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 Post subject: Using Bayes Theorem to Support Theism?
PostPosted: Mon Jan 08, 2018 5:47 pm 
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On another thread our beloved Dr.W said
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Just to put your mind at ease; unless they have read my post above, most folks would not even realize that the new posts have anything to do with DCP. These posts will be topical and not personal.

The first will be one that I hope you will tune in for. DCP did a 'link and leave' drive-by regarding Bayes' theorem on his blog that ostensibly defends Mormonism and its faithful. I'm gobsmacked that he would be so careless when attending to his faithful flock.

No doubt due to his lack of reading in the sciences, he apparently doesn't realize that many of the most powerful arguments against theism emerge from the application of Bayesian analysis.

In my opinion, and that of many others including the recently discussed Sean Carroll, there is no better tool than that provided by the good Reverend Bayes for knocking down pretty much every argument for theism there is, especially those supposedly based on science (or better said pseudo-science, e.g. cosmological fine tuning, etc.) or on objective reality in general.


Oh man I have just GOT to read this one!!! Come on Dr.W, this is right up your alley! And it's of high interest to me as well. Michael Martin also has shown Bayes Theorem and how it comports to being used to show the resurrection of Jesus is fundamentally improbable in the extreme. I shall put that out here also.

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Last edited by Philo Sofee on Sat Jan 13, 2018 4:58 pm, edited 2 times in total.

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 Post subject: Re: Daniel Peterson Using Bayes Theorem to Support Theism?!?
PostPosted: Mon Jan 08, 2018 6:49 pm 
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Philo, are you an atheist now?

I'm asking because it's really hard to tell by your posts. :lol:

(Just playing around with you)

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 Post subject: Re: Daniel Peterson Using Bayes Theorem to Support Theism?!?
PostPosted: Mon Jan 08, 2018 8:38 pm 
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I'm an atheist on Mondays, Thursdays, and Saturdays (the original sabbath). On all other days I am an unknowing agnostic wannabe believer, but have nothing to hang my hat onto.

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 Post subject: Re: Daniel Peterson Using Bayes Theorem to Support Theism?!?
PostPosted: Mon Jan 08, 2018 8:41 pm 
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Philo Sofee wrote:
Oh man I have just GOT to read this one!!! Come on Dr.W, this is right up your alley! And it's of high interest to me as well. Michael Martin also has shown Bayes Theorem and how it comports to being used to show the resurrection of Jesus is fundamentally improbable in the extreme. I shall put that out here also.

My intention was to wait until Lemmie's plagiarism threads received the attention and research support they needed to be effective before deflecting attention to DCP's other work product deficiencies.

Not to worry though. Review of DCP's 2017 blog posts alone yielded several pages of notes regarding his science related misunderstandings, misattributions and overall apologetic nonsense - all of which will eventually be addressed. l am on the road this week and do not plan to post the first of these until I return.

Since you have already started this thread on Bayesian analysis related to theism, I will post my comments on the subject here when I return.

Once again, my intent for these posts, once they are started, is that they be topical, objective and dispassionate - not personal.

That said, I have a small favor to ask of you. Would you mind editing your OP title to remove DCP's name?

"Using Bayes Theorem to Support Theism?" would be a perfectly reasonable thread title, and one under which I think folks would be more comfortable posting - myself included.

Thank you.

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 Post subject: Re: Daniel Peterson Using Bayes Theorem to Support Theism?!?
PostPosted: Mon Jan 08, 2018 9:57 pm 
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Philo Sofee wrote:
I'm an atheist on Mondays, Thursdays, and Saturdays (the original sabbath). On all other days I am an unknowing agnostic wannabe believer, but have nothing to hang my hat onto.


Great - Then on Tuesdays, Wednesdays, Fridays and Sundays you should consider just leaving your hat on. . . and resting.

Belief can be -and often is - many things to many people. Clearly it can be (and has been) very harmful, destructive and dangerous to humanity. It has also brought forth tremendous good, hope, adhesiveness and decency to countless cultures and generations.

So, I don't know what this belief is that you "wannabe", but among the many choices that are available for your consideration/evaluation, a personal belief that removes our bondage and provides rest is, in my view, on the table.

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 Post subject: Re: Daniel Peterson Using Bayes Theorem to Support Theism?!?
PostPosted: Wed Jan 10, 2018 6:30 am 
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Dr.W wrote:
Would you mind editing your OP title to remove DCP's name?

I honestly did not know this is possible. How do I edit the title?

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 Post subject: Re: Daniel Peterson Using Bayes Theorem to Support Theism?!?
PostPosted: Wed Jan 10, 2018 7:20 am 
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Philo Sofee wrote:
Dr.W wrote:
Would you mind editing your OP title to remove DCP's name?

I honestly did not know this is possible. How do I edit the title?

