Yes or No Philosophy
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Elliot Temple
Jul 29, 2017, 8:28:01 PM7/29/17
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I found and solved a mistake in Critical Rationalism.
http://fallibleideas.com/essays/yes-no-argument
This is a short argument. The "Learn more" link at the bottom has a lot more explanation.
Elliot Temple
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http://fallibleideas.com/essays/yes-no-argument
This is a short argument. The "Learn more" link at the bottom has a lot more explanation.
Elliot Temple
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Damián Gil
Jul 31, 2017, 5:22:22 AM7/31/17
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2017-07-30 2:27 GMT+02:00 Elliot Temple <cu...@curi.us>:
I found and solved a mistake in Critical Rationalism.
http://fallibleideas.com/essays/yes-no-argument
This is a short argument. The "Learn more" link at the bottom has a lot more explanation.
Elliot Temple
I read Elliot Temple "I found and solved a mistake in Critical Rationalism" mail, and I would like to reply. Note I'm not a native English speaker.
Deductive and Plausible Reasoning
A moment's thought makes it clear that our policeman's conclusion was not a logical deduction
from the evidence; for there may have been a perfectly innocent explanation for everything. It
might be, for example, that this gentleman was the owner of the jewelry store and he was coming
home from a masquerade party, and didn't have the key with him. But just as he walked by
his store a passing truck threw a stone through the window; and he was only protecting his own
property.
Now while the policeman's reasoning process was not logical deduction, we will grant that it
had a certain degree of validity. The evidence did not make the gentleman's dishonesty certain,
but it did make it extremely plausible. This is an example of a kind of reasoning in which we have
all become more or less profi cient, necessarily, long before studying mathematical theories. We are
hardly able to get through one waking hour without facing some situation (i.e., will it rain or won't
it?) where we do not have enough information to permit deductive reasoning; but still we must
decide immediately what to do.
You say: "To choose between the ideas, look for another (more demanding, more ambitious) problem which one of the ideas solves and one doesn't. Whatever criteria you may have for preferring one solution over another, specify it in a problem so that one idea is a solution to that problem and the other is refuted."
But that doesn`t seem to help much. I can't easily think of a problem which one of the ideas solves and the other one doesn't. I simply subdivide the problem into subproblems (how probable is that a masked man returning from a masquerade party coincides with the exact moment a truck throws a stone and breaks the window of his own store?) and do a very fast and crude estimate of the probabilities. Then I detain the masked man.
Edwin T. Jaynes starts his book "Probability Theory: The logic of Science, with the following example:
Suppose some dark night a policeman walks down a street, apparently deserted; but suddenly he
hears a burglar alarm, looks across the street, and sees a jewelry store with a broken window. Then
a gentleman wearing a mask comes crawling out through the broken window, carrying a bag which
turns out to be full of expensive jewelry. The policeman doesn't hesitate at all in deciding that this
gentleman is dishonest. But by what reasoning process does he arrive at this conclusion? Let us
fi rst take a leisurely look at the general nature of such problems.
hears a burglar alarm, looks across the street, and sees a jewelry store with a broken window. Then
a gentleman wearing a mask comes crawling out through the broken window, carrying a bag which
turns out to be full of expensive jewelry. The policeman doesn't hesitate at all in deciding that this
gentleman is dishonest. But by what reasoning process does he arrive at this conclusion? Let us
fi rst take a leisurely look at the general nature of such problems.
Deductive and Plausible Reasoning
A moment's thought makes it clear that our policeman's conclusion was not a logical deduction
from the evidence; for there may have been a perfectly innocent explanation for everything. It
might be, for example, that this gentleman was the owner of the jewelry store and he was coming
home from a masquerade party, and didn't have the key with him. But just as he walked by
his store a passing truck threw a stone through the window; and he was only protecting his own
property.
Now while the policeman's reasoning process was not logical deduction, we will grant that it
had a certain degree of validity. The evidence did not make the gentleman's dishonesty certain,
but it did make it extremely plausible. This is an example of a kind of reasoning in which we have
all become more or less profi cient, necessarily, long before studying mathematical theories. We are
hardly able to get through one waking hour without facing some situation (i.e., will it rain or won't
it?) where we do not have enough information to permit deductive reasoning; but still we must
decide immediately what to do.
So, Mr, Elliot Temple, you now have two hypotheses: a) the masked man is a burglar and b) he was coming home from a masquerade party. Which hypothesis would you support with your Yes/No philosophy?
I think this is a case where there are more than two solutions to a problem. Which is better? I know how I would solve it. I would, however vaguely, assign a measure of goodness to both of them, a probability, and then I would choose the most probable one. But that is forbidden by your philosophy. So, what would you do?
You say: "To choose between the ideas, look for another (more demanding, more ambitious) problem which one of the ideas solves and one doesn't. Whatever criteria you may have for preferring one solution over another, specify it in a problem so that one idea is a solution to that problem and the other is refuted."
But that doesn`t seem to help much. I can't easily think of a problem which one of the ideas solves and the other one doesn't. I simply subdivide the problem into subproblems (how probable is that a masked man returning from a masquerade party coincides with the exact moment a truck throws a stone and breaks the window of his own store?) and do a very fast and crude estimate of the probabilities. Then I detain the masked man.
Yours sincerly
Damian Gil
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Elliot Temple
Jul 31, 2017, 5:34:09 AM7/31/17
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You can look up if he's the owner of the jewelry store or not. There are ownership records. This is a bad example of a probabilistic scenario because you can fact check his story.
If it was a genuinely probabilistic scenario, then you could come up with a single non-refuted theory about the situation, e.g. "there is an 50% chance the die i rolled and didn't look at yet has a number from 1-3 face up". even if the odds were uneven, you should accept the single theory that it's an 83% chance of 1-5, rather than claim "it rolled 1-5 is more likely to be true than it's a 6, so i'll claim to know it landed on 1-5, and i could be wrong but that's the best i can do".
FYI I just spent a month creating educational material explaining this stuff. If you want to learn how it works more, I recommend you get the additional material linked at the bottom of the essay.
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If it was a genuinely probabilistic scenario, then you could come up with a single non-refuted theory about the situation, e.g. "there is an 50% chance the die i rolled and didn't look at yet has a number from 1-3 face up". even if the odds were uneven, you should accept the single theory that it's an 83% chance of 1-5, rather than claim "it rolled 1-5 is more likely to be true than it's a 6, so i'll claim to know it landed on 1-5, and i could be wrong but that's the best i can do".
FYI I just spent a month creating educational material explaining this stuff. If you want to learn how it works more, I recommend you get the additional material linked at the bottom of the essay.
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Damián Gil
Jul 31, 2017, 6:21:39 AM7/31/17
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Maybe you can look afterwards if he's the owner. But you have to make the decision now, in the street. Remember: you are the policeman, not the judge. We face this kind of decisions with insufficient information all the time.
I think it really is a probabilistic scenario. The only difference with die rolling is that dice are precision mechanisms intended to make our usual induction schemes useless. But both are scenarios of induction.
However, I see that you don't have any problem with saying "I accept the theory that it's a 83% chance of 1-5". You shouldn't have any problem with the policeman thinking "The probability that this fellow's a burglar must be over 95%. Let's detain him". But in both cases you use a quantity (precise in the first case, somewhat vague in the second). You use a degree of goodness for the hypothesis.
I'll look at your material at the bottom, but I don't have much faith. I'm not so sure as you that "the problem of induction" is indeed solved.
Thanks for your time.
Damian Gil
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Elliot Temple
Jul 31, 2017, 6:42:23 AM7/31/17
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On Jul 31, 2017, at 3:21 AM, Damián Gil <dami...@gmail.com> wrote:
> Maybe you can look afterwards if he's the owner. But you have to make the decision now, in the street. Remember: you are the policeman, not the judge. We face this kind of decisions with insufficient information all the time.
>
> I think it really is a probabilistic scenario. The only difference with die rolling is that dice are precision mechanisms intended to make our usual induction schemes useless. But both are scenarios of induction.
>
> However, I see that you don't have any problem with saying "I accept the theory that it's a 83% chance of 1-5". You shouldn't have any problem with the policeman thinking "The probability that this fellow's a burglar must be over 95%. Let's detain him". But in both cases you use a quantity (precise in the first case, somewhat vague in the second). You use a degree of goodness for the hypothesis.
Consider the idea:
> Maybe you can look afterwards if he's the owner. But you have to make the decision now, in the street. Remember: you are the policeman, not the judge. We face this kind of decisions with insufficient information all the time.
>
> I think it really is a probabilistic scenario. The only difference with die rolling is that dice are precision mechanisms intended to make our usual induction schemes useless. But both are scenarios of induction.
>
> However, I see that you don't have any problem with saying "I accept the theory that it's a 83% chance of 1-5". You shouldn't have any problem with the policeman thinking "The probability that this fellow's a burglar must be over 95%. Let's detain him". But in both cases you use a quantity (precise in the first case, somewhat vague in the second). You use a degree of goodness for the hypothesis.
"I accept the theory that it's an 83% chance of 1-5"
Don't judge that idea according to any quantity. It's non-refuted and its rivals are refuted, so judge it "yes".
The idea mentions a quantity which is different than being judged according to a quantity.
It's like how you judge "That cow weighs 500 lbs". There's a quantity mentioned in the idea (quantity of weight of the cow), but one's judgement of the idea is just "yes" (given we just put the cow on a scale and the reading was 500 lbs).
In practice, people often do judge by quantities (e.g. amount of support or goodness of an idea). But I'm saying that's a mistake and there's a better way.
