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Bayesian Argument for Religion

DisKamper
Posts: 63
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6/19/2015 1:30:51 AM
Posted: 1 year ago
Let's say that we are trying to provide explanations for a certain experimental observation. Let X and Y be competing explanations. Let R be the result of our experiment. Our goal is to find which one of P(X|R) and P(Y|R) one is higher in order to find the more likely explanation. In order to do this we can attempt to find P(X|R)/P(Y|R). According to Bayes' Theorem:

P(X|R) = P(R|X)*P(R)/P(X)
P(Y|R) = P(R|Y)*P(R)/P(Y)

Dividing:

P(X|R)/P(Y|R) = [P(R|X)*P(Y)]/[P(R|Y)*P(X)]

P(X) and P(Y) are the absolute probabilities of explanations X and Y. P(R|X) and P(R|Y) are the probabilities of the experimental result occurring given explanation X and Y respectively.

To make things concrete I will give a scientific example. Let R be an experiment showing that planets seem to backtrack from an observer on Earth. Let X be a heliocentric explanation and Y be a geocentric explanation. P(R|X) is very high. P(R|Y) on the other hand is not very high since one would think that planets would be likely to rotate in simple circular motion around Earth if a geocentric model were true. P(Y) and P(X) are equal by symmetry; rationally, there is no way to tell which explanation by itself is more likely without any evidence. P(X|R)/P(Y|R) is above 1. Thus, it is likely that the Earth revolves around the sun.

Applying this to religion, let X be an explanation for current reality without involving divine force, and Y be one that does involve divine force. P(R|X) is quite high. P(R|Y), on the other hand, is arguably lower since one might imagine world with a divine force to seem very different from the chaotic turmoil we see today. Indeed, some might imagine it to be almost magical. In any case, P(R|X) is unequivocally greater than or equal to P(R|Y). Like in the last example, the rational person would equate P(X) and P(Y) since there is no way to tell which is higher in the absence of evidence. However, a person with faith would base their decisions on other factors in the absence of evidence rather than trying to avoid the decision like the rational person. A person with faith in Y would thus set P(Y) to be much higher than P(X). Thus, to a person with faith, it is perfectly reasonable to say that a god exists.

To summarize, people can logically believe in a god because those people use faith in the absence of evidence. People who do not believe in a god can also logically do so because they prefer to use symmetry in the absence of evidence.
Nicoszon_the_Great
Posts: 167
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6/19/2015 3:35:06 AM
Posted: 1 year ago
At 6/19/2015 1:30:51 AM, DisKamper wrote:
Let's say that we are trying to provide explanations for a certain experimental observation. Let X and Y be competing explanations. Let R be the result of our experiment. Our goal is to find which one of P(X|R) and P(Y|R) one is higher in order to find the more likely explanation. In order to do this we can attempt to find P(X|R)/P(Y|R). According to Bayes' Theorem:

P(X|R) = P(R|X)*P(R)/P(X)
P(Y|R) = P(R|Y)*P(R)/P(Y)

Dividing:

P(X|R)/P(Y|R) = [P(R|X)*P(Y)]/[P(R|Y)*P(X)]

P(X) and P(Y) are the absolute probabilities of explanations X and Y. P(R|X) and P(R|Y) are the probabilities of the experimental result occurring given explanation X and Y respectively.

To make things concrete I will give a scientific example. Let R be an experiment showing that planets seem to backtrack from an observer on Earth. Let X be a heliocentric explanation and Y be a geocentric explanation. P(R|X) is very high. P(R|Y) on the other hand is not very high since one would think that planets would be likely to rotate in simple circular motion around Earth if a geocentric model were true. P(Y) and P(X) are equal by symmetry; rationally, there is no way to tell which explanation by itself is more likely without any evidence. P(X|R)/P(Y|R) is above 1. Thus, it is likely that the Earth revolves around the sun.

