Molly the Mathematician: Thought Experiment

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Molly the Mathematician: Thought Experiment

Postby peterhurford on 2012-08-05T07:06:00

This thought experiment is pretty neat, and pretty relevant to hedonism, wireheading, etc:

Suppose Molly spent her whole life trying to prove a fiendishly difficult theorem. She finally thinks she's achieved it, and has some other mathematicians check her proof. Molly receives their answer, believes it wholeheartedly, then dies the next day. It is later discovered, after her death, that she was told the wrong answer.

Which of the following scenarios is better for Molly?

1) The mathematicians (mistakenly) tell her the proof is flawed, when in fact it is correct.
2) The mathematicians (mistakenly) tell her the proof is correct, when in fact it is flawed.
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Re: Molly the Mathematician: Thought Experiment

Postby Hedonic Treader on 2012-08-05T11:09:00

Probably 2), if she is like most other humans, who like being right and agreed with.
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Re: Molly the Mathematician: Thought Experiment

Postby RyanCarey on 2012-08-05T12:11:00

Given the usual assumptions that the mathematicians will not feel guilty for lying, that lying will not become a habit, and that Molly could never discover the lie, a classical utilitarian will favour 2. A preference utilitarian would usually favour 2, but this can vary.

For a consequentialist who values knowledge itself, or the attainment of knowledge, it could be more complex.
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Re: Molly the Mathematician: Thought Experiment

Postby Hedonic Treader on 2012-08-05T12:57:00

RyanCarey wrote:Given the usual assumptions that the mathematicians will not feel guilty for lying, that lying will not become a habit, and that Molly could never discover the lie, a classical utilitarian will favour 2. A preference utilitarian would usually favour 2, but this can vary.

It's not about lying. It's about an honest mistake.
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Re: Molly the Mathematician: Thought Experiment

Postby Arepo on 2012-08-06T12:53:00

The question is about what's better for Molly. From an HU perspective or any other strain of util that believes what's inside people's heads is worth more than mysterious nonphysical properties of the universe, 2) is obviously better.

For the rest of us, 1) is better - Molly has discovered some theorem that likely has positive expectation for human development.
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Re: Molly the Mathematician: Thought Experiment

Postby peterhurford on 2012-08-06T18:15:00

Let's change it up a bit more. You are Molly. Would you rather die thinking you solved the theorem when you actually didn't, or rather die thinking you didn't solve the theorem when you actually did?
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Re: Molly the Mathematician: Thought Experiment

Postby RyanCarey on 2012-08-07T00:38:00

Correction noted Hedonictreader.

Ok, I am now Molly. I tend to favour thinking I solved the problem. But I go further. I don't think any preference about whether I actually solved the problem can be given any regard because this state of affairs doesn't actually penetrate my consciousness. All my knowledge and opinions relate to my inner representation of the world and so I'm only 'allowed' to have preferences about those. At least that's my current intuition.
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Re: Molly the Mathematician: Thought Experiment

Postby peterhurford on 2012-08-07T03:07:00

RyanCarey wrote:All my knowledge and opinions relate to my inner representation of the world and so I'm only 'allowed' to have preferences about those. At least that's my current intuition.


Why do you think you're desires have to be restricted like that?
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Re: Molly the Mathematician: Thought Experiment

Postby RyanCarey on 2012-08-07T07:38:00

It seems 'unreasonable' that I could formulate any preference about the external world because I have no 'knowledge of it'...
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Re: Molly the Mathematician: Thought Experiment

Postby peterhurford on 2012-08-07T19:12:00

Here's another way of thinking about it:

I have a living mother, and I desire for her to stay in good health. Now, while morbid, let's hypothetically assume that tomorrow, my Dad calls and informs me that my mother died. At what point was my desire no longer satisfied -- when my mother died, or when I was notified of the news?