> I'll look at your material at the bottom, but I don't have much faith. I'm not so sure as you that "the problem of induction" is indeed solved.
- Elliot
>
> Thanks for your time.
>
> Damian Gil
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Damián Gil
Jul 31, 2017, 7:35:46 AM7/31/17
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So, lets summarize:
In my opinion, the policeman has two hypotheses:
a) the masked man is a burglar
b) the masked man comes from a masquerade party
The two hypotheses are mutually incompatible, so he quickly calculates a gross probability for the hypotheses, 99% vs 1 % and decides to detain him, because he is very probably a burglar.
I don't know if I understand you well. You seem to accept my prior claim that the policeman is making a probabilistic reasoning. Something like this:
a) I accept the theory that there is (crudely) a 99% chance that the masked man is a burglar
b) I accept the theory that there is a 1% chance that the masked man comes from a masquerade.
I accept both theories, because both are non-refuted. So I don't know really why should I detain him, although I guess it's because the probability of burglary is higher than the probability of party.
That sounds like the same thing to me. With so many words, the burglar is going to escape! Is this your position? If it is, I don't see the superiority of the philosophy. I've looked at the bottom of your page and you can be sure I'm not going to pay 400$ for this wisdom.;)
Damian Gil
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Elliot Temple
Jul 31, 2017, 12:33:27 PM7/31/17
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On Jul 31, 2017, at 4:35 AM, Damián Gil <dami...@gmail.com> wrote:
> So, lets summarize:
>
> In my opinion, the policeman has two hypotheses:
> a) the masked man is a burglar
> b) the masked man comes from a masquerade party
>
> The two hypotheses are mutually incompatible, so he quickly calculates a gross probability for the hypotheses, 99% vs 1 % and decides to detain him, because he is very probably a burglar.
>
> I don't know if I understand you well. You seem to accept my prior claim that the policeman is making a probabilistic reasoning. Something like this:
>
> a) I accept the theory that there is (crudely) a 99% chance that the masked man is a burglar
> b) I accept the theory that there is a 1% chance that the masked man comes from a masquerade.
>
> I accept both theories, because both are non-refuted. So I don't know really why should I detain him, although I guess it's because the probability of burglary is higher than the probability of party.
>
> That sounds like the same thing to me. With so many words, the burglar is going to escape! Is this your position? If it is, I don't see the superiority of the philosophy. I've looked at the bottom of your page and you can be sure I'm not going to pay 400$ for this wisdom.;)
GISTE answered you, and also you didn’t respond about BoI and induction.
> So, lets summarize:
>
> In my opinion, the policeman has two hypotheses:
> a) the masked man is a burglar
> b) the masked man comes from a masquerade party
>
> The two hypotheses are mutually incompatible, so he quickly calculates a gross probability for the hypotheses, 99% vs 1 % and decides to detain him, because he is very probably a burglar.
>
> I don't know if I understand you well. You seem to accept my prior claim that the policeman is making a probabilistic reasoning. Something like this:
>
> a) I accept the theory that there is (crudely) a 99% chance that the masked man is a burglar
> b) I accept the theory that there is a 1% chance that the masked man comes from a masquerade.
>
> I accept both theories, because both are non-refuted. So I don't know really why should I detain him, although I guess it's because the probability of burglary is higher than the probability of party.
>
> That sounds like the same thing to me. With so many words, the burglar is going to escape! Is this your position? If it is, I don't see the superiority of the philosophy. I've looked at the bottom of your page and you can be sure I'm not going to pay 400$ for this wisdom.;)
I have a question, since you seem to have an opinion on the price: How much would you pay for the _Yes or No Philosophy_? (Also, did you estimate what the profit maximizing price is?)
- Elliot
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Damián Gil
Jul 31, 2017, 12:51:06 PM7/31/17
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---------- Forwarded message ----------
From: Damián Gil <dami...@gmail.com>
Date: 2017-07-31 18:35 GMT+02:00
Subject: Re: [BoI] Yes or No Philosophy
To: Nunya bizness <cuz_good_is_str...@yahoo.com>
Cc: FI <fallibl...@yahoogroups.com>
From: Damián Gil <dami...@gmail.com>
Date: 2017-07-31 18:35 GMT+02:00
Subject: Re: [BoI] Yes or No Philosophy
To: Nunya bizness <cuz_good_is_str...@yahoo.com>
Cc: FI <fallibl...@yahoogroups.com>
Nunya bizness: you keep recoiling and compounding the problem, to no use. For example: you say "his solution to P2 is this. I don’t yet know if this man is a thief or the owner of the house, so I’ll detain him until I can make a find out, using reasonable means to do so". He could well have come with another solution: "so I'll presume his innocence and set him free. Poor man, anyone can be coming from a masquerade party. I don't want to risk detaining an innocent man, as he almost surely is". Why does he prefers the first solution?
Because this is somewhat fatiguing, I will answer only those of your statements that seem to me most preposterous and dangerously approaching intellectual dishonesty.
1) I said that if you met someone in the street who had only a one in a trillion chance of being guilty of something, you wouldn't bother to detain him or check any records, and would let him free. You answered that this is too vague to discuss and there aren't enough details to judge whether or not he should be detained. Are you, you know, like a crazy person? Why do you say that? One in a trillion is a number, very low but not vague. And I don't need to state the circumstances of the case every time. The circumstances can be very varied between cases (in ours, he was coming from a masquerade party, his own store was in his path, a truck passed by just in that moment, managed to project a rock(?), and the rock shattered the crystal (!)) but in the end you must make a judgement that compounds all the circumstances. And that one is a probability judgement.
2) You say that the court operates on reasonable doubt. That means that you think doubts can be reasonable or unreasonable. What's the frontier between them? Is the masquerade hypothesis unreasonable or reasonable? You can never be sure that someone is guilty, nor innocent. Judges make mistakes even when they don't have reasonable doubts, and a wise judge once said that society should attempt to make statistics about the percentage of error in penal and civil trials. So, if you thought that the probability of guilt, based on the evidence you have, evidence which is finite (although you like to defer, you can't search for more evidence indefinitely) was 99.9%, would you imprison a murder suspect? Would you imprison on a 90% probability? These are not questions without meaning. Which level of doubt becomes an unreasonable level for a prison term is a debatable question. But the fact that there are levels in doubt means that there is a degree of belief in the theories that cause those doubts.
Suppose you only had the evidence I have shown. The property records are missing. There is no more evidence to be found. The circumstances are critical, you have to judge. I would send the masked man to prison. With doubt, as always, but I would send him. Would you stand there, doing nothing, short-circuited in a cloud of sparks?
Don't follow David Deutsch too fanatically, my friends. Someone can be very intelligent and be very very nutty. For example, check his views on parenting. Sooo nutty...
Damián Gil
Because this is somewhat fatiguing, I will answer only those of your statements that seem to me most preposterous and dangerously approaching intellectual dishonesty.
1) I said that if you met someone in the street who had only a one in a trillion chance of being guilty of something, you wouldn't bother to detain him or check any records, and would let him free. You answered that this is too vague to discuss and there aren't enough details to judge whether or not he should be detained. Are you, you know, like a crazy person? Why do you say that? One in a trillion is a number, very low but not vague. And I don't need to state the circumstances of the case every time. The circumstances can be very varied between cases (in ours, he was coming from a masquerade party, his own store was in his path, a truck passed by just in that moment, managed to project a rock(?), and the rock shattered the crystal (!)) but in the end you must make a judgement that compounds all the circumstances. And that one is a probability judgement.
2) You say that the court operates on reasonable doubt. That means that you think doubts can be reasonable or unreasonable. What's the frontier between them? Is the masquerade hypothesis unreasonable or reasonable? You can never be sure that someone is guilty, nor innocent. Judges make mistakes even when they don't have reasonable doubts, and a wise judge once said that society should attempt to make statistics about the percentage of error in penal and civil trials. So, if you thought that the probability of guilt, based on the evidence you have, evidence which is finite (although you like to defer, you can't search for more evidence indefinitely) was 99.9%, would you imprison a murder suspect? Would you imprison on a 90% probability? These are not questions without meaning. Which level of doubt becomes an unreasonable level for a prison term is a debatable question. But the fact that there are levels in doubt means that there is a degree of belief in the theories that cause those doubts.
Suppose you only had the evidence I have shown. The property records are missing. There is no more evidence to be found. The circumstances are critical, you have to judge. I would send the masked man to prison. With doubt, as always, but I would send him. Would you stand there, doing nothing, short-circuited in a cloud of sparks?
Don't follow David Deutsch too fanatically, my friends. Someone can be very intelligent and be very very nutty. For example, check his views on parenting. Sooo nutty...
Damián Gil
2017-07-31 16:43 GMT+02:00 Nunya bizness <cuz_good_is_stronger_than_ev...@yahoo.com>:
On Jul 31, 2017, at 9:07 AM, Damián Gil <dami...@gmail.com> wrote:
> Nunya bizzness: you appear to have made several mistakes.
>
> The first one is that your T3 or third theory, is not a theory at all. It's not an hypothesis. "I'll treat them both as potentially true and detain him" is only a disposition of your will, not a theory. "I don't know shit" is also not a theory. You could only call that a theory forcing the meaning a lot. Or, if you will, if what you meant was that you can't be absolutely sure of the truth of either T1 or T2, it is an obvious fact, a quasi-tautology (I think all of us agree in that you can never be absolutely sure of anything). Surely true, but not very useful to the policeman.
The context is a choice that the policeman must make.
The policeman’s first problem was to determine whether or not the person is a thief or not. I’ll call this P1.