Applying this to religion, let X be an explanation for current reality without involving divine force, and Y be one that does involve divine force. P(R|X) is quite high. P(R|Y), on the other hand, is arguably lower since one might imagine world with a divine force to seem very different from the chaotic turmoil we see today. Indeed, some might imagine it to be almost magical. In any case, P(R|X) is unequivocally greater than or equal to P(R|Y). Like in the last example, the rational person would equate P(X) and P(Y) since there is no way to tell which is higher in the absence of evidence. However, a person with faith would base their decisions on other factors in the absence of evidence rather than trying to avoid the decision like the rational person. A person with faith in Y would thus set P(Y) to be much higher than P(X). Thus, to a person with faith, it is perfectly reasonable to say that a god exists.

To summarize, people can logically believe in a god because those people use faith in the absence of evidence. People who do not believe in a god can also logically do so because they prefer to use symmetry in the absence of evidence.

So basically we can't DISPROVE therefor unfounded assertions are also logical.
Skepticalone
Posts: 6,125
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6/19/2015 7:30:18 AM
Posted: 1 year ago
At 6/19/2015 1:30:51 AM, DisKamper wrote:
Let's say that we are trying to provide explanations for a certain experimental observation. Let X and Y be competing explanations. Let R be the result of our experiment. Our goal is to find which one of P(X|R) and P(Y|R) one is higher in order to find the more likely explanation. In order to do this we can attempt to find P(X|R)/P(Y|R). According to Bayes' Theorem:

P(X|R) = P(R|X)*P(R)/P(X)
P(Y|R) = P(R|Y)*P(R)/P(Y)

Dividing:

P(X|R)/P(Y|R) = [P(R|X)*P(Y)]/[P(R|Y)*P(X)]

P(X) and P(Y) are the absolute probabilities of explanations X and Y. P(R|X) and P(R|Y) are the probabilities of the experimental result occurring given explanation X and Y respectively.

To make things concrete I will give a scientific example. Let R be an experiment showing that planets seem to backtrack from an observer on Earth. Let X be a heliocentric explanation and Y be a geocentric explanation. P(R|X) is very high. P(R|Y) on the other hand is not very high since one would think that planets would be likely to rotate in simple circular motion around Earth if a geocentric model were true. P(Y) and P(X) are equal by symmetry; rationally, there is no way to tell which explanation by itself is more likely without any evidence. P(X|R)/P(Y|R) is above 1. Thus, it is likely that the Earth revolves around the sun.

Applying this to religion, let X be an explanation for current reality without involving divine force, and Y be one that does involve divine force. P(R|X) is quite high. P(R|Y), on the other hand, is arguably lower since one might imagine world with a divine force to seem very different from the chaotic turmoil we see today. Indeed, some might imagine it to be almost magical. In any case, P(R|X) is unequivocally greater than or equal to P(R|Y). Like in the last example, the rational person would equate P(X) and P(Y) since there is no way to tell which is higher in the absence of evidence. However, a person with faith would base their decisions on other factors in the absence of evidence rather than trying to avoid the decision like the rational person. A person with faith in Y would thus set P(Y) to be much higher than P(X). Thus, to a person with faith, it is perfectly reasonable to say that a god exists.

To summarize, people can logically believe in a god because those people use faith in the absence of evidence. People who do not believe in a god can also logically do so because they prefer to use symmetry in the absence of evidence.

Essentially, you are stating believers can rationally believe in God because they believe (have faith). FYI, that's not rational.
This thread is like eavesdropping on a conversation in a mental asylum. - Bulproof

You can call your invisible friends whatever you like. - Desmac

What the hell kind of coked up sideshow has this thread turned into. - Casten
UndeniableReality
Posts: 1,897
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6/19/2015 7:45:47 AM
Posted: 1 year ago
At 6/19/2015 1:30:51 AM, DisKamper wrote:
Let's say that we are trying to provide explanations for a certain experimental observation. Let X and Y be competing explanations. Let R be the result of our experiment. Our goal is to find which one of P(X|R) and P(Y|R) one is higher in order to find the more likely explanation. In order to do this we can attempt to find P(X|R)/P(Y|R). According to Bayes' Theorem:

P(X|R) = P(R|X)*P(R)/P(X)
P(Y|R) = P(R|Y)*P(R)/P(Y)

Dividing:

P(X|R)/P(Y|R) = [P(R|X)*P(Y)]/[P(R|Y)*P(X)]

P(X) and P(Y) are the absolute probabilities of explanations X and Y. P(R|X) and P(R|Y) are the probabilities of the experimental result occurring given explanation X and Y respectively.

