Yes, it sure is close. But not exact. — JeffJo

So you're willing to commit to the conclusion that Sleeping Beauty's credence that the 2¹⁰⁰-sided die rolled a 1 is $\approx {2\over3}$, i.e. she should be fairly confident that the die rolled a 1?

Because I take that as a reductio ad absurdum. If Sleeping Beauty is rational then her credence should be $1\over{2^{100}}$, i.e. she should be almost certain that the die didn't roll a 1.

The waking-day ratio is a red herring.

These are your exact words:

Her credence in "1" as the die-roll result is N/(N+M-1). — JeffJo

If this is our experiment:

1. We roll a 2¹⁰⁰-sided die
2. Sleeping Beauty is woken up over 2¹⁰¹ days if it rolls a 1
3. Sleeping Beauty is woken up just once if it doesn't roll a 1

Then $N = 2^{101}$ and $M = 2^{100}$.

Therefore, according to your reasoning, her credence is ${2^{101}}\over{2^{101}+2^{100}-1}$ which $\approx {2\over3}$. You can see here if you don't believe me.

It is a fact that if this is our experiment

1. We roll a 2¹⁰⁰-sided die
2. Sleeping Beauty is woken up over 2¹⁰¹ days if it rolls a 1
3. Sleeping Beauty is woken up just once if it doesn't roll a 1

Then your reasoning entails that Sleeping Beauty's credence that the die rolled a 1 is $2\over3$.

Therefore, your options are:

1. Commit to the conclusion that her credence is $2\over3$
2. Accept that her credence isn't $2\over3$ and so that your reasoning is fallacious
3. Arbitrarily decide that your reasoning only works for an $m \times n$ grid of a sufficiently small size

So which is it?

I think that any rational person will go with (2).

And then presenting the 2/3 answer as a general case — JeffJo

I'm not.

I'm saying that if this is our experiment:

1. We roll a 2¹⁰⁰-sided die
2. Sleeping Beauty is woken up over 2¹⁰¹ days if it rolls a 1
3. Sleeping Beauty is woken up just once if it doesn't roll a 1

Then your reasoning entails that Sleeping Beauty's credence that the die rolled a 1 is $2\over3$, because that's how the waking-day ratio works out.

And I think this is a reductio ad absurdum against your reasoning. A rational person's credence should just be $1\over{2^{100}}$. Therefore, it is wrong to consider the waking-day ratio.

One of the things I really like about PlushForums is that when I click on a discussion it takes me to the last comment I viewed, and not just the first/last page.

Does Discourse do that?

These were your exact words:

Her credence when asked is 1/3, because of the four possible cells in the 2x2 array, one is eliminated and only one of the remaining three is Heads. — JeffJo

This can be generalised as:

Her credence when asked is ${a}\over{b}$, because of the $i$ possible cells in the $n \times m$ array, $j$ are eliminated and only $a$ of the remaining $b$ has Outcome X.

In the traditional problem the rules are:

- A coin is tossed
- If the coin lands on tails then Sleeping Beauty is woken on Day 1 and Day 2
- If the coin lands on heads then Sleeping Beauty is woken on Day 1

Given this, and where Outcome X is the coin landing on tails, the values are:

$n = 2\\m = 2\\i=4\\j=1\\a=2\\b=3$

Your reasoning entails that Sleeping Beauty's credence that the coin landed on tails is ${2}\over{3}$.

In a slightly different version of the problem the rules are:

- A 6-sided die is rolled
- If the die rolls a 1 then Sleeping Beauty is woken on Day 1, Day 2, ... and Day 10
- If the die rolls a 2 then Sleeping Beauty is woken on Day 1
- If the die rolls a 3 then Sleeping Beauty is woken on Day 1
- If the die rolls a 4 then Sleeping Beauty is woken on Day 1
- If the die rolls a 5 then Sleeping Beauty is woken on Day 1
- If the die rolls a 6 then Sleeping Beauty is woken on Day 1

Given this, and where Outcome X is the die rolling a 1, the values are:

$n = 6\\m = 10\\i=60\\j=45\\a=10\\b=15$

Given that ${{10}\over{15}} = {{2}\over{3}}$, your reasoning entails that Sleeping Beauty's credence that the die rolled a 1 is ${2}\over{3}$.