At some point the policeman ran out of time before he could find a solution to P1. So he set that problem aside and created a new problem, P2.
P2 is this. Given that I don’t have a solution to P1, what should I do?
His solution to P2 is this. I don’t yet know if this man is a thief or the owner of the house, so I’ll detain him until I can make a find out, using reasonable means to do so.
> The second one is that instead of thinking "I'll treat them both as potentially true and detain him", you could instead have said "I'll treat them both as potentially true and set him free", but you chose the first one, and there had to be a reason.
Agreed.
> Maybe you acted on behalf of the precautionary principle. But your "precautionary" detaining (first I detain him, afterwards I check the records) implicitly means you assign (maybe unconsciously) a somewhat high probability of guilt and a somewhat low probability of innocence.
No
> If you met someone in the street who had only a one in a trillion chance of being guilty of something, you wouldn't bother to detain him or check any records, and would let him free.
This is too vague to discuss. There aren’t enough details to judge whether or not he should be detained.
> Maybe if you detained him it would be you who would be prosecuted instead, for police abuse.
I don’t know the laws that policemen must abide by. But given what I know, I think I’d win that case.
> So implicitly you have chosen T1, that the man is a burglar, at least momentarily. Maybe afterwards you'll have to change your opinion, but now you have chosen T1. T2 has very low probability and T3 is not a theory, it's an intention.
No. I haven’t chosen T1. I only didn’t rule it out yet.
> The third error (the least important one, because it only postpones the problem) is that both Mr. Temple and you seem to think that checking the property records is not probabilistic, and can "rule out" something. How can you be 100% sure that the records are correct?
The yes-no philosophy does not seek 100% sureness. Fallibility implies that that’s impossible. So the yes-no philosophy rejects it as a goal.
> Maybe there was an involuntary error. Maybe the masked man had previously forged them.
Possible. And if the policeman or a detective had a reason to believe that something is up (or even just a gut feeling), they could investigate further. And if they found some evidence, they could charge him and then a court would take it from there.
> The fact that the probability of it is very low doesn't mean it's not possible (as in the masquerade hypothesis). In a bayesian, probabilistic approach, checking the records and seeing that the house is not owned by the masked man would only decrease your subjective belief in his innocence even more, that's it. In the real world, all declarations of truth are probabilistic. Even the property records. To say it another way: Not only the policeman must make a probabilistic decision in little time. The judge will also make a probabilistic decision, only with more time and evidence.
No. The court operates on reasonable doubt. That means that in some situations, there is no reasonable doubt, and it’s ok to make a judgement and sentence the person to jail. That means that we don’t treat ALL theories as doubtful. We only have doubt about theories that we have reason to believe are wrong.
> Another error, this one by Mr. Temple:
>
> To say "There is a 50% chance of rain tomorrow" is not the same thing as saying "There is a 50% relative humidity" or "This cow weights 500 lbs". The last two ones are declarations of truth, or hypothesis, or theories (as you like to name them) with a quantity in each one (humidity, weight). But a "50% chance" is not a quantity in the physical world, or a correlate to any quantity. It is (in the bayesian approach) a degree of belief. "There is a 50% chance of rain tomorrow" includes both a statement that it will rain (a yes/no statement, without any quantity) and the degree of belief in it. And to have a degree of belief in a yes/no statement is a direct violation of the yes-no philosophy. That's the gist of it.
The 50% chance of rain is a bad example. The models used to decide the percentages are horrible. Have you investigated them? I did some and I’m not impressed.
A better example to use is this. There is a 50% chance that this 6-sided die will come out 3 or below. Call this theory T.
I have no reasonable doubts about T. Therefore I decide it’s true.
There is no degree of belief in a theory here. It’s just yes or no.
Probabilities are ok to be used for physical events. But not for believing in theories.
Note that even for physical events, you can’t interpret them without theories. So even when you’re using probabilities to consider physical events, you’re using yes-no philosophy to judge the theories explaining the physical events and why they have the probabilities that they have in the light of those theories.
— GISTE
Damián Gil
Jul 31, 2017, 1:15:53 PM7/31/17
to Anonymous FI, beginning-...@googlegroups.com, fI, FIGG
This is starting to get confusing. Apparently there are a lot of discussion groups.
Anonymous FI: I like your position better than GISTE. If the probability of guilty is sufficiently high, arrest him. If not, don't arrest him. Seems more reasonable than "One in a trillion? That's too vague, there is not enough information to know".You can say two things:
One:
I have two ideas. One is that there is a probability of 99% of guilt. The other is that there is a 1% probability of innocence. Those two ideas are non-refuted, so I don't choose between them. I accept them both provisionally. And since the probability within the first idea is much higher, I will arrest this damned burglar.
Two:
I think this man is guilty, and believe it with a 99% probability or degree of belief. (I mean, if this situation repeated itself a lot of times, I think I would be right 99% of times). Let's arrest him.
I think this man is guilty, and believe it with a 99% probability or degree of belief. (I mean, if this situation repeated itself a lot of times, I think I would be right 99% of times). Let's arrest him.
What I mean is that One and Two are the same thing. But Two is simpler. At least for the physical reality, the degree of belief in a non-probabilistic statement is the same as the non-refuted belief in a probabilistic statement. Whow! What did I just write?
Note: when I said that I wouldn't pay 400$ I was joking. If Mr. Temple wants to know, maybe I'd pay 2 or 3 euros, no more. I'm a busy man and I don't think I'd find anything substantially different from the content of Mr. Deutsch books. I mean no disrespect. You're obviously very intelligent people. I'm just practical.
Damian Gil
2017-07-31 18:52 GMT+02:00 Anonymous FI <anonymousfa...@gmail.com>:
On Jul 31, 2017, at 7:43 AM, Nunya bizness cuz_good_is_stronger_than_evil@yahoo.com [fallible-ideas] <fallibl...@yahoogroups.com> wrote:
On Jul 31, 2017, at 9:07 AM, Damián Gil <dami...@gmail.com> wrote:
Nunya bizzness: you appear to have made several mistakes.
The first one is that your T3 or third theory, is not a theory at all. It's not an hypothesis. "I'll treat them both as potentially true and detain him" is only a disposition of your will, not a theory. "I don't know shit" is also not a theory. You could only call that a theory forcing the meaning a lot. Or, if you will, if what you meant was that you can't be absolutely sure of the truth of either T1 or T2, it is an obvious fact, a quasi-tautology (I think all of us agree in that you can never be absolutely sure of anything). Surely true, but not very useful to the policeman.
The context is a choice that the policeman must make.
The policeman’s first problem was to determine whether or not the person is a thief or not. I’ll call this P1.
At some point the policeman ran out of time before he could find a solution to P1. So he set that problem aside and created a new problem, P2.
P2 is this. Given that I don’t have a solution to P1, what should I do?
His solution to P2 is this. I don’t yet know if this man is a thief or the owner of the house, so I’ll detain him until I can make a find out, using reasonable means to do so.
GISTE, your posts about this are pretty good!
Here, it would have been better if you said something like, “by ‘theory’ we mean any idea whatsoever. if you interpret our statements that way, then they’ll make more sense to you.”
Also there’s no need to avoid probability *within* ideas, just probability *of* ideas. Talking in terms of probability is reasonable for dealing with
1) probabilistic physical events (e.g. dice rolls)
2) incomplete information scenarios where you’re making guesses relating to proportions of a population. e.g. you can imagine the scenario happened 100,000 times. if you believe 90,000/100,000 people found in circumstances like that are robbers, then arrest him. but if you believe 5/100,000 people found in these circumstances are robbers, don’t arrest him. it’s fine to arrest some innocent people (arresting them isn’t charging them with a crime, let alone convicting them) but you don’t want to arrest a large number of innocent people per guilty person.
the basic thing here is you don’t know some details, but you know the common possibilities and how common they are. so then you try to form one non-refuted statistical theory.
this is an approximation. how are the probability estimates made in a case like this? using explanations, not hard data. so in a less trivial case, we’d have to talk about WHY we make certain guesses about the proportions in the broader population, and perhaps even whether counter-factuals scenarios are a correct concept or not. nevertheless there’s nothing really wrong with probabilistic constructs about populations like “8 out of 10 girls who say X to me are flirting with me”. one can have an estimated understanding of the overall frequencies of traits in the population of girls you meet at clubs, or about the population of jewelry store owners.
Elliot Temple
Jul 31, 2017, 1:38:37 PM7/31/17
to BoI, FIGG, FI
The important thing is not to mix up
1) the probability OF an idea (being true)
and
2) an idea ABOUT a probability.
(1) is a mistake. (2) is fine.
- Elliot
On Jul 31, 2017, at 10:15 AM, Damián Gil <dami...@gmail.com> wrote:
> This is starting to get confusing. Apparently there are a lot of discussion groups.
>
> Anonymous FI: I like your position better than GISTE. If the probability of guilty is sufficiently high, arrest him. If not, don't arrest him. Seems more reasonable than "One in a trillion? That's too vague, there is not enough information to know".
>
> You can say two things:
>
> One:
>
> I have two ideas. One is that there is a probability of 99% of guilt. The other is that there is a 1% probability of innocence. Those two ideas are non-refuted, so I don't choose between them. I accept them both provisionally. And since the probability within the first idea is much higher, I will arrest this damned burglar.
>
> Two:
>
> I think this man is guilty, and believe it with a 99% probability or degree of belief. (I mean, if this situation repeated itself a lot of times, I think I would be right 99% of times). Let's arrest him.