To make things concrete I will give a scientific example. Let R be an experiment showing that planets seem to backtrack from an observer on Earth. Let X be a heliocentric explanation and Y be a geocentric explanation. P(R|X) is very high. P(R|Y) on the other hand is not very high since one would think that planets would be likely to rotate in simple circular motion around Earth if a geocentric model were true. P(Y) and P(X) are equal by symmetry; rationally, there is no way to tell which explanation by itself is more likely without any evidence. P(X|R)/P(Y|R) is above 1. Thus, it is likely that the Earth revolves around the sun.

Applying this to religion, let X be an explanation for current reality without involving divine force, and Y be one that does involve divine force. P(R|X) is quite high. P(R|Y), on the other hand, is arguably lower since one might imagine world with a divine force to seem very different from the chaotic turmoil we see today. Indeed, some might imagine it to be almost magical. In any case, P(R|X) is unequivocally greater than or equal to P(R|Y). Like in the last example, the rational person would equate P(X) and P(Y) since there is no way to tell which is higher in the absence of evidence. However, a person with faith would base their decisions on other factors in the absence of evidence rather than trying to avoid the decision like the rational person. A person with faith in Y would thus set P(Y) to be much higher than P(X). Thus, to a person with faith, it is perfectly reasonable to say that a god exists.

To summarize, people can logically believe in a god because those people use faith in the absence of evidence. People who do not believe in a god can also logically do so because they prefer to use symmetry in the absence of evidence.

The problem with Bayesian inference in the absence of data or evidence is that all of the priors are made up, which you just demonstrated. If you set priors such that your preferred belief comes up to be more "likely", does that make the belief rational or justified in any empirical way? It's similar to saying that a belief is rational because you can make up premises that lead to a favourable conclusion. It doesn't make the premises (or priors) valid.

I'm not a frequentist or a Bayesian, by the way. Combined approaches, such as empirical Bayes, are the way to go when there is data. WIthout data, computing "probabilities" is a meaningless exercise in different ways one can express their biases.

Bradley Efron has some good discussions on the topic. For example, this one is relevant here: http://statweb.stanford.edu...
Raisor
Posts: 4,461
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6/19/2015 9:18:02 AM
Posted: 1 year ago
Like Jmk said, the problem with this argument is you have four probabilities you have to estimate for an output. The left side of the equation is equally sensitive to each of these probabilities, getting any of them wrong can lead to the wrong conclusion. You can't just point to one variable and say it dominates the output.

Humans are notoriously bad at applying intuitions to probabilistic problems, and we have only inductive non empirical arguments to estimate these probabilities.

It also cuts both ways- one could argue the problem of evil is a strong argument for setting the input such that the output suggests no god.
DisKamper
Posts: 63
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6/19/2015 12:20:03 PM
Posted: 1 year ago
So basically we can't DISPROVE therefor unfounded assertions are also logical.

Yes. I am arguing that when there is an absence of evidence any explanation could work.
DisKamper
Posts: 63
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6/19/2015 12:23:40 PM
Posted: 1 year ago
Essentially, you are stating believers can rationally believe in God because they believe (have faith). FYI, that's not rational.

I'm arguing that people who believe in God are not people who base all their inferences on evidence. People who only use evidence would avoid assuming anything in the absence of evidence. Perhaps the people who believe in God are not rational, but I think their belief is logically consistent with the assumptions they made in the lack of evidence.
DisKamper
Posts: 63
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6/19/2015 12:40:08 PM
Posted: 1 year ago
The problem with Bayesian inference in the absence of data or evidence is that all of the priors are made up, which you just demonstrated. If you set priors such that your preferred belief comes up to be more "likely", does that make the belief rational or justified in any empirical way? It's similar to saying that a belief is rational because you can make up premises that lead to a favourable conclusion. It doesn't make the premises (or priors) valid.