In my extreme version of the problem the rules are:

- A 2¹⁰⁰-sided die is rolled
- If the die rolls a 1 then Sleeping Beauty is woken on Day 1, Day 2, ... and Day 2¹⁰¹
- If the die rolls a 2 then Sleeping Beauty is woken on Day 1
- If the die rolls a 3 then Sleeping Beauty is woken on Day 1
...
- If the die rolls a 2¹⁰⁰ then Sleeping Beauty is woken on Day 1

Given this, and where Outcome X is the die rolling a 1, the values are:

$n = 2^{100}\\m = 2^{101}\\i=2^{201}\\j=2^{201}-2^{101}+2^{100}-1\\a=2^{101}\\b=2^{101}+2^{100}-1$

Given that ${{2^{101}}\over{2^{101}+2^{100}-1}} \approx {{2}\over{3}}$, your reasoning entails that Sleeping Beauty's credence that the die rolled a 1 is approximately ${2}\over{3}$.

Whereas Halfers will say the only thing that Sleeping Beauty needs to consider is the coin toss/die roll, and so her credence in each of these situations is:

- The coin landed on tails: $1\over2$
- The 6-sided die rolled a 1: $1\over6$
- The 2¹⁰⁰-sided die rolled a 1: $1\over{2^{100}}$

Why are you saying the values are wrong? Since there are one and a half awakenings on average per run, it's to be expected that the EV of a single bet placed on any given awakening be exactly two thirds of the EV of a bets placed on any given run. — Pierre-Normand

It's wrong because the expected returns aren't £33.333... if betting on heads or £66.666... if betting on tails.

I am not conflating the two. I am rather calculating the EV in the standard way by calculating the weighed sum of the payouts, where the payout of each potential occurrence is weighted by its respective probability (i.e. my credence in that occurrence being actual). I am pointing out that both the Halfer interpretation of SB's credence (that tracks payouts/awakenings) and the Thirder interpretation (that tracks payouts/runs) of SB's credence yield the exact same EV/run (and they also yield the same EV/awakening) and hence Halfer and Thirders must agree on rational betting strategies despite favoring different definitions of what constitutes SB's "credence". — Pierre-Normand

So then can you set out your calculations? These are mine:

$E(H) = {1\over2} \times £100 = £50\\E(T) = {1\over2} \times £100 \times 2 = £100$

I assume yours will take this form?

$E(H) = {1\over3} \times £? = £?\\E(T) = {2\over3} \times £? = £?$

It just seems to me that you're putting the cart before the horse and arguing that because E(T) = 2 × E(H) then C(T) = $2\over3$ which is a nonsensical inference.

And, once again, I think that this inference is shown most evidently to be nonsensical when we consider the case with the 2¹⁰⁰-sided die. It just doesn't matter what the payout structure is or whether I'm asked my credence that the die rolled a 1, my credence that this is a die-rolled-a-1 run, or my credence that this is a die-rolled-a-1 awakening: my answer is always going to be $1\over{2^{100}}$, and I think any rational person would answer the same.

The Online Safety Act applies to all websites that are accessible in the UK, regardless of where the owners live/are incorporated or where the website is hosted.

I really don't understand what point you're trying to argue. The facts are that (a) if we are to continue to provide access to UK residents then we must comply with the Online Safety Act and that (b) it is better for a private limited company to risk being fined £18 million than for Jamal to risk personally being fined £18 million.

I think you have a misunderstanding of the Online Safety Act. If we don't comply then the Office of Communications (Ofcom) can fine us (up to £18 million or 10% of revenue, whichever is higher) or take us down.

It has nothing to do with private individuals suing us because they believe they've been harmed.

It wasn't a typo.

Given a 2¹⁰⁰-sided die there are 2¹⁰⁰ rows, and given that there are 2¹⁰¹ days there are 2¹⁰¹ columns. That gives us a 2¹⁰⁰ × 2¹⁰¹ matrix, i.e. 2²⁰¹ cells.

The "die rolled a 1" row has 2¹⁰¹ cells where I'm awake. Each other row has 1 cell where I'm awake.