>
> What I mean is that One and Two are the same thing. But Two is simpler. At least for the physical reality, the degree of belief in a non-probabilistic statement is the same as the non-refuted belief in a probabilistic statement. Whow! What did I just write?
>
> Note: when I said that I wouldn't pay 400$ I was joking. If Mr. Temple wants to know, maybe I'd pay 2 or 3 euros, no more. I'm a busy man and I don't think I'd find anything substantially different from the content of Mr. Deutsch books. I mean no disrespect. You're obviously very intelligent people. I'm just practical.
>
> Damian Gil
>
>
>
1) the probability OF an idea (being true)
and
2) an idea ABOUT a probability.
(1) is a mistake. (2) is fine.
- Elliot
On Jul 31, 2017, at 10:15 AM, Damián Gil <dami...@gmail.com> wrote:
> This is starting to get confusing. Apparently there are a lot of discussion groups.
>
> Anonymous FI: I like your position better than GISTE. If the probability of guilty is sufficiently high, arrest him. If not, don't arrest him. Seems more reasonable than "One in a trillion? That's too vague, there is not enough information to know".
>
> You can say two things:
>
> One:
>
> I have two ideas. One is that there is a probability of 99% of guilt. The other is that there is a 1% probability of innocence. Those two ideas are non-refuted, so I don't choose between them. I accept them both provisionally. And since the probability within the first idea is much higher, I will arrest this damned burglar.
>
> Two:
>
> I think this man is guilty, and believe it with a 99% probability or degree of belief. (I mean, if this situation repeated itself a lot of times, I think I would be right 99% of times). Let's arrest him.
>
> What I mean is that One and Two are the same thing. But Two is simpler. At least for the physical reality, the degree of belief in a non-probabilistic statement is the same as the non-refuted belief in a probabilistic statement. Whow! What did I just write?
>
> Note: when I said that I wouldn't pay 400$ I was joking. If Mr. Temple wants to know, maybe I'd pay 2 or 3 euros, no more. I'm a busy man and I don't think I'd find anything substantially different from the content of Mr. Deutsch books. I mean no disrespect. You're obviously very intelligent people. I'm just practical.
>
> Damian Gil
>
>
>
> On Jul 31, 2017, at 7:43 AM, Nunya bizness cuz_good_is_str...@yahoo.com [fallible-ideas] <fallibl...@yahoogroups.com> wrote:
>
> On Jul 31, 2017, at 9:07 AM, Damián Gil <dami...@gmail.com> wrote:
>
> Nunya bizzness: you appear to have made several mistakes.
>
> The first one is that your T3 or third theory, is not a theory at all. It's not an hypothesis. "I'll treat them both as potentially true and detain him" is only a disposition of your will, not a theory. "I don't know shit" is also not a theory. You could only call that a theory forcing the meaning a lot. Or, if you will, if what you meant was that you can't be absolutely sure of the truth of either T1 or T2, it is an obvious fact, a quasi-tautology (I think all of us agree in that you can never be absolutely sure of anything). Surely true, but not very useful to the policeman.
>
> The context is a choice that the policeman must make.
>
> The policeman’s first problem was to determine whether or not the person is a thief or not. I’ll call this P1.
>
> At some point the policeman ran out of time before he could find a solution to P1. So he set that problem aside and created a new problem, P2.
>
> P2 is this. Given that I don’t have a solution to P1, what should I do?
>
> His solution to P2 is this. I don’t yet know if this man is a thief or the owner of the house, so I’ll detain him until I can make a find out, using reasonable means to do so.
>
> GISTE, your posts about this are pretty good!
>
> Here, it would have been better if you said something like, “by ‘theory’ we mean any idea whatsoever. if you interpret our statements that way, then they’ll make more sense to you.”
>
> Also there’s no need to avoid probability *within* ideas, just probability *of* ideas. Talking in terms of probability is reasonable for dealing with
>
> 1) probabilistic physical events (e.g. dice rolls)
>
> 2) incomplete information scenarios where you’re making guesses relating to proportions of a population. e.g. you can imagine the scenario happened 100,000 times. if you believe 90,000/100,000 people found in circumstances like that are robbers, then arrest him. but if you believe 5/100,000 people found in these circumstances are robbers, don’t arrest him. it’s fine to arrest some innocent people (arresting them isn’t charging them with a crime, let alone convicting them) but you don’t want to arrest a large number of innocent people per guilty person.
>
> the basic thing here is you don’t know some details, but you know the common possibilities and how common they are. so then you try to form one non-refuted statistical theory.
>
> this is an approximation. how are the probability estimates made in a case like this? using explanations, not hard data. so in a less trivial case, we’d have to talk about WHY we make certain guesses about the proportions in the broader population, and perhaps even whether counter-factuals scenarios are a correct concept or not. nevertheless there’s nothing really wrong with probabilistic constructs about populations like “8 out of 10 girls who say X to me are flirting with me”. one can have an estimated understanding of the overall frequencies of traits in the population of girls you meet at clubs, or about the population of jewelry store owners.
>
>
>
> On Jul 31, 2017, at 9:07 AM, Damián Gil <dami...@gmail.com> wrote:
>
> Nunya bizzness: you appear to have made several mistakes.
>
> The first one is that your T3 or third theory, is not a theory at all. It's not an hypothesis. "I'll treat them both as potentially true and detain him" is only a disposition of your will, not a theory. "I don't know shit" is also not a theory. You could only call that a theory forcing the meaning a lot. Or, if you will, if what you meant was that you can't be absolutely sure of the truth of either T1 or T2, it is an obvious fact, a quasi-tautology (I think all of us agree in that you can never be absolutely sure of anything). Surely true, but not very useful to the policeman.
>
> The context is a choice that the policeman must make.
>
> The policeman’s first problem was to determine whether or not the person is a thief or not. I’ll call this P1.
>
> At some point the policeman ran out of time before he could find a solution to P1. So he set that problem aside and created a new problem, P2.
>
> P2 is this. Given that I don’t have a solution to P1, what should I do?
>
> His solution to P2 is this. I don’t yet know if this man is a thief or the owner of the house, so I’ll detain him until I can make a find out, using reasonable means to do so.
>
> GISTE, your posts about this are pretty good!
>
> Here, it would have been better if you said something like, “by ‘theory’ we mean any idea whatsoever. if you interpret our statements that way, then they’ll make more sense to you.”
>
> Also there’s no need to avoid probability *within* ideas, just probability *of* ideas. Talking in terms of probability is reasonable for dealing with
>
> 1) probabilistic physical events (e.g. dice rolls)
>
> 2) incomplete information scenarios where you’re making guesses relating to proportions of a population. e.g. you can imagine the scenario happened 100,000 times. if you believe 90,000/100,000 people found in circumstances like that are robbers, then arrest him. but if you believe 5/100,000 people found in these circumstances are robbers, don’t arrest him. it’s fine to arrest some innocent people (arresting them isn’t charging them with a crime, let alone convicting them) but you don’t want to arrest a large number of innocent people per guilty person.
>
> the basic thing here is you don’t know some details, but you know the common possibilities and how common they are. so then you try to form one non-refuted statistical theory.
>
> this is an approximation. how are the probability estimates made in a case like this? using explanations, not hard data. so in a less trivial case, we’d have to talk about WHY we make certain guesses about the proportions in the broader population, and perhaps even whether counter-factuals scenarios are a correct concept or not. nevertheless there’s nothing really wrong with probabilistic constructs about populations like “8 out of 10 girls who say X to me are flirting with me”. one can have an estimated understanding of the overall frequencies of traits in the population of girls you meet at clubs, or about the population of jewelry store owners.
>
>
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Damián Gil
Jul 31, 2017, 2:03:39 PM7/31/17
to Nunya bizness, beginning-...@googlegroups.com, FI
You people don't seem to be aware that you have an annoying technique for discussion. Dividing the text in fragments, indenting them, and not responding to half of the challenges posed is very annoying to the receptor. I'll try to do it your way so you may know how it feels.
>> Nunya bizness: you keep recoiling and compounding the problem, to no use. For example: you say "his solution to P2 is this. I don’t yet know if this man is a thief or the owner of the house, so I’ll detain him until I can make a find out, using reasonable means to do so". He could well have come with another solution: "so I'll presume his innocence and set him free. Poor man, anyone can be coming from a masquerade party. I don't want to risk detaining an innocent man, as he almost surely is". Why does he prefers the first solution?
>Anon answered this in another email
Who the hell is Anon? The Anonymous one?
> and you replied to that email saying you agree.
No I didn't.
> So i’ll leave it alone.
You better do. You only postponed the answer to a question.
>> Because this is somewhat fatiguing, I will answer only those of your statements that seem to me most preposterous and dangerously approaching intellectual dishonesty.
>>
>> 1) I said that if you met someone in the street who had only a one in a trillion chance of being guilty of something, you wouldn't bother to detain him or check any records, and would let him free. You answered that this is too vague to discuss and there aren't enough details to judge whether or not he should be detained. Are you, you know, like a crazy person?
>as far as i know, when someone calls someone crazy, it’s a way to delegitimize his ideas.
Sometimes. It could also be a way to vent frustration. Or a sincere question, like when Evey Hammond asked V (of Vendetta) the same thing, sincerely interested in the answer. I would like to know, because this discussions are tiring.
>>> Why do you say that?
Nunya: silence
>>>One in a trillion is a number, very low but not vague. And I don't need to state the circumstances of the case every time. The circumstances can be very varied between cases (in ours, he was coming from a masquerade party, his own store was in his path, a truck passed by just in that moment, managed to project a rock(?), and the rock shattered the crystal (!)) but in the end you must make a judgement that compounds all the circumstances. And that one is a probability judgement.