It's not justified in any empirical way, I agree. Most statisticians try to use uniform priors in the absence of any evidence (i.e. P(X) = P(Y)). This is perhaps the most rational way to pick priors. Those who believe that P(X) < P(Y) are making a different assumption. Both assumptions are not based on evidence. Priors could, of course, be changed to support any explanation. For this reason, the principle of using uniform priors seems justified. However, I am arguing that those who don't believe in uniform priors simply use different principles to pick priors.

I'm not a frequentist or a Bayesian, by the way. Combined approaches, such as empirical Bayes, are the way to go when there is data. WIthout data, computing "probabilities" is a meaningless exercise in different ways one can express their biases.


I agree that beliefs in God are meaningless in the sense that they make assumptions that are not based on evidence. However, they are logically consistent given their assumptions.
DisKamper
Posts: 63
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6/19/2015 12:44:10 PM
Posted: 1 year ago
At 6/19/2015 9:18:02 AM, Raisor wrote:
Like Jmk said, the problem with this argument is you have four probabilities you have to estimate for an output. The left side of the equation is equally sensitive to each of these probabilities, getting any of them wrong can lead to the wrong conclusion. You can't just point to one variable and say it dominates the output.

Humans are notoriously bad at applying intuitions to probabilistic problems, and we have only inductive non empirical arguments to estimate these probabilities.

It also cuts both ways- one could argue the problem of evil is a strong argument for setting the input such that the output suggests no god.

Of course, anyone could shift the priors to support any explanation they want. I am simply arguing that those who believe in a god are shifting the priors in a way that counters no evidence. Personally, I think that in the absence of information, all priors should be equal, but those who believe in a god have a different belief here.
UndeniableReality
Posts: 1,897
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6/19/2015 12:48:32 PM
Posted: 1 year ago
At 6/19/2015 12:40:08 PM, DisKamper wrote:
The problem with Bayesian inference in the absence of data or evidence is that all of the priors are made up, which you just demonstrated. If you set priors such that your preferred belief comes up to be more "likely", does that make the belief rational or justified in any empirical way? It's similar to saying that a belief is rational because you can make up premises that lead to a favourable conclusion. It doesn't make the premises (or priors) valid.


It's not justified in any empirical way, I agree. Most statisticians try to use uniform priors in the absence of any evidence (i.e. P(X) = P(Y)). This is perhaps the most rational way to pick priors. Those who believe that P(X) < P(Y) are making a different assumption. Both assumptions are not based on evidence. Priors could, of course, be changed to support any explanation. For this reason, the principle of using uniform priors seems justified. However, I am arguing that those who don't believe in uniform priors simply use different principles to pick priors.

That's right. Uniform priors are usually used when we have no way of evaluating the relative probabilities of different elements in a set about which we wish to make a decision. Is there a rational justification for assuming a non-uniform probability distribution in the absence of empirical data? Is it a matter simply of "I prefer this approach to choosing priors over this other approach", or is one approach demonstrably less biased than another?

I'm not a frequentist or a Bayesian, by the way. Combined approaches, such as empirical Bayes, are the way to go when there is data. WIthout data, computing "probabilities" is a meaningless exercise in different ways one can express their biases.


I agree that beliefs in God are meaningless in the sense that they make assumptions that are not based on evidence. However, they are logically consistent given their assumptions.

Yes, It is possible to arbitrarily devise a set of premises in order to support almost any conclusion. This is why logic is insufficient for identifying correct conclusions apart from logically consistent conclusions.
Nicoszon_the_Great
Posts: 167
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6/19/2015 12:51:00 PM
Posted: 1 year ago
At 6/19/2015 12:23:40 PM, DisKamper wrote:
Essentially, you are stating believers can rationally believe in God because they believe (have faith). FYI, that's not rational.

I'm arguing that people who believe in God are not people who base all their inferences on evidence. People who only use evidence would avoid assuming anything in the absence of evidence. Perhaps the people who believe in God are not rational, but I think their belief is logically consistent with the assumptions they made in the lack of evidence.