So in total there are 2¹⁰¹ + 2¹⁰⁰ - 1 cells where I'm awake. $2\over3$ of these cells appear on the "die rolled a 1" row. Therefore, according to your reasoning, after waking up your credence that the die rolled a 1 is $2\over3$.

He was banned — probably for low post quality — but then he created a new account, so we banned him again, but then he created a new account, so we banned him again, ...

This repeated literally hundreds of times. He just would not stop. Every day for months we were banning his new accounts and it was driving us crazy so we just gave up and turned off direct registration.

I don't see how the memory of this man is not all but water under the proverbial bridge. What have you to fear in the present day and age as far as this person is concerned? — Outlander

Are you asking about Marco?

He's an annoying fucking twat, as elucidated with exceptional eloquence here.

Suffice it to say he's the reason this forum became invitation-only.

I've been here for 5 years. I've seen the name "Porat" come up a few times, but with such intensity and quiet understanding between those who seem to know, it's... curious. — Outlander

Before https://thephilosophyforum.com there was another forum. The owner of the old forum sold it to a man named Eric Porat. Some of us had concerns about him, and the future of the forum, so Jamal made this place and we moved over.

See this is why places like this, at least in the Lounge, should have a topic or something where past "legends" (or villains to some) can have their stories told unbiased from both sides of the proverbial fire. — Outlander

See here for an unbiased account of Marco.

@Jamal

If Marco comes back I may have to burn the place to the ground.

As above, replace the coin with a 2¹⁰⁰-sided die. If it lands on a 1 then you are woken up on 2¹⁰¹ days otherwise you are only woken up on one day. After being woken up you are asked your credence that the die landed on a 1. The experiment is not repeated.

If you follow your reasoning then you have to claim that your credence is $2\over3$. You believe that the die most likely landed on a 1. I take this as a reductio ad absurdum against your reasoning. It's a fallacy to think of the problem as being represented by a $2^{100} \times 2^{101}$ matrix. Not being woken up isn't an "activity" comparable to playing football, hence why it's a false analogy.

If this were to happen to me my credence would be $1\over{2^{100}}$. The die almost certainly didn't land on a 1.

It's a false analogy because "not being woken up" is nothing like "playing football". It's a mistake to consider "Heads + Tuesday" at all. We can simplify the experiment as such:

1. On Sunday, Sleeping Beauty is put to sleep
2. A coin is flipped
3. On Monday, Sleeping Beauty is woken up and asked her credence that the coin landed on heads
4. If the coin landed on heads then Sleeping Beauty is told the outcome and the experiment ends
5. If the coin landed on tails then Sleeping Beauty is put back to sleep
6. On Tuesday, Sleeping Beauty is woken up and asked her credence that the coin landed on heads
7. Sleeping Beauty is told the outcome and the experiment ends

Her credence when asked is $1\over2$.

This is even more obvious when we replace the coin with a 2¹⁰⁰-sided die. If it lands on a 1 then she is woken 2¹⁰¹ times, otherwise she is woken once. After being woken up she is asked her credence that the die landed on a 1. The experiment is not repeated.

Halfers say that her credence is $1\over{2^{100}}$ and Thirders say that her credence is $2\over3$. I think any reasonable person would agree with the Halfer.

If she is interviewed before playing football her credence that the coin landed on tails is not 1, but if she is interviewed after playing football her credence that the coin landed on tails is 1.

Playing football is additional information, but nothing like that is available in the traditional problem, and so your example is a false analogy.

If Monday is tennis and Tuesday is football then waking up and playing either tennis or football is new information that allows you to rule out one possibility: if you play tennis then you can rule out that today is Tuesday and if you play football then you can rule out that today is Monday.

You can't rule out that today is Monday or that today is Tuesday before playing either tennis or football, which is why your example is a false analogy.

If God does exist, then that is not God. — Bishop Whalon

This is such a nonsense claim.

I'll be making an announcement when it's open for new sign-ups. As I say, around March. — Jamal

I assume this means that the new site will use a new URL for a time? Because if the new site immediately uses https://thephilosophyforum.com then nobody will ever see the announcement on this site because this site will be using a different URL that nobody will know.