Nunya: silence
>>> 2) You say that the court operates on reasonable doubt. That means that you think doubts can be reasonable or unreasonable. What's the frontier between them?
>an unreasonable doubt is like this.
>1+1=2 is fallible, so maybe it’s wrong. i’m doubtful. so i’ll reject it.
>1+1=2 is fallible, so maybe it’s wrong. i’m doubtful. so i’ll reject it.
So the only unreasonable doubts must be about logical fallacies, or can they be about the physical world, too? Too easy.
>> Is the masquerade hypothesis unreasonable or reasonable?
>before the policeman has any evidence to rule it out, it’s reasonable.
Are you sure you're not crazy? Like Iñigo Montoya said in The Princess Bride, "You keep using that word. I don't think it means what you think it means".
>> You can never be sure that someone is guilty, nor innocent.
>Right. For this reason a case can be appealed.
Not for that reason. In that case it could be appealed indefinitely, any number of times. But it can`t. The reason for the appeals is to reduce the probability of a final wrong judgement, not to be sure of its correctness.
>This recognizes the fallibility of the court’s judgement.
>>> Judges make mistakes even when they don't have reasonable doubts, and a wise judge once said that society should attempt to make statistics about the percentage of error in penal and civil trials. So, if you thought that the probability of guilt, based on the evidence you have, evidence which is finite (although you like to defer, you can't search for more evidence indefinitely) was 99.9%, would you imprison a murder suspect?
[silence]
>>>Would you imprison on a 90% probability?
[silence]
>>>These are not questions without meaning. Which level of doubt becomes an unreasonable level for a prison term is a debatable question. But the fact that there are levels in doubt means that there is a degree of belief in the theories that cause those doubts.
>No.
No... what?
>A judge would send someone to prison for murder if and only if there was no reasonable doubt that he committed a murder.
Yeah. But which level of doubt seems reasonable varies between people. I repeat: the existence of levels of doubt implies the existence of levels of belief.
>>> Suppose you only had the evidence I have shown. The property records are missing. There is no more evidence to be found.
>The policeman could have asked the man for any records that would make the policeman believe that he owns the house. For example, pieces of mail with his name on it. Or pictures in the house with this guy’s face in them. Those aren’t even records of ownership, but I bet a policeman would be satisfied with that in most cases.
What part of "Suppose you only had the evidence I have shown" and "There is no more evidence to be found" don't you understand?
>> The circumstances are critical, you have to judge. I would send the masked man to prison. With doubt, as always, but I would send him. Would you stand there, doing nothing, short-circuited in a cloud of sparks?
>No I wouldn’t.
>If a court has reasonable doubt that he committed a murder, then they shouldn’t convict him of murder.
>If a court has reasonable doubt that he committed a murder, then they shouldn’t convict him of murder.
Aha! You mentioned before that the masquerade hypothesis seemed "reasonable" to you. And I've put you in a situation in which there is no more evidence. So I understand that you wouldn't convict a masked man going out of a shattered crystal store with a sack of jewelry in absence of more evidence. You have a very serious epistemological problem at hand, worst than you believe...
>> Don't follow David Deutsch too fanatically, my friends.
>We don’t do that.
Yes you do.
>Or rather, it’s wrong to do so.
Yes it is.
>I’m sure some new people do do that. I know i have. Maybe I still do in some cases, but I’m trying to find and fix those. People should make their own judgments instead of blindly believing people based on authority.
The critical skill is being able to be convinced by better arguments, not forcing your own when they start to crumble.
>Note that Elliot has found mistakes in David’s ideas. His yes-no philosophy refutes David’s hard-to-vary concept. (Or maybe it’s better to say that the yes-no philosophy explains why the hard-to-vary concept is not useful.)
Maybe. But I didn't have to read Elliot to know it was bogus.
>> Someone can be very intelligent and be very very nutty. For example, check his views on parenting. Sooo nutty…
>I’m aware of David’s views on parenting. It basically brings the moral ideas of liberalism and the epistemological ideas of Karl Popper to parenting. What do you have against these ideas?
>> Someone can be very intelligent and be very very nutty. For example, check his views on parenting. Sooo nutty…
>I’m aware of David’s views on parenting. It basically brings the moral ideas of liberalism and the epistemological ideas of Karl Popper to parenting. What do you have against these ideas?
That they are nutty.
Damián Gil
2017-07-31 19:22 GMT+02:00 Nunya bizness <cuz_good_is_str...@yahoo.com>:
On Jul 31, 2017, at 11:51 AM, Damián Gil <dami...@gmail.com> wrote:
> ---------- Forwarded message ----------
> From: Damián Gil <dami...@gmail.com>
> Date: 2017-07-31 18:35 GMT+02:00
> Subject: Re: [BoI] Yes or No Philosophy
> To: Nunya bizness <cuz_good_is_stronger_than_ev...@yahoo.com>
> Cc: FI <fallible-ideas@yahoogroups.com>
>
>
> Nunya bizness: you keep recoiling and compounding the problem, to no use. For example: you say "his solution to P2 is this. I don’t yet know if this man is a thief or the owner of the house, so I’ll detain him until I can make a find out, using reasonable means to do so". He could well have come with another solution: "so I'll presume his innocence and set him free. Poor man, anyone can be coming from a masquerade party. I don't want to risk detaining an innocent man, as he almost surely is". Why does he prefers the first solution?
Anon answered this in another email, and you replied to that email saying you agree. So i’ll leave it alone.
> Because this is somewhat fatiguing, I will answer only those of your statements that seem to me most preposterous and dangerously approaching intellectual dishonesty.
>
> 1) I said that if you met someone in the street who had only a one in a trillion chance of being guilty of something, you wouldn't bother to detain him or check any records, and would let him free. You answered that this is too vague to discuss and there aren't enough details to judge whether or not he should be detained. Are you, you know, like a crazy person?
as far as i know, when someone calls someone crazy, it’s a way to delegitimize his ideas.
> Why do you say that? One in a trillion is a number, very low but not vague. And I don't need to state the circumstances of the case every time. The circumstances can be very varied between cases (in ours, he was coming from a masquerade party, his own store was in his path, a truck passed by just in that moment, managed to project a rock(?), and the rock shattered the crystal (!)) but in the end you must make a judgement that compounds all the circumstances. And that one is a probability judgement.
>
> 2) You say that the court operates on reasonable doubt. That means that you think doubts can be reasonable or unreasonable. What's the frontier between them?
an unreasonable doubt is like this.
1+1=2 is fallible, so maybe it’s wrong. i’m doubtful. so i’ll reject it.
> Is the masquerade hypothesis unreasonable or reasonable?
before the policeman has any evidence to rule it out, it’s reasonable.
> You can never be sure that someone is guilty, nor innocent.
Right. For this reason a case can be appealed. This recognizes the fallibility of the court’s judgement.
> Judges make mistakes even when they don't have reasonable doubts, and a wise judge once said that society should attempt to make statistics about the percentage of error in penal and civil trials. So, if you thought that the probability of guilt, based on the evidence you have, evidence which is finite (although you like to defer, you can't search for more evidence indefinitely) was 99.9%, would you imprison a murder suspect? Would you imprison on a 90% probability? These are not questions without meaning. Which level of doubt becomes an unreasonable level for a prison term is a debatable question. But the fact that there are levels in doubt means that there is a degree of belief in the theories that cause those doubts.
No. A judge would send someone to prison for murder if and only if there was no reasonable doubt that he committed a murder.
> Suppose you only had the evidence I have shown. The property records are missing. There is no more evidence to be found.
The policeman could have asked the man for any records that would make the policeman believe that he owns the house. For example, pieces of mail with his name on it. Or pictures in the house with this guy’s face in them. Those aren’t even records of ownership, but I bet a policeman would be satisfied with that in most cases.
> The circumstances are critical, you have to judge. I would send the masked man to prison. With doubt, as always, but I would send him. Would you stand there, doing nothing, short-circuited in a cloud of sparks?
No I wouldn’t.
If a court has reasonable doubt that he committed a murder, then they shouldn’t convict him of murder.
> Don't follow David Deutsch too fanatically, my friends.
We don’t do that. Or rather, it’s wrong to do so. I’m sure some new people do do that. I know i have. Maybe I still do in some cases, but I’m trying to find and fix those. People should make their own judgments instead of blindly believing people based on authority.
Note that Elliot has found mistakes in David’s ideas. His yes-no philosophy refutes David’s hard-to-vary concept. (Or maybe it’s better to say that the yes-no philosophy explains why the hard-to-vary concept is not useful.)
> Someone can be very intelligent and be very very nutty. For example, check his views on parenting. Sooo nutty…
I’m aware of David’s views on parenting. It basically brings the moral ideas of liberalism and the epistemological ideas of Karl Popper to parenting. What do you have against these ideas?
— GISTE
Damián Gil
Aug 1, 2017, 9:16:20 AM8/1/17
to Kate Sams, beginning-...@googlegroups.com, FI, FIGG
Well, at last! Kate Sams has discovered one of many instances in which Nunya Bizness either doesn't adress my question or aswers a slightly different one. It's not fun anymore...
Let's start again. I promise I won't call no one crazy anymore. I suppose it's not your fault.