But then you also have to consider the claims made by any particular religious group. Christians, for example, generally believe that the Earth was once flooded very rapidly up to the highest mountain peaks. Now the logistics behind the ark aside we know that there was NEVER a flood to that magnitude. We know what happens when a large body of water rapidly moves through a normally dry area, the Missoula glacial flood left very distinct land marks and traces when it flooded the pacific northwest. Those traces are not seen in places like the Himalayas, the Alps, Africa, or South America. Now that discredits the idea that there was a global flood, meaning its far more likely that a smaller event occurred and was greatly exaggerated. So this means that we cannot necessarily trust the writers of these books to be factual or objective if they're willing to stretch the truth to make it more interesting. Did Moses actually part the Red(Reed) sea? Did Jesus actually raise Lazarus from the dead? Was there actually a resurrection? The entirety of the book comes into question unless they can provide some evidence, yet since that seems scarce its reasonable to take the stance, for the moment, that Yaweh does not exist as the only real text referencing him is questionable. Now that's not to say that NO god exists AT ALL. There's a very good chance their's a deistic god, a different religion's interpretation is right, or that there's a god out there who's yet to reveal himself. But until the moment that we can say 'yes' with certainty we should not found these groups, we should not cater law to them, and we should not allow them to enforce upon us.
Nicoszon_the_Great
Posts: 167
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6/19/2015 12:53:14 PM
Posted: 1 year ago
At 6/19/2015 12:51:00 PM, Nicoszon_the_Great wrote:
At 6/19/2015 12:23:40 PM, DisKamper wrote:
Essentially, you are stating believers can rationally believe in God because they believe (have faith). FYI, that's not rational.

I'm arguing that people who believe in God are not people who base all their inferences on evidence. People who only use evidence would avoid assuming anything in the absence of evidence. Perhaps the people who believe in God are not rational, but I think their belief is logically consistent with the assumptions they made in the lack of evidence.

But then you also have to consider the claims made by any particular religious group. Christians, for example, generally believe that the Earth was once flooded very rapidly up to the highest mountain peaks. Now the logistics behind the ark aside we know that there was NEVER a flood to that magnitude. We know what happens when a large body of water rapidly moves through a normally dry area, the Missoula glacial flood left very distinct land marks and traces when it flooded the pacific northwest. Those traces are not seen in places like the Himalayas, the Alps, Africa, or South America. Now that discredits the idea that there was a global flood, meaning its far more likely that a smaller event occurred and was greatly exaggerated. So this means that we cannot necessarily trust the writers of these books to be factual or objective if they're willing to stretch the truth to make it more interesting. Did Moses actually part the Red(Reed) sea? Did Jesus actually raise Lazarus from the dead? Was there actually a resurrection? The entirety of the book comes into question unless they can provide some evidence, yet since that seems scarce its reasonable to take the stance, for the moment, that Yaweh does not exist as the only real text referencing him is questionable. Now that's not to say that NO god exists AT ALL. There's a very good chance their's a deistic god, a different religion's interpretation is right, or that there's a god out there who's yet to reveal himself. But until the moment that we can say 'yes' with certainty we should not found these groups, we should not cater law to them, and we should not allow them to enforce upon us.

This is also disregarding the fact that the entire Noah story was borrowed from the epic of Gilgamesh.
Skepticalone
Posts: 6,125
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6/19/2015 1:53:30 PM
Posted: 1 year ago
At 6/19/2015 12:23:40 PM, DisKamper wrote:
Essentially, you are stating believers can rationally believe in God because they believe (have faith). FYI, that's not rational.

I'm arguing that people who believe in God are not people who base all their inferences on evidence. People who only use evidence would avoid assuming anything in the absence of evidence. Perhaps the people who believe in God are not rational, but I think their belief is logically consistent with the assumptions they made in the lack of evidence.

Absense of evidence is evidence when there is a reasonable expectation for it. There is a reasonable expectation for evidence for many stories in the Bible (in which God is said to have participated), yet there is none. Believing something for which there is no evidence, but for which we have good reason to expect, is not rational.
This thread is like eavesdropping on a conversation in a mental asylum. - Bulproof

You can call your invisible friends whatever you like. - Desmac

What the hell kind of coked up sideshow has this thread turned into. - Casten