in the sample space, I suppose.


The sample space is either head and tails, or awakened states.

Tuesdays and Heads is clearly and obviously not in the sample space. It is not a possible outcome, she will be never be interviewed on Heads and Tuesday.

You are not paying attention to what the plus means, where it shows up and where it doesn't show up.

Do you agree? — Andrew M

What on Earth do you think that tag question does?

I just gave you my response and I am not going to wade through your clear misunderstanding of Lewis's argument.

Oh good. I thought the OP didn't make this clear. The halvers would have it right if she went into this thing blind. — noAxioms

It says right in the OP, " Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details." That is the first line of the problem.

Lewis agrees with me that there is no new relevant information which would allow reallocation of credibility. I just disagree with Lewis that that condition excludes the 1/3 position.

Do you agree? — Andrew M

No, and I already commented on Lewis and Elga.

Also Lewis is arguing that 2/3 is a consequence of Elga's 1/3 position. Lewis is arguing for the 1/2. Elga is the one arguing the 1/3, and both of their responses have already been posted, by myself.

Lewis argues two cases, L2, which is P(Heads)=1/2=P(Tails) and then he notes quod erat demonstrandum. Then moves on to L6 which is P with the plus. Read the article to find out why it has a plus.

If you can argue the 1/3 without doing the experiment, then you are arguing a prior.

She is never told it is Monday, there is no relevant self-locating information, and she knew there were only three possible awake periods before the experiment. Everything we know is everything she knows before the experiment therefore 1/3 is a prior. We don't have any privy information here.

If two doors had a 2/3 chance, and you eliminate one of them, then the 2/3 is reallocated to the remaining door and now that one door has a 2/3 chance. That is the Monty Hall problem and why you should change doors.

Anyway, I've never encountered anyone who agrees with me on this. — tom

That is because you are wrong. Knowing which door is empty is the new information which calls for a reallocation of credibility. You know now one of the the possible empty doors. Yes there is still an empty door but before there were two empty doors and now you know at least one of them. That is a real reason to reallocate credibility.

Note that Beauty (as a halfer) does the same thing when she is told that it is Monday. For a halfer, P(Heads|Monday) = 2/3 so, on attaining that self-locating information, she updates P(Heads) to be 2/3. — Andrew M

She is never told it is Monday, each awaking is the same, there is no hint as to which day it is; temporally she is uncertain of her location.

So what "self-locating information" allows her to reallocate credibility? You need to be specific. If I am working on a Bayesian analysis, and I get up to go to the bathroom, siting on the toilet doesn't count as new relevant information. Just her waking up is not good enough, she has to actually gain new information.