Likewise, as utilitarians, we presumably care about the suffering of others. We want this suffering to go away; that matters to us. So what would happen if we could take a pill that would delude us into thinking that all suffering was eliminated? Is that a win for the utilitarian, the most cost effective way to eliminate all suffering? And if that wouldn't work for you, how do you have a desire that "reaches out of your head" and actually matters for the real world? And assuming you go along with this, could other desires be analogous, say a desire to actually solve a math problem regardless of whether I think I solved it?
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Re: Molly the Mathematician: Thought Experiment

Postby Ruairi on 2012-08-08T09:25:00

Very interesting Peter!

I was going to write a post about why such a drug wouldn't be a win but then I realised I needed to think about it more.

If such a drug existed it sounds awesome! Although I'd be very scared of getting addicted and not caring about suffering anymore because it felt like it was gone. Is there a name for the emotion of feeling that you have done good?
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Re: Molly the Mathematician: Thought Experiment

Postby RyanCarey on 2012-08-08T13:34:00

Yes, it's pride, Ruairi! What a shame that in Christianity that beautiful feeling is labelled a sin!

Peter, to get us to agree that this drug is good, you have to make some unusual stipulations that the person taking the drug had absolutely no capacity to improve the world until they took the drug. If so, it would seem to be merciful to give such a disempowered person this drug so that they could feel proud and happy.
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Re: Molly the Mathematician: Thought Experiment

Postby peterhurford on 2012-08-08T20:43:00

Ruairi wrote:If such a drug existed it sounds awesome! Although I'd be very scared of getting addicted and not caring about suffering anymore because it felt like it was gone.


RyanCarey wrote:Peter, to get us to agree that this drug is good, you have to make some unusual stipulations that the person taking the drug had absolutely no capacity to improve the world until they took the drug.


I'm not trying to argue that the drug is worth taking. In fact, I'd really prefer it not be taken at all, because I'd much rather utilitarians focus on actual real-world problems rather than delude themselves into thinking they're helping.

But in refusing my "you now think suffering doesn't exist" drug, there's the point I'm trying to make -- utilitarians are fond of thinking that the suffering of others *actually* matters and *actually* ought to be reduced, not that we should merely convince ourselves that we've reduced it. In thinking this, I attempt to demonstrate that utilitarians (and other people) care about states of the world outside their own head.

Why not take the drug, even if people continue to suffer? After you take the drug, you won't care.
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Re: Molly the Mathematician: Thought Experiment

Postby Ruairi on 2012-08-09T09:38:00

I guess you could say I have "ethics" and selfish preferences".

Drugs for selfish preferences is good, but not for ethics, because the ethic does "reach outside your head".

Now, if I was just about to die, sure, give me the pride drug, but that's only because I can't help anymore and don't need to be motivated.

Did that answer all of it?
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Re: Molly the Mathematician: Thought Experiment

Postby Hedonic Treader on 2012-08-09T10:55:00

peterhurford wrote:Why not take the drug, even if people continue to suffer? After you take the drug, you won't care.

Why take the drug? Why care that your future self will keep caring, and therefore suffering from the awareness? The argument implies default acceptance of egoism. Intuitively understandable but logically unfounded.

RyanCarey wrote:It seems 'unreasonable' that I could formulate any preference about the external world because I have no 'knowledge of it'...

Strictly speaking, the future always necessarily exists in "the external world", from the perspective of the present. Any preference that orders your actions according to predicted causal effects would then be "unreasonable". It is also not true that we don't have knowledge about the external world. Evolution wouldn't have created these brains if their world models weren't at least narrowly aligned with the external world.

I think the true difference is the definition of value, i.e. what counts as utility, not the fact that it exists in the outside world. For hedonism, value is determined by the quality of how perspectives feel, even if it is not your current perspective. But there is no universally compelling argument that you have to accept hedonism.
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Re: Molly the Mathematician: Thought Experiment

Postby peterhurford on 2012-08-09T18:11:00

Ruairi wrote:I guess you could say I have "ethics" and selfish preferences".