There is a severe disease and there are 4 medicines that can be used to treat it. No one knows the mechanism by which these drugs act on the disease (that's quite common, in fact). So the government organizes two clinical trials:
Trial 1: 100 subjects, 50 in each arm
Drug A cured 20% of the patients (10 patients)
Drug B cured 10% of the patients (5 patients)
Trial 2: 10000 subjects, 5000 in each arm
Drug C cured 20% of the patients (1000 patients)
Drug D cured 10% of the patients (500 patients)
Then a scientist says:
"Drug A is better than Drug B; and Drug C is better than drug D. But I have more degree of confidence in my second statement.
For me, the scientist is a man with common sense. My question is ¿do you believe the scientist is wrong in any way? In which one? Please be precise.
Damián Gil
Justin Mallone
Aug 1, 2017, 1:29:47 PM8/1/17
to beginning-...@googlegroups.com, fiGG, Alisa Zinov'yevna Rosenbaum petrogradphilosopher@gmail.com [fallible-ideas]
On Aug 1, 2017, at 9:16 AM, Damián Gil <dami...@gmail.com> wrote:
>
> Well, at last! Kate Sams has discovered one of many instances in which Nunya Bizness either doesn't adress my question or aswers a slightly different one. It's not fun anymore...
It's important to be open to have your premises challenged, and that includes the questions you think are important.
>
> Well, at last! Kate Sams has discovered one of many instances in which Nunya Bizness either doesn't adress my question or aswers a slightly different one. It's not fun anymore...
Lots of people find it fun...
> Let's start again. I promise I won't call no one crazy anymore. I suppose it's not your fault.
>
>
> There is a severe disease and there are 4 medicines that can be used to treat it. No one knows the mechanism by which these drugs act on the disease (that's quite common, in fact).
>
> So the government organizes two clinical trials:
>
> Trial 1: 100 subjects, 50 in each arm
>
> Drug A cured 20% of the patients (10 patients)
> Drug B cured 10% of the patients (5 patients)
>
> Trial 2: 10000 subjects, 5000 in each arm
>
> Drug C cured 20% of the patients (1000 patients)
> Drug D cured 10% of the patients (500 patients)
>
> Then a scientist says:
>
> "Drug A is better than Drug B; and Drug C is better than drug D. But I have more degree of confidence in my second statement.
>
> For me, the scientist is a man with common sense. My question is ¿do you believe the scientist is wrong in any way? In which one? Please be precise.
But to get at what I think your point is ... one can have a criticism of a sample size as being too low to draw conclusions from about the effectiveness of some drug. But in that case, it's too low to draw conclusions from! So you shouldn't use it to draw conclusions...like if 100 subjects is too low to talk about drug effectiveness, it's too low. Period. In such a case, 100 subject studies might still be useful for some purposes (like maybe you want to make sure the drug doesn't kill 50% of the people you give it to before you run the 10000 subject study...) But you can't use it to talk about relative drug effectiveness.
Also, once you hit whatever the sufficient n-size is for being able to talk about relative drug effectiveness (in light of our knowledge of statistics), that's it, you've hit it. So say the sufficient n-size for making statements was 500. So you can talk about relative drug effectiveness if the size of the study was 500, or 501, or 10000, or 10001.
If the sufficient n-size for making such statements was higher than 100 but less than 10000 in the examples above, then the scientist should confine his evaluations to drugs C and D, since he can't make statements about A and B.
If the sufficient n-size for making such statements was 100 or below, then, no, the scientist shouldn't talk in terms of greater confidence about his judgment regarding C and D. He can talk about A relative to B and C relative to D. But both studies are over the threshold for being able to talk about the effectiveness of the drugs....
If the sufficient n-size for making such statements was above 10000, he can't evaluate the drug effectiveness at all...
BTW, by what seems to be your logic (i.e. higher sample size = more confidence), you'd have to talk about having a higher confidence in statements about a 10,001 subject study than a 10,000 subject study. But common sense would say that there's not really any difference there. You wanna be on the side of common sense, but common sense seems to be on your side with one set of numbers and on the Yes/No epistemology side with another set of numbers. So there's a contradiction there worth exploring that can't be resolved by appeals to common sense.
-JM
Damián Gil
Aug 1, 2017, 3:20:56 PM8/1/17
to beginning-...@googlegroups.com, Alisa Zinov'yevna Rosenbaum petrogradphilosopher@gmail.com [fallible-ideas]
2017-08-01 19:29 GMT+02:00 Justin Mallone <just...@gmail.com>:
On Aug 1, 2017, at 9:16 AM, Damián Gil <dami...@gmail.com> wrote:
>
> Let's start again. I promise I won't call no one crazy anymore. I suppose it's not your fault.
>
>
> There is a severe disease and there are 4 medicines that can be used to treat it. No one knows the mechanism by which these drugs act on the disease (that's quite common, in fact).
>
> So the government organizes two clinical trials:
>
> Trial 1: 100 subjects, 50 in each arm
>
> Drug A cured 20% of the patients (10 patients)
> Drug B cured 10% of the patients (5 patients)
>
> Trial 2: 10000 subjects, 5000 in each arm
>
> Drug C cured 20% of the patients (1000 patients)
> Drug D cured 10% of the patients (500 patients)
>
> Then a scientist says:
>
> "Drug A is better than Drug B; and Drug C is better than drug D. But I have more degree of confidence in my second statement.
>
> For me, the scientist is a man with common sense. My question is ¿do you believe the scientist is wrong in any way? In which one? Please be precise.
Your hypo leaves much to be desired. To know whether you can judge the effectiveness of the drugs based on the study, you'd need to know about things like whether the study was blinded, what potential sources of error were considered and addressed, etc.
My "hypo" is a simplification to make a point. The relevant issue here is not the methodology of the studies, but that the methodology is exactly the same in both (I didn't bother to specify that, but... well, I assume we are trying to understand each other here. But if you want, suppose they are good (triple-blinded, consecutive patients, etc). That's irrelevant to the key point, which is: When the scientist says "I have more degree of confidence in my second statement" (or in the second trial), is he saying something absurd? Is he wrong to do that? I would like, first of all, a clear answer to that question. It's a very simple question.
But to get at what I think your point is ...
Thank you for getting to the point. Not everyone does it...
one can have a criticism of a sample size as being too low to draw conclusions from about the effectiveness of some drug. But in that case, it's too low to draw conclusions from! So you shouldn't use it to draw conclusions...like if 100 subjects is too low to talk about drug effectiveness, it's too low. Period. In such a case, 100 subject studies might still be useful for some purposes (like maybe you want to make sure the drug doesn't kill 50% of the people you give it to before you run the 10000 subject study...) But you can't use it to talk about relative drug effectiveness.
Also, once you hit whatever the sufficient n-size is for being able to talk about relative drug effectiveness (in light of our knowledge of statistics), that's it, you've hit it. So say the sufficient n-size for making statements was 500. So you can talk about relative drug effectiveness if the size of the study was 500, or 501, or 10000, or 10001.
If the sufficient n-size for making such statements was higher than 100 but less than 10000 in the examples above, then the scientist should confine his evaluations to drugs C and D, since he can't make statements about A and B.
If the sufficient n-size for making such statements was 100 or below, then, no, the scientist shouldn't talk in terms of greater confidence about his judgment regarding C and D. He can talk about A relative to B and C relative to D. But both studies are over the threshold for being able to talk about the effectiveness of the drugs....
If the sufficient n-size for making such statements was above 10000, he can't evaluate the drug effectiveness at all...
Why do you believe that these thresholds exist? They don't. There is no magic threshold above which you can talk about the effectiveness of a drug (or any estimated difference in proportions, like in this case), and below which you can't.
Suppose you have a man that is throwing a die repeatedly in a casino. You are wondering if the dice is fair or not. In the first throw, he scores a six. You think: well, he had a 1/6 chance, let's see. In the second throw, he scores another six. You think: 1/36, maybe he just got lucky. In the third throw, he again scores a six: incredible luck!. He goes that way for quite a long time. Now there are, I don't know, like 32 sixes in a row. Eventually, you call the security of the casino.
Attention now: the number of throws at which you decide to call security depends on a lot of things: the stakes being played, your confidence in the security, your honesty, etc. But all that is irrelevant to my point, because it doesn't change these key facts:
1.-From your point of view, the higher the number of consecutive sixes, the more confidence you'll have that the man is cheating and the die is not fair, and the less confidence you'll have that the man is playing fairly. Warning: if you don't agree with that, I will enter a state of profound despair.
2.-There is no magic threshold. The more sixes in a row, the higher the confidence in his cheating. That's it. It's invalid to deduce "if he throws more than [arbitrary threshold] sixes, then he is cheating. If not, he is innocent". There is no such threshold.
The same is true with the sample size in the studies. The more sample size you have, the more confidence you'll have in the results, ceteris paribus. The first trial would give you little confidence, to be sure. Probably too low to overpower other considerations, like the price of the drugs, or the side effects of each one. But what would you do with the dubious result you have is irrelevant to my point. My point is that, the more sample size you have, the less dubious the result will be. Well, my real point is that if "confidence" or "dubiousness" can grow or diminish, then there is such thing as a degree of confidence in a statement. All bayesian statistics is based on that. For a bayesian, probability is subjective. Probability is a degree of confidence that depends of the information that an observer has about the world.
BTW, by what seems to be your logic (i.e. higher sample size = more confidence),
My logic is indeed that the higher the sample size, the more confidence, a basic tenet of statistics (that's why everyone tries to do big studies if possible) and I also want you to be clear if you agree with that.
you'd have to talk about having a higher confidence in statements about a 10,001 subject study than a 10,000 subject study. But common sense would say that there's not really any difference there.
Common sense would say nothing like that. You can bet I'll have a higher confidence in a study with 10001 subjects than in one with 10000. It's true I would have only a little more, because 10001 is only a little more than 10000, but I would. The contrary would be illogical. Because if I had the same confidence in a study with 10001 than in a study with 10000, then I would have to have the same confidence in a study with 10002 than in a study with 10000. And so on. And at some time or other, the contradiction would be not only evident (as it is for me), but absolutely flagrant (and then it would be evident for everyone, or so I hope, you can never be sure).
You wanna be on the side of common sense, but common sense seems to be on your side with one set of numbers and on the Yes/No epistemology side with another set of numbers. So there's a contradiction there worth exploring that can't be resolved by appeals to common sense.
Common sense seems only to be on my side in this case, I'm afraid. But I don't want to rely on any vagueness or argument of authority. I said that, in my opinion, the scientist statement "I have more degree of confidence in the second trial" is common sense. But I'm not "appealing" to your common sense (except in a very basic way). I'm just appealing to logic.
Damián Gil
-JM
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Elliot Temple
Aug 1, 2017, 3:42:50 PM8/1/17
to BoI, FIGG, FI
What do you care about "more degree of confidence" or "the more confidence you'll have that the man is cheating and the die is not fair"? (These quotes are from the post included below.) Is it an imprecise statement about what bets you would and wouldn't take?
You have to decide, for any given state of the evidence, whether or not to accept various conclusions or not. E.g. at one state of the evidence you decide NOT to accuse the man of cheating, and later with a different state of the evidence you decide TO accuse him of cheating. You have to judge: given the evidence, my knowledge of statistics, my knowledge of cheating, my understanding of the consequences of making an accusation, company policy, the potential for violence, etc, is it a good idea to accuse him of cheating at this time, yes or no?
You don't have to decide how confident you are, which is vague. What you have to decide is whether to act. If you define "confidence" in a precise way, then you may be able to measure it and refer to that measurement in an idea. An idea could be about a candidate solution, explanation, criticism, problem, etc...
You can also make a judgement like: out of millions of casino visitors, 75 out of 100 people who we have this evidence about are cheaters. It's hard to do that very precisely, and there's various limitations and ways this kind of analysis can go wrong, e.g. by having a systematic bias. But, there ARE various ways to estimate it which do have SOME value. You can then expose that judgement (about 75/100 people) to criticism and decide YES or NO about it. You may decide to (tentatively, fallibly) accept it as a fact. You could then refer to that fact in an idea about what action to take, in a criticism, etc. I explain about the use of facts, including facts about statistics, in the _Yes or No Philosophy_ educational package. http://fallibleideas.com/yes-or-no-philosophy (I know you already saw it, Damián Gil, but I'm linking it for other readers.)
> <Random number generation chiste.gif>
> Virus-free. www.avg.com
You have to decide, for any given state of the evidence, whether or not to accept various conclusions or not. E.g. at one state of the evidence you decide NOT to accuse the man of cheating, and later with a different state of the evidence you decide TO accuse him of cheating. You have to judge: given the evidence, my knowledge of statistics, my knowledge of cheating, my understanding of the consequences of making an accusation, company policy, the potential for violence, etc, is it a good idea to accuse him of cheating at this time, yes or no?
You don't have to decide how confident you are, which is vague. What you have to decide is whether to act. If you define "confidence" in a precise way, then you may be able to measure it and refer to that measurement in an idea. An idea could be about a candidate solution, explanation, criticism, problem, etc...
You can also make a judgement like: out of millions of casino visitors, 75 out of 100 people who we have this evidence about are cheaters. It's hard to do that very precisely, and there's various limitations and ways this kind of analysis can go wrong, e.g. by having a systematic bias. But, there ARE various ways to estimate it which do have SOME value. You can then expose that judgement (about 75/100 people) to criticism and decide YES or NO about it. You may decide to (tentatively, fallibly) accept it as a fact. You could then refer to that fact in an idea about what action to take, in a criticism, etc. I explain about the use of facts, including facts about statistics, in the _Yes or No Philosophy_ educational package. http://fallibleideas.com/yes-or-no-philosophy (I know you already saw it, Damián Gil, but I'm linking it for other readers.)
>
> The same is true with the sample size in the studies. The more sample size you have, the more confidence you'll have in the results, ceteris paribus. The first trial would give you little confidence, to be sure. Probably too low to overpower other considerations, like the price of the drugs, or the side effects of each one. But what would you do with the dubious result you have is irrelevant to my point. My point is that, the more sample size you have, the less dubious the result will be. Well, my real point is that if "confidence" or "dubiousness" can grow or diminish, then there is such thing as a degree of confidence in a statement. All bayesian statistics is based on that. For a bayesian, probability is subjective. Probability is a degree of confidence that depends of the information that an observer has about the world.
>
>
> BTW, by what seems to be your logic (i.e. higher sample size = more confidence),
>
> My logic is indeed that the higher the sample size, the more confidence, a basic tenet of statistics (that's why everyone tries to do big studies if possible) and I also want you to be clear if you agree with that.
>
> you'd have to talk about having a higher confidence in statements about a 10,001 subject study than a 10,000 subject study. But common sense would say that there's not really any difference there.
>
>
> Common sense would say nothing like that. You can bet I'll have a higher confidence in a study with 10001 subjects than in one with 10000. It's true I would have only a little more, because 10001 is only a little more than 10000, but I would. The contrary would be illogical. Because if I had the same confidence in a study with 10001 than in a study with 10000, then I would have to have the same confidence in a study with 10002 than in a study with 10000. And so on. And at some time or other, the contradiction would be not only evident (as it is for me), but absolutely flagrant (and then it would be evident for everyone, or so I hope, you can never be sure).
>
>
> You wanna be on the side of common sense, but common sense seems to be on your side with one set of numbers and on the Yes/No epistemology side with another set of numbers. So there's a contradiction there worth exploring that can't be resolved by appeals to common sense.
>
> Common sense seems only to be on my side in this case, I'm afraid. But I don't want to rely on any vagueness or argument of authority. I said that, in my opinion, the scientist statement "I have more degree of confidence in the second trial" is common sense. But I'm not "appealing" to your common sense (except in a very basic way). I'm just appealing to logic.
>
> Damián Gil
>
>
> -JM
>
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> The same is true with the sample size in the studies. The more sample size you have, the more confidence you'll have in the results, ceteris paribus. The first trial would give you little confidence, to be sure. Probably too low to overpower other considerations, like the price of the drugs, or the side effects of each one. But what would you do with the dubious result you have is irrelevant to my point. My point is that, the more sample size you have, the less dubious the result will be. Well, my real point is that if "confidence" or "dubiousness" can grow or diminish, then there is such thing as a degree of confidence in a statement. All bayesian statistics is based on that. For a bayesian, probability is subjective. Probability is a degree of confidence that depends of the information that an observer has about the world.
>
>
> BTW, by what seems to be your logic (i.e. higher sample size = more confidence),
>
> My logic is indeed that the higher the sample size, the more confidence, a basic tenet of statistics (that's why everyone tries to do big studies if possible) and I also want you to be clear if you agree with that.
>
> you'd have to talk about having a higher confidence in statements about a 10,001 subject study than a 10,000 subject study. But common sense would say that there's not really any difference there.
>
>
> Common sense would say nothing like that. You can bet I'll have a higher confidence in a study with 10001 subjects than in one with 10000. It's true I would have only a little more, because 10001 is only a little more than 10000, but I would. The contrary would be illogical. Because if I had the same confidence in a study with 10001 than in a study with 10000, then I would have to have the same confidence in a study with 10002 than in a study with 10000. And so on. And at some time or other, the contradiction would be not only evident (as it is for me), but absolutely flagrant (and then it would be evident for everyone, or so I hope, you can never be sure).
>
>
> You wanna be on the side of common sense, but common sense seems to be on your side with one set of numbers and on the Yes/No epistemology side with another set of numbers. So there's a contradiction there worth exploring that can't be resolved by appeals to common sense.
>
> Common sense seems only to be on my side in this case, I'm afraid. But I don't want to rely on any vagueness or argument of authority. I said that, in my opinion, the scientist statement "I have more degree of confidence in the second trial" is common sense. But I'm not "appealing" to your common sense (except in a very basic way). I'm just appealing to logic.
>
> Damián Gil
>
>
> -JM
>
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Damián Gil
Aug 1, 2017, 5:13:24 PM8/1/17
to beginning-...@googlegroups.com
2017-08-01 21:42 GMT+02:00 Elliot Temple <cu...@curi.us>:
Welcome back, Mr. Temple.
In my previous mail, I demanded clarification, to be able to pinpoint better the cause of the disagreement. Please clarify (if you don't feel like it, it's sufficient with a yes or a no, like in your philosophy). Do you agree or not with these:
-The scientist is wrong in saying that he has more confidence in trial 2, 'cos speaking of levels of confidence is illogical.
-From your point of view, the higher the number of consecutive sixes, the more confidence you'll have that the man is cheating and the die is not fair, and the less confidence you'll have that the man is playing fairly. Warning: if you don't agree with that, I will enter a state of profound despair.
-There is no magic threshold. The more sixes in a row, the higher the confidence in his cheating. That's it. It's invalid to deduce "if he throws more than [arbitrary threshold] sixes, then he is cheating. If not, he is innocent". There is no such threshold.
Note to the people out there: If the respondents don't bother to reply at least to this, at least with a yes or a no, I will not reply.
Now, let's see what you're saying.
What do you care about "more degree of confidence" or "the more confidence you'll have that the man is cheating and the die is not fair"? (These quotes are from the post included below.) Is it an imprecise statement about what bets you would and wouldn't take?
Remember I'm not a native english speaker. I don't know if "what do you care about" is a slang phrase or something. Talking literally, what I care about is no one's business. The relevant thing is that the degree of confidence can increase or decrease, not if I care much about it or not.
The confidence someone has in a statement can be very imprecise, like in the case of a common man treating a difficult problem; or very precise, like in the case of a bayesian statistician treating a very simple problem, like the hypothetical die. A statistician can state his degree of confidence in a very precise, numerical way. For example, he can assume initially that the die is fair, and the proportion of sixes must be 1/6. Each time the die is rolled, the statistician can give you the exact posterior odds ratio. Say he calculates it after quite a lot of sixes and the result is 5:1. That means that, given his current knowledge (I insist that probability is subjective, it depends of the state of knowledge of the observer, so different observers can precisely calculate different probabilities for the same event) cheating is exactly five times more probable than innocence. But all of this is irrelevant. The degree of confidence in a statement can be vague or precise, but the point is that it _exists_. It's not illogical to talk about it.
You have to decide, for any given state of the evidence, whether or not to accept various conclusions or not.
E.g. at one state of the evidence you decide NOT to accuse the man of cheating, and later with a different state of the evidence you decide TO accuse him of cheating. You have to judge: given the evidence, my knowledge of statistics, my knowledge of cheating, my understanding of the consequences of making an accusation, company policy, the potential for violence, etc, is it a good idea to accuse him of cheating at this time, yes or no?
You are mixing thinking and acting. I can wonder if the man is a cheater independently of my actions, purely for intellectual curiosity. The manner in which I decide to act is irrelevant to the question at hand, namely, ¿how sure can I be that he is a cheater?
You don't have to decide how confident you are, which is vague. What you have to decide is whether to act.
Wheter to act or not depends on many things. One of the most important ones is how confident I am. So obviously I have to decide how confident I am. I can do it in a very precise manner of very vaguely, but I have to do it.
If you define "confidence" in a precise way, then you may be able to measure it and refer to that measurement in an idea. An idea could be about a candidate solution, explanation, criticism, problem, etc...
I don't understand this, unless you say it in a trivial sense. If I define confidence very precisely, as a statistician hopes to do, well, yes, I can refer to that confidence level. So? Don't bother to reply. Won't get us anywhere...
You can also make a judgement like: out of millions of casino visitors, 75 out of 100 people who we have this evidence about are cheaters.
Correct. That's maybe what a cartoon frequentist statistician would say. I agree.
It's hard to do that very precisely, and there's various limitations and ways this kind of analysis can go wrong, e.g. by having a systematic bias. But, there ARE various ways to estimate it which do have SOME value.
Agreed.
You can then expose that judgement (about 75/100 people) to criticism and decide YES or NO about it. You may decide to (tentatively, fallibly) accept it as a fact. You could then refer to that fact in an idea about what action to take, in a criticism, etc.
Yes you could. And I would not object. But in some moment you will have to take the step. We (tentatively) know that *in the past*, out of millions of visitors, 75% of people like this were cheaters". That's maybe interesting, but the most interesting thing is if *this one in front of me* is a cheater. You cannot be absolutely sure that he is, nor absolutely sure that he isn`t. You have to make a guess based on previous knowledge. And you can be very confident in that guess or not very confident. That's the whole point. If instead of millions of previous similar visitors, you only had data about twenty, you would be less confident on your judgement.
That's all. Remember. I will not reply if you don't try to answer my questions.
Thanks.
Damián Gil
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Elliot Temple
Aug 1, 2017, 5:25:13 PM8/1/17
to BoI, FIGG, FI
On Aug 1, 2017, at 2:13 PM, Damián Gil <dami...@gmail.com> wrote:
> 2017-08-01 21:42 GMT+02:00 Elliot Temple <cu...@curi.us>:
>> What do you care about "more degree of confidence" or "the more confidence you'll have that the man is cheating and the die is not fair"? (These quotes are from the post included below.) Is it an imprecise statement about what bets you would and wouldn't take?
>
> Remember I'm not a native english speaker. I don't know if "what do you care about" is a slang phrase or something. Talking literally, what I care about is no one's business. The relevant thing is that the degree of confidence can increase or decrease, not if I care much about it or not.
The question there was what difference the "degree of confidence" makes to anything? (Why care? What does it matter?) That led into my explanation of in what ways the degree of confidence does and doesn't matter, and is vague.
> 2017-08-01 21:42 GMT+02:00 Elliot Temple <cu...@curi.us>:
>> What do you care about "more degree of confidence" or "the more confidence you'll have that the man is cheating and the die is not fair"? (These quotes are from the post included below.) Is it an imprecise statement about what bets you would and wouldn't take?
>
> Remember I'm not a native english speaker. I don't know if "what do you care about" is a slang phrase or something. Talking literally, what I care about is no one's business. The relevant thing is that the degree of confidence can increase or decrease, not if I care much about it or not.
>> You can then expose that judgement (about 75/100 people) to criticism and decide YES or NO about it. You may decide to (tentatively, fallibly) accept it as a fact. You could then refer to that fact in an idea about what action to take, in a criticism, etc.
>
> Yes you could. And I would not object. But in some moment you will have to take the step. We (tentatively) know that *in the past*, out of millions of visitors, 75% of people like this were cheaters". That's maybe interesting, but the most interesting thing is if *this one in front of me* is a cheater. You cannot be absolutely sure that he is, nor absolutely sure that he isn`t. You have to make a guess based on previous knowledge. And you can be very confident in that guess or not very confident. That's the whole point. If instead of millions of previous similar visitors, you only had data about twenty, you would be less confident on your judgement.
Justin Mallone
Aug 2, 2017, 5:46:08 PM8/2/17
to beginning-of-infinity@googlegroups.com Infinity, FIGG, Elliot Temple curi@curi.us [fallible-ideas]
On Aug 1, 2017, at 3:20 PM, Damián Gil <dami...@gmail.com> wrote:
>
> 2017-08-01 19:29 GMT+02:00 Justin Mallone <just...@gmail.com>:
>
>
>> one can have a criticism of a sample size as being too low to draw conclusions from about the effectiveness of some drug. But in that case, it's too low to draw conclusions from! So you shouldn't use it to draw conclusions...like if 100 subjects is too low to talk about drug effectiveness, it's too low. Period. In such a case, 100 subject studies might still be useful for some purposes (like maybe you want to make sure the drug doesn't kill 50% of the people you give it to before you run the 10000 subject study...) But you can't use it to talk about relative drug effectiveness.
>>
>> Also, once you hit whatever the sufficient n-size is for being able to talk about relative drug effectiveness (in light of our knowledge of statistics), that's it, you've hit it. So say the sufficient n-size for making statements was 500. So you can talk about relative drug effectiveness if the size of the study was 500, or 501, or 10000, or 10001.
>>
>> If the sufficient n-size for making such statements was higher than 100 but less than 10000 in the examples above, then the scientist should confine his evaluations to drugs C and D, since he can't make statements about A and B.
>>
>> If the sufficient n-size for making such statements was 100 or below, then, no, the scientist shouldn't talk in terms of greater confidence about his judgment regarding C and D. He can talk about A relative to B and C relative to D. But both studies are over the threshold for being able to talk about the effectiveness of the drugs....
>>
>> If the sufficient n-size for making such statements was above 10000, he can't evaluate the drug effectiveness at all...
>>
>
>
> Why do you believe that these thresholds exist? They don't. There is no magic threshold above which you can talk about the effectiveness of a drug (or any estimated difference in proportions, like in this case), and below which you can't.
Do you think scientists should make a *general judgement* about the relative effectiveness of some drug vs another based on n size = 2?
>
> 2017-08-01 19:29 GMT+02:00 Justin Mallone <just...@gmail.com>:
>
>
>> one can have a criticism of a sample size as being too low to draw conclusions from about the effectiveness of some drug. But in that case, it's too low to draw conclusions from! So you shouldn't use it to draw conclusions...like if 100 subjects is too low to talk about drug effectiveness, it's too low. Period. In such a case, 100 subject studies might still be useful for some purposes (like maybe you want to make sure the drug doesn't kill 50% of the people you give it to before you run the 10000 subject study...) But you can't use it to talk about relative drug effectiveness.
>>
>> Also, once you hit whatever the sufficient n-size is for being able to talk about relative drug effectiveness (in light of our knowledge of statistics), that's it, you've hit it. So say the sufficient n-size for making statements was 500. So you can talk about relative drug effectiveness if the size of the study was 500, or 501, or 10000, or 10001.
>>
>> If the sufficient n-size for making such statements was higher than 100 but less than 10000 in the examples above, then the scientist should confine his evaluations to drugs C and D, since he can't make statements about A and B.
>>
>> If the sufficient n-size for making such statements was 100 or below, then, no, the scientist shouldn't talk in terms of greater confidence about his judgment regarding C and D. He can talk about A relative to B and C relative to D. But both studies are over the threshold for being able to talk about the effectiveness of the drugs....
>>
>> If the sufficient n-size for making such statements was above 10000, he can't evaluate the drug effectiveness at all...
>>
>
>
> Why do you believe that these thresholds exist? They don't. There is no magic threshold above which you can talk about the effectiveness of a drug (or any estimated difference in proportions, like in this case), and below which you can't.
> Suppose you have a man that is throwing a die repeatedly in a casino. You are wondering if the dice is fair or not. In the first throw, he scores a six. You think: well, he had a 1/6 chance, let's see. In the second throw, he scores another six. You think: 1/36, maybe he just got lucky. In t