In summary, rational credence doesn’t float free of betting; it aligns with whatever gets checked. If we check one answer per run, rational calibration yields 1/2. If we check one answer per awakening, rational calibration yields 2/3 (or 6/11 in the die case). The same coin is being talked about, but the Halfer and Thirder interpretations of SB’s credence refer to different scorecards. Given one scorecard and one payout structure, everyone agrees on the rational betting strategy in normal cases. — Pierre-Normand

In both cases one's credence in the outcome of the coin toss is $1\over2$. We use this credence, in conjunction with the payout structure, to determine which betting strategy has the greater expected return, which is one's credence in the outcome multiplied by the reward multiplied by the number of bets one can make given that outcome.

Single bet before being put to sleep with option to change after being woken up
$E(H) = {1\over2} \times £100 = £50\\E(T) = {1\over2} \times £100 = £50$

Independent bets after being woken up
$E(H) = {1\over2} \times £100 = £50\\E(T) = {1\over2} \times £100 \times 2 = £100$

We even perform these calculations before being put to sleep, and so have already determined our betting strategy. Being put to sleep and woken up changes nothing.

You certainly shouldn't perform these calculations after being woken up:

$E(H) = {1\over3} \times £100 = £33.333...\\E(T) = {2\over3} \times £100 = £66.666...$

Although the ratio is correct, the actual values are very wrong.

The mistake I think you continue to make is to conflate "the expected return if I always bet on Tails is twice the expected return if I always bet on Heads" and "my credence that the coin landed on Tails/that this is a Tails awakening is twice my credence that the coin landed on Heads/that this is a Heads awakening".

I’ll address your extreme case separately, since it appeals to different (nonlinear) subjective utility considerations. — Pierre-Normand

The logic of the extreme case is the same as the simple case. It doesn't matter if the die has two sides and we're woken twice if it lands on a 1 (and once otherwise) or if it has 2¹⁰⁰ sides and we're woken 2¹⁰¹ times if it lands on a 1 (and once otherwise). Given that the experiment is only performed once, no rational person's credence in the outcome of the die roll (or the "type" of awakening one is in) should be determined by the ratio of awakenings in the long run. I think this is self-evident in the extreme case, and this reasoning must also hold in the simple case, else you'd have to argue that the logic changes when the number of sides is >= some $n$ which is prima facie absurd.

So it's not wrong when other people use the word, "God" in a way that implies that it is male living in another dimension that wants you to do its bidding and exists? Mass delusions exist which can make many people say the same wrong things.

Me saying someone is wrong is not what makes them wrong. It is the distinction between the words they use and the reality of the situation that makes them wrong. Me saying they are wrong is just representative of that truth, but is not what makes it true. — Harry Hindu

I don't understand what you're saying here.

Someone is wrong if they claim that God exists but they're not wrong if they claim that the word "God" means "creator deity" (or whatever).

And I don't understand how this relates to the topic under discussion. Are you saying that English-speaking people don't use the word "man" to refer to those whose gender is male (regardless of sex) or are you saying that people whose gender is male (regardless of sex) don't exist?

Relative to this alternative payout structure, your own Halfer reasoning is unnecessary. — Pierre-Normand

Yes, I have tried to argue this point several times. A rational person's credence in the outcome of the coin toss is unrelated to the betting strategy that yields the greater expected return in the long run, and is why any argument to the effect of "if I bet on Tails then I will win $2\over3$ bets, therefore my credence that the coin landed on Tails is $2\over3$" is a non sequitur. The most profitable betting strategy is established before being put to sleep when one’s credence is inarguably $1\over2$, showing this disconnect.

After waking up you just either believe that the coin most likely landed on Tails or you don't, and I think my extreme example shows that no rational person’s credence will be based on some counterfactual ratio of awakenings in the way that Thirders say. It seems absurd for anyone to answer anything other than $1\over{2^{100}}$, regardless of how you “choose” to interpret the question.

That's not what I said. I said that the idea that because language can evolve a certain way, doesn't mean it should. If English evolved rapidly into an ambiguous and locally defined set of terms and meanings in each state, we would have a difficult time talking to one another at all. Just because something can occur, doesn't mean its the best outcome for what language's purpose is.

...