Hedonic Treader wrote:The argument implies default acceptance of egoism. Intuitively understandable but logically unfounded.


I'm not arguing for egoism. In fact, I'm using the denial of egoism to argue against total wireheading, or any assumption that the best thing we can do for people is to stimulate their happiness/pleasure centers.

Essentially, we care about utilitarianism. We care about this in a way that we demand it to be genuine, not something that we're deceived into, even if we stimulate our "genuineness" centers as Brian argued. We care about this in a way that "extends out of our mind". This is why we would reject the utilitarianism pill -- we're not simply pride junkies (though it may play a part), but care about the outcome as well.

Take this back to Molly. If it's possible for people to care about others apart from the personal mental glow brain state that caring induces and to not want to be deceived about helping, then I suggest it's also possible for people to care about other things, like *actually* solving math problems, *actually* making scientific discoveries, *actually* composing music, etc.

This is why, if I were Molly, I would want 1 picked for myself, because I *actually* want to accomplish my goals, not think I had them accomplished. (Though I don't know Molly's preferences, so maybe she would prefer to be deceived.)

Likewise, I *actually* want my Mom to be in good health, not merely avoid all knowledge of her ill-fortune. And I *actually* want utility maximized, not merely deceive myself into thinking it has been. And I actually want to live out a utopian life, not be wireheaded. (Though wireheading may be a part of a utopian life, as long as it's not the whole thing. I do like pleasure, it's just not the only thing I like.)

Does that make sense?
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Re: Molly the Mathematician: Thought Experiment

Postby rehoot on 2012-08-11T16:36:00

peterhurford wrote:Which of the following scenarios is better for Molly?

1) The mathematicians (mistakenly) tell her the proof is flawed, when in fact it is correct.
2) The mathematicians (mistakenly) tell her the proof is correct, when in fact it is flawed.


I can answer in two ways. For me personally, I want the truth. I have a clearly defined, primary epistemological goal: to understand truth to the best of my ability. I do not, however, go around forcing truth on others while disregarding their ability to handle it. As for what is best for Molly, I don't know her so I don't know if she would have been suicidal had I told her that she was wrong. If I had good evidence that she was emotionally stable and sought truth, I would tell her the truth.

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Re: Molly the Mathematician: Thought Experiment

Postby peterhurford on 2012-08-11T17:39:00

rehoot wrote:I can answer in two ways. For me personally, I want the truth. I have a clearly defined, primary epistemological goal: to understand truth to the best of my ability. I do not, however, go around forcing truth on others while disregarding their ability to handle it. As for what is best for Molly, I don't know her so I don't know if she would have been suicidal had I told her that she was wrong. If I had good evidence that she was emotionally stable and sought truth, I would tell her the truth.


Our intuitions seem to match on this; I would give an identical answer. However, we seem to be in the minority here at Felicifia (which is fine).
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Re: Molly the Mathematician: Thought Experiment

Postby Nap on 2012-08-14T23:34:00

It is also not true that we don't have knowledge about the external world. Evolution wouldn't have created these brains if their world models weren't at least narrowly aligned with the external world.


Ammmm... okay so this is just horribly wrong.

There are VERY few things that we can show to be true, none of them deal with the outside world. Any claim that we can is just so easy to disprove.

Here is an example, there are two people talking (person 1 and person 2):

1) Evolution wouldn't have created these brains if their world models weren't at least narrowly aligned with the external world.

2) Your assuming that evolution is true.

1) Any number of evidences prove that it is.

2) Name one.

1) Fossils in different rock formation correlate to a time period, some fossils are only in certain layers.

2) You are assuming aliens didn't organize them like that.

1) I've never seen an alien do that, or an alien at all for that matter and I can't imagine why they would.

2) You are assuming just because you can't see them they are not there. You are also assuming because you can't think of a reason they wouldn't have one, maybe we are alien test subjects put on a planet with fake signs of evolution to trick us for their experiments.