Edit your opening post and it lets you edit the title as well.

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 Post subject: Re: Using Bayes Theorem to Support Theism?!?
PostPosted: Wed Jan 10, 2018 7:35 pm 
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THANK YOU! I honestly did not know that.

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 Post subject: Re: Using Bayes Theorem to Support Theism?!?
PostPosted: Fri Jan 12, 2018 6:35 am 
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You could use Bayes's Theorem to support just about anything, if you included the right assumptions. For instance:

Quote:
Hypothesis: The Moon is made of cheese.
Data: The Moon looks yellow.

1) It's obviously fairly plausible a priori that the Moon is made of cheese, so let's set the prior probability P(H) of the hypothesis at 50%.

2) If the Moon were made of cheese, it would definitely look yellow, because all true cheese is yellow. So the probability P(D|H) of the data, given the hypothesis, is a flat 100%.

3) If the Moon were not made of cheese, then the only other possibility is for it to be made of plasticene, which comes in ten colors, all of which are a priori equally likely, and only one of which is yellow. So out of all the possibilities a priori, 50% are cheese (and therefore yellow), and 5% are yellow plasticene, making a prior probability P(D) for the Moon to look yellow of 55%.

4) Bayes's Theorem is P(H|D) = P(D|H) x P(H) / P(D). In our case this gives the Bayesian probability that Moon is made of cheese, given that it looks yellow, as 1 x 0.5 / 0.55 = 91% (to two figures).

So we can really be quite confident that the Moon is made of cheese.


The assumptions about lunar composition in the above argument are, of course, ridiculous. The Bayesian part, however, is perfectly valid.

Garbage in, garbage out.


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 Post subject: Re: Using Bayes Theorem to Support Theism?!?
PostPosted: Fri Jan 12, 2018 8:22 am 
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Physics Guy wrote:
You could use Bayes's Theorem to support just about anything, if you included the right assumptions. For instance:

Quote:
Hypothesis: The Moon is made of cheese.
Data: The Moon looks yellow.

1) It's obviously fairly plausible a priori that the Moon is made of cheese, so let's set the prior probability P(H) of the hypothesis at 50%.

2) If the Moon were made of cheese, it would definitely look yellow, because all true cheese is yellow. So the probability P(D|H) of the data, given the hypothesis, is a flat 100%.

3) If the Moon were not made of cheese, then the only other possibility is for it to be made of plasticene, which comes in ten colors, all of which are a priori equally likely, and only one of which is yellow. So out of all the possibilities a priori, 50% are cheese (and therefore yellow), and 5% are yellow plasticene, making a prior probability P(D) for the Moon to look yellow of 55%.

4) Bayes's Theorem is P(H|D) = P(D|H) x P(H) / P(D). In our case this gives the Bayesian probability that Moon is made of cheese, given that it looks yellow, as 1 x 0.5 / 0.55 = 91% (to two figures).

So we can really be quite confident that the Moon is made of cheese.

The assumptions about lunar composition in the above argument are, of course, ridiculous. The Bayesian part, however, is perfectly valid.

Garbage in, garbage out.

When Bayes gets abused in my experience, it's like this, but more subtle. The problem is people have terrible quantitative intuitions for low probability estimation. We really can't pick apart a .01% plausibility and a .00001% plausibility, but this can matter a lot in Bayesian analysis. Bayes works best on subjects where the numbers are known, not where they have to be intuited. The more subjective judgment that goes into priors the more "ehhh" we should be feeling.


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 Post subject: Re: Using Bayes Theorem to Support Theism?!?
PostPosted: Sat Jan 13, 2018 9:58 am 
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Yes, and that's a really important point.

Sometimes Bayes's Theorem can really give rigorous results. I've used it to compute the inherent uncertainty in defining the position of a dark soliton—a sort of bubble of low gas density—in a Bose-condensed gas, due to the fact that there are only a finite number of atoms in the gas. If you could observe the gas with infinite resolution, you'd see an atom here and an atom there, with nothing in between ... so what exactly does it even mean to have a void somewhere? Bayes's Theorem can let you define that, and it tells you that the bubble location is inherently somewhat fuzzy—and just how fuzzy.

In less cut-and-dried contexts, though, nobody should be bamboozled by the apparent rigor of Bayes's Theorem into swallowing arguments that should really be greeted, as you say, with, "ehh." That's why I still like my deliberately ridiculous example: bad Bayesian arguments may not all be as easy to recognize as mine, but they are all just as bad, and Bayes's Theorem doesn't help them a bit. Garbage is still garbage even when the bag is tied with a Bayesian bow.


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 Post subject: Re: Using Bayes Theorem to Support Theism?
PostPosted: Sun Jan 14, 2018 10:02 am 
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As Philo indicated in the OP, I suggested on another thread that the mention of Bayesian analysis on a supposedly faith promoