Without further ado:
Suppose that a priori X has probability a of being true. We now look for evidence for X of a certain type. Suppose that there is a probablity b that we find this evidence if X is true and probability b' that we find this evidence if X is false. We will assume a<1 (otherwise we wouldn't bother looking for evidence) and that b>b' (otherwise it couldn't be said that the evidence we're looking for is evidence for X).
So we have four possibilities:
1. X is true and we find evidence for X: probability ab
2. X is true and we don't find evidence for X: probability a(1-b)
3. X is false and we find evidence for X: probability (1-a)b'
4. X is false and we don't find evidence for X: probability (1-a)(1-b')
Theorem:
Under the hypotheses above, the conditional probability that X is true given that we failed to find the evidence is a(1-b)/(a(b'-b)+1-a').
Proof:
Use Bayes' Theorem.
Some basic rearrangement shows this is always less than a given the above hypotheses. It doesn't matter if we are unable to assign an a priori probability, this holds whatever value a has as long as it's less than 1. And if we don't know that b>b' then we shouldn't be in the business of looking for evidence. If the experiment we're doing is any good then b'=0 but as has been shown, the result holds even if we relax this condition.
So clearly failing to find evidence for X should lower our estimate of the probability that X is true. The theorem shows that under the original hypotheses the conditional probability is never 1, and so while we have evidence of absence, we don't have a proof. But if we can look for enough independent types of evidence it's quite possible for the conditional probability to get close to 1.
DUSCUISS!
Thr resot ios prtetty straighjt-forwafrd, I'm sure.
Transltration can ber exprected tomortpow.
Really, it depends on how thouroughly you look for said evidence and how it's interpreted.
If I look in my basement and say the absence of dinosaur bones there is evidence of absence of the existence of dinosaurs; then I'm an idiot. And so is anyone who would agree with me based on that lack of evidence.
If I find chicken bones in my trash and conclude they are dinosaur bones, I am also an idiot.
It comes down to thoroughness of the search for evidence, and the interpretation of said evidence.
Absence of evidence can be (but is not necessarily) evidence of absence.
Really, it depends on how thouroughly you look for said evidence and how it's interpreted.
If I look in my basement and say the absence of dinosaur bones there is evidence of absence of the existence of dinosaurs; then I'm an idiot. And so is anyone who would agree with me based on that lack of evidence.
If I find chicken bones in my trash and conclude they are dinosaur bones, I am also an idiot.
It comes down to thoroughness of the search for evidence, and the interpretation of said evidence.
=> The conælciusoonsion of my argumernt.
The titelse is worded to get atttynyteiont because I alweays get ignmored when I sayu somethjging smart.
<(QoQ<) You make Pig-moticon cry.
Awesome Dude... you do know that its now forbidden to bring up religion, right? Your also too drunk to type properly. You might want to delete this thread and sleep it off man.
When did religion come up. I thought this was about probabilities.
There exist people who like to "quote" Carl Sagan, saying that "absence of evidence is not evidence of absence." Carl Sagan did not say that. He said the opposite and used the statement as an example of extremely poor logic used by the religious.I believe this is the part where religion came up.
I'm not well versed on what it refers to; but if I am interpreting it correctly, it refers to a lack of evidence of the existance of the divine.
But, whatever. No one wins when you debate theology. So I'll just stay out of that one.
There exist people who like to "quote" Carl Sagan, saying that "absence of evidence is not evidence of absence." Carl Sagan did not say that. He said the opposite and used the statement as an example of extremely poor logic used by the religious.I believe this is the part where religion came up.
I'm not well versed on what it refers to; but if I am interpreting it correctly, it refers to a lack of evidence of the existance of the divine.
But, whatever. No one wins when you debate theology. So I'll just stay out of that one.
I agree. Keep religion out. I have my beliefs and you have yours. lets keep it that way.
Your posts are difficult to read tonight.
We have seen this before.
What are you drinking?
i'm currently playing chrono cross. i've got an undead clown and a pink... dog... who talksh with a lishp fighting wraiths alongside my silent progaonist with oversized weaponry. i think a nice shot or seven of what he's having would my my night that much more awesome.
You should try to avoid posting logical expressions when drinking... well, I used to do something similar, heh.
I believe this is the part where religion came up.
I'm not well versed on what it refers to; but if I am interpreting it correctly, it refers to a lack of evidence of the existance of the divine.
But, whatever. No one wins when you debate theology. So I'll just stay out of that one.
That's just the context in which Sagan said it and has nothing to do with my views; it's just relevant and I felt a need to explain why he said it. He also used it in the context of stories of alien abductions, among many, many others. I simply exposed a fallacy (I'm not the first; this is a very popular piece of proof among skeptics).
But, whatever. No one wins when you debate theology. So I'll just stay out of that one.
Well, according to Pascal, we either all win or we all lose...
Well, according to Pascal, we either all win or we all lose...
I'm always amazed that a mathematician as renowned as he was could fail to grasp such a simple error in basic statistics.
I'm always amazed that a mathematician as renowned as he was could fail to grasp such a simple error in basic statistics.
Care to elaborate?
Oh, Awesome, you so wasted.
He always is.
Care to elaborate?
Pascal's Wager is flawed because it only takes into account two faiths and assumes that you should default to his faith. What if the premises included all faiths? Would you then be better of with his faith or with no faith?
I don't want to turn this into a religious discussion. If you want to discuss this further we should probably do it with PMs or on another site. I am open to continuing the discussion.
What if the premises included all faiths? Would you then be better of with his faith or with no faith?
But that doesn't matter, does it? I thought the wager was about god(s) in general, not a specific one. After all, a god - any god - gives your life some amount of sense, as opposed to atheism (in his view). At least, that's how I always understood the story.
But that doesn't matter, does it? I thought the wager was about god(s) in general, not a specific one. After all, a god - any god - gives your life some amount of sense, as opposed to atheism (in his view). At least, that's how I always understood the story.
His wager is about a specific god. If it is about gods in general, then you would be better off as a non-believer.
Which, as the primary fuel of classical philosophers, is probably okay.
His wager is about a specific god. If it is about gods in general, then you would be better off as a non-believer.
Not really. The reward for being right as a non-believer is nothing really. Just being able to do what you want in life. The reward for being right as a believer in the correct religion (if there is one) is a pleasant afterlife. The punishment for being wrong as an unbeliever is one of the many hells, lower rebirths, etc (depending on what faith is correct). The punishment for being a believer in the wrong religion is the same as for the unbeliever. The original premise is still sound, you just need to put about as much effort into choosing a religion as he did on the wager itself. You still stand to gain nothing and risk everything as an unbeliever. You stand to gain everything and risk everything as a believer.
What you've presented is merely a simplification of the four errors fundamental to statistical theory and sampling problems.
Thus, your "1,2,3,and 4" descriptors are really better and more simply presented as alpha, beta, gamma, and delta errors as in used in statistics and study design.
In any event, failing to find evidence is not acceptable practice for true scientific endeavor. In order to present a theory that something is false, it's more acceptable to postulate that it is true and then proceed to test out that theory in exacting manner - known as the "null hypothsesis."
This is not merely a passive failing to find evidence, but an exacting and purposeful search for the reality of the situation and a treatment of findings according to sophisticated tools.
The probability that a fact is true even when all evidence we have gathered shows it to be false is called a beta error or a "false negative." With a strong enough sampling of the whole population or reality, you can increase the estimated power of the study until it approaches one, but unless you know the extent of the whole and the fraction of that which you're sampling, it's impossible to determine the power of your study unless you predefine a specific subset and hold your statement to be true only for that subset.
Not really. The reward for being right as a non-believer is nothing really. Just being able to do what you want in life. The reward for being right as a believer in the correct religion (if there is one) is a pleasant afterlife. The punishment for being wrong as an unbeliever is one of the many hells, lower rebirths, etc (depending on what faith is correct). The punishment for being a believer in the wrong religion is the same as for the unbeliever. The original premise is still sound, you just need to put about as much effort into choosing a religion as he did on the wager itself. You still stand to gain nothing and risk everything as an unbeliever. You stand to gain everything and risk everything as a believer.
But I don't think that was Pascal's point. I always understood him to say, "Look, it doesn't even matter what religion you believe in, or even none at all... the existence of a metaphysical presence at all is what makes your life meaningful.", or something along those lines. Because note how he doesn't say you win if you believe... you win if god(s) exist, whether you believe in them, in anything else, or in nothing at all. Because a metaphysical existence validates our own as fitting into some larger scheme, as opposed to being some random and meaningless spawn of chaos.
But I don't think that was Pascal's point. I always understood him to say, "Look, it doesn't even matter what religion you believe in, or even none at all... the existence of a metaphysical presence at all is what makes your life meaningful.", or something along those lines. Because note how he doesn't say you win if you believe... you win if god(s) exist, whether you believe in them, in anything else, or in nothing at all. Because a metaphysical existence validates our own as fitting into some larger scheme, as opposed to being some random and meaningless spawn of chaos.
I think you are confusing the initial argument he uses regarding faith v. reason. That isn't the wager, that is the foundation of the wager.
It has been a while since I read Pascal, but I remember winning being defined as believing and god existing. You don't win if you believe but god doesn't exist. And I also remember bigger point, winning is achieving salvation and losing is being denied salvation. He was speaking specifically from a judeo-christian point of view, and used a coin toss as the metaphor (God Exists or he doesn't). But from a modern point of view, its more like a d20 roll (or d100 if you want to be **** about sects and minor faiths).