The point is simple, I can play this game indefinitely, there is nothing you can say to PROVE 100% beyond a shadow of a doubt that any thing about "the outside world" is true. You can't even prove that you exist in the way you think you do. You could be in the matrix, you could be a computer program programmed to think its human, you could be a prisoner in a cave looking at shadows cast by a fire and hold those shadows to be real, you could be any one of an unlimited other things than what you think are.

This isn't new, Plato knew this almost 1500 years ago.

At the highest levels of thinking, meaning with out making any assumptions and only looking at truth, you have no knowledge of the external world.

It seems 'unreasonable' that I could formulate any preference about the external world because I have no 'knowledge of it'...


It's not that we can't be alien test subjects, its just so unlikely insight of the current evidence we have no choice (no choice if we wish to remain as rational as possible) but to proceed as if it wasn't true.

Sorry if that got off topic, its just so important to never forget this.

Back onto topic what I just said does have meaning here. I'm never satisfied by questions like this, I must always have detail that defeat the point of them.

Because we can never know some thing (there is a gray area for example math, but lets ignore that for now) 100% people being honest is one of the most important things, ever. It's quite sad seeing as how the worst of us completely disregard truths importance and the best of us can't help but lie occasionally, however we must strive for it anyway.

As for the specific question its worded interestingly. In neither choice is she being lied to and in both what ever she is told isn't the truth. Seeing as either way its not the truth I need to ask myself what differences exist between the two.

On the one hand Molly might feel like her goal in life is gone once she completes her work, this causing her to be depressed. On the other hand if she is told she is wrong she might be depressed for failing.

The problem doesn't state if this would have any real impact on the rest of the world, she might have been working on some thing some one else solved for the fun of it, so in this specific problem we don't need to worry about a greater good for every one but Molly, the question even asks "what is best for Molly."

I think it shouldn't matter which answer is given, either way she is not given truth and either way it has no consequence on others.

1 seems to have no benefits unless she is so extremely devoted to solving it that she becomes depressed after solving it. 2 seems to have no benefits other than to satisfy her need to feel accomplished or proud (both of which are flawed emotions when trying to find truth, necessary for now maybe, but still flaws).

Edit: I need to clarify why even if she was right why she's not given truth.

If she thinks her right answer is wrong she wont think its right anymore (thank you captain obvious). So now we are back to square one where she is wrong again. So either way she is wrong, one way she just thing she's right.

The reason why its bad to think you are right when you are wrong is so you try to find the right answer, here however Molly getting the right answer is not an option because she'll die before she can rework it to get a right answer even is she knows she is wrong.

And again the problem specifies that it doesn't matter what she thinks it wont change other peoples lives (the problem doesn't say this I'm just assuming because it seems this is about Molly not other people, so if its about her we need to eliminate other variables) so if she thinks she got a right or wrong answer other people will find the actual right answer with out consequence to them.

So ya, my conclusion is that it doesn't matter. I guess just do what ever makes her happiest even if she is only made happy or sad because of a human flaw.
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Re: Molly the Mathematician: Thought Experiment

Postby yboris on 2012-08-15T19:55:00

Clearly (2) ;)

This is similar to what frustrated me in reading Derek Parfit's "What Makes Someone's Life Go Best".

It seems 'cleaner' to think about "better for me" in terms of experiences only. Once defined as such, the answer (2) is clearly the right one. It seems to me that the disagreement between people on this issue is often at a level that's analogous to "sound" from a falling tree in a forest (is there sound when no one is around?). When '"sound" means "vibrations of air" the answer is clearly different from when "sound" means "sensation in sentient being's brain".

I'm all ears for comments ;)
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Re: Molly the Mathematician: Thought Experiment

Postby peterhurford on 2013-02-11T00:23:00

Elijah wrote:To me, these thought experiments are close to a reductio of utilitarianism: i think that truth, success, valor, achievement, etc. are valuable independent of happiness.


I think, at worst, they're an argument for preference utilitarianism over hedonistic utilitarianism.
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Re: Molly the Mathematician: Thought Experiment

Postby peterhurford on 2013-02-11T03:26:00

Elijah wrote:In the case of the Molly thought experiemtn, yes. Not necessarily in the case of other thought experimetns that isolate goods from happiness.


What thought experiment do you have in mind?
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Re: Molly the Mathematician: Thought Experiment

Postby Arepo on 2013-02-12T13:01:00

peterhurford wrote:
Elijah wrote:To me, these thought experiments are close to a reductio of utilitarianism: i think that truth, success, valor, achievement, etc. are valuable independent of happiness.


I think, at worst, they're an argument for preference utilitarianism over hedonistic utilitarianism.


I would say the opposite. They show that what we want isn't necessarily congruent with any good experience. (or rather, I'd say it's not an argument for anything, only a demonstration that the two theories actually differ, but that has less rhetorical punch ;))

I strongly suspect Elijah's thought experiment suffers from the availability heuristic. When we think about ourselves (dying falsely believing we’ll be famous) or (dying falsely believing we won’t) we’re incorporating a model of ourselves based on the one we observe right now, which effectively reverses our intuitions – we’re in practice comparing (dying accurately believing we’ll be famous) or (dying accurately believing we won’t).
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Re: Molly the Mathematician: Thought Experiment

Postby peterhurford on 2013-02-12T20:55:00

I've seen Haidt's scenarios, and nearest that I can tell, I'm immune to "moral dumbfounding"; I "bite the bullet" on all of his hypotheticals. I do, however, sympathize with the fictional Molly and would rather my proof be correct and be misinformed about it than the other way around. Rather, I have preferences not just for subjective states but for objective world states -- I want the world to be one way rather than another.

I also think all utilitarians agree with me and have at least one desire for a particular objective world state -- a world state of maximum happiness. No utilitarian I know would accept my "pill" that merely deludes them into thinking they have accomplished this goal; they want the goal to "actually happen", even if it occurs after their death.

I'm perfectly fine with people having different intuitions than I do. But I don't want to be wireheaded in the hedonic utilitarian sense. I want to live a life that has a narrative of objective/actual accomplishments and experiences. I'd be fine with doing that in a computer simulation, of course, but only if I was with other actual minds and not merely deluded into thinking so.

Essentially, solipsism is horrifying.
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Re: Molly the Mathematician: Thought Experiment

Postby Arepo on 2013-02-12T23:18:00

I also think all utilitarians agree with me and have at least one desire for a particular objective world state -- a world state of maximum happiness. No utilitarian I know would accept my "pill" that merely deludes them into thinking they have accomplished this goal; they want the goal to "actually happen", even if it occurs after their death.


You're mixing 'preference as source of value' with 'conclusion derived from ethical system which we'll call a "preference"'. They basically unrelated, and one of the reasons I dislike preference utilitarianism is its constant trading on the ambiguity of the keyword.

I have no emotional attachment to a utilitronium shockwave - quite the opposite. Nonetheless, congruent with my worldview, I would launch one of I could. Taking a pill that made me think one had been launched wouldn't obviously make me happy (I'd be too busy being confused about how I still existed for one thing), and obviously wouldn't make anyone else happy, so it's perfectly consistent with HU to eschew it.
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Re: Molly the Mathematician: Thought Experiment

Postby peterhurford on 2013-02-12T23:42:00

Arepo wrote:I have no emotional attachment to a utilitronium shockwave - quite the opposite. Nonetheless, congruent with my worldview, I would launch one of I could. Taking a pill that made me think one had been launched wouldn't obviously make me happy (I'd be too busy being confused about how I still existed for one thing), and obviously wouldn't make anyone else happy, so it's perfectly consistent with HU to eschew it.


Thus you clearly value something (a particular world state, even) that isn't about happiness. Thus value isn't all about happiness.

I guess I'm confused why certain utilitarians care about my happiness but don't care about the other things that I value.
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