Of course, I never denied this, nor does this address my point. What I'm noting is that there are more beneficial and less beneficial ways for language to evolve. Its a constant balance between clarity of communication, efficiency in effort, and applicability to a wider audience. Thus, it is not foolish to debate whether words should mean something. — Philosophim

What you literally said, and what I am replying to, was "the terms man and woman indicate a person's age and sex, not gender" and this is factually incorrect. The terms are sometimes used to indicate a person's sex and sometimes used to indicate a person's gender.

Whether or not you think they should be used this way, and whether or not I think the word "slay" should be used to mean "impressive", is irrelevant to the factual matter of how English-speaking people actually use these words.

According to you, so far, the trans community and its supporters are free to advocate for their particular language uses. But other people are not supposed to advocate for their own particular language uses — baker

I'm saying that words can have more than one meaning, and that one of the meanings of the word "man" is "someone whose gender is male".

I'm not sure what you mean by "advocating" for a particular language use. If you don't want to use the word "man" to mean "someone whose gender is male" or the word "slay" to mean "impressive", then don't. But to argue that these words don't also mean these things is factually incorrect. Such usages are sufficiently widespread that they count as alternative meanings and not (intentional or unintentional) misuses, e.g. using the word "cat" to mean "dog".

No, it is not foolish at all. That's the entire point of English class. Present participles, conjuctive disjunctions (What are you functions?) are all a means to ensure that we have stable rules and approaches to grammar and communication. Because the entire purpose of language is to clearly communicate a concept in a way that can be easily understood by other parties in the language without debate. — Philosophim

To paraphrase Captain Barbossa, they're more what you'd call guidelines than actual rules. And, once again, natural languages just aren't the perfectly logical, consistent, and unambiguous things you seem to want them to be.

The above paragraph is a prime example. You "shouldn't" start a sentence with a conjunction. Except I do it all the time.

And of course people will deny that words mean certain things. If I started calling the Big Bang God and told you, "You believe in God", you would have an issue. It is quite reasonable to debate why we should or should use certain language and meanings for those words. If I said "subjectivity" was actually the same definition as 'objectivity', there would be a lot of people on these forums telling me, "No, you're wrong". — Philosophim

Get enough people using a word in a different-than-normal way and its meaning changes. That's how languages evolve. Imagine how silly Shakespeare would seem if we brought him back to life and he bitched about us not speaking Ye Olde Englishe properly.

Earlier, you talked about being a fool for battling others on how to use words. Then, given your contibutions here, you must be talking about yourself ... — baker

It's foolish to argue that words should or shouldn't mean something, or to deny the empirical fact that they are used to mean certain things.

some people still believe that dictionaries should have a normative function — baker

Well, they don't. Even the Académie Française, which is putatively the "authority" on the French language, can't do this. Natural languages just aren't the sort of things that can be dictated in this way. You can pretend, or say "well, it's not recognized by such-and-such an organization" but why should anyone care about that? I'm going to continue to slay despite your protestations.

Not everyone uses it that way. And since there is in fact no divine dictionary, nothing is set in stone. And so the battle for the meaning of a word is ongoing. — baker

Not everyone uses the word "slay" to mean "impressive" (or whatever it means to youths these days), but that is nonetheless one of its meanings.

If you don't want to use the word "man" to refer to anyone whose gender is male, regardless of sex, then don't. But it's bizarre to suggest that other people are wrong if they do use it that way. It's prominent enough to warrant being considered another meaning.

Her Thirder-credence would then be pragmatically relevant to selecting the destination most likely to afford her a sunny trip. — Pierre-Normand

Again, there's not much sense in this so-called "pragmatically relevant" credence. Even before being put to sleep – and even before the die is rolled – I know both that the die is most likely to not land on a 6 and that betting that it did will offer the greater expected return in the long run. So after waking up I can – and will – continue to know that the die most likely did not land on a 6 and that betting that it did will offer the greater expected return in the long run, and so I will bet against my credence.

With respect to "pragmatic relevance", Thirder reasoning is unnecessary, so if there's any sense in it it must be somewhere else.

Under the Thirder interpretation, all three of those biconditionally related "experienced" events are actual on average 2/3 of the times that SB is experiencing a typical awakening episode. — Pierre-Normand

My argument is that a rational person should not – and would not – reason this way when considering their credence, and this is most obvious when I am woken up 2¹⁰¹ times if the coin lands heads 100 times in a row (or once if it doesn't).

It is true that if this experiment were to be repeated 2¹⁰¹ times then we could expect $2\over3$ of all awakenings to occur after the coin landed heads every time, but it's also irrelevant. The experiment is only performed once. I strongly believe that it is irrational for one's credence to consider this long term average; a rational person, after waking up and knowing that the experiment is only performed once, will only consider the sheer improbability of the coin landing heads every time. Their credence remains ${1\over{2^{100}}}$. There is no ambiguity in the question or the answer.

Thirder reasoning only has its place, if it has a place at all, if both a) the experiment is repeated 2¹⁰¹ times and b) Sleeping Beauty is also made to forget between experiments. It matters that the problem does not stipulate these two conditions.

I answered your question.

Your opening post shows that you understand the distinction between sex and gender, given that you use the phrases "female who expresses with male gender" and "male who expresses with female gender".

I am explaining to you that the English word "man" can mean "a person whose biological sex is male" and it can mean "a person whose gender is male".

Despite your apparent suggestion that words should only mean one thing, they sometimes don't. Natural languages are messy. Accept it.

It doesn’t have just one meaning. It can refer to sex or it can refer to gender. This isn’t to say that it is equally likely to refer to gender as sex.

And what does the word 'man' mean without those modifiers? — Philosophim

It's an umbrella term that includes cis men and trans men.

What do those modifiers mean when they're added to the base word 'man'? — Philosophim

A cis man is someone whose sex is male and gender is male. A trans man is someone whose sex is female and gender is male.

Yes, you logically said that. — Philosophim

No, I didn't. I said that the word "man" is used to refer to cis men and used to refer to trans men.

No, it is not an empirical fact that when people generally use the word man, that they are thinking it is equally as likely that it is an adult human female behaving like a man. — Philosophim

I didn't say that.

So i guess to increase her odds, she bets tails 100% of the time since she can't remember which phase of the experiment she's in, and the 2/3rds tailsers make a profit off the gambling? — ProtagoranSocratist

It doesn't increase her odds but it does increase her expected return in the long run.

On this point it's worth considering an extreme example I provided two years ago.

I am put to sleep and a coin is tossed 100 times. If it lands heads every time then I am woken up, interviewed, and put back to sleep 2¹⁰¹ times, otherwise I am woken up, interviewed, and put back to sleep once.

When being interviewed, I am asked a) my credence that the coin landed heads every time and b) to place a bet on the outcome.

All of these are true:

1. If I know that the experiment will be performed once
a. My credence is ${1\over{2^{100}}}$
b. I will bet that the coin did not land heads every time

2. If I know that the experiment will be performed 2¹⁰¹ times
a. My credence is ${1\over{2^{100}}}$
b. I will bet that the coin did land heads every time

I strongly believe that a perfectly rational agent like Sleeping Beauty will believe and do the same. Thirder reasoning seems to be that if (2b) results in twice as many successful bets then (1a) is false, and that simply doesn't follow, either for me or for Sleeping Beauty.

This ignores the definitions I've given above — Philosophim

It doesn't ignore it. I am simply explaining the empirical fact that your definition is inconsistent with how English speakers actually use the words.

You can argue that some word shouldn't mean something, but that's not the same as arguing that it doesn't mean that thing.

Whether you like it or not, the words "man" and "woman" are used to refer also to transmen and transwomen.

Correct, but good vocabulary should be clear, unambiguous, and logical. — Philosophim

No natural language is clear, unambiguous, and logical. Certainly not English. Maybe check out Loglan if that's your interest.

My question to you then is, "Why should we change the term man to mean gender instead of sex by default?" — Philosophim

There's nothing about language that we should do; there's just what we actually do. And what we actually do is use the word "man" to refer also to transmen.

I am noting that in the general context in regards to sex and gender, 'man' refers to a person's age and sex, not gender. — Philosophim

A word's meaning is determined by how its users use it. If a sufficient number of English speakers use the word "man" to refer to both trans men and cis men, fully recognising the biological differences between the two, then the word "man" refers to both sex and gender.

There's no divine dictionary that dictates what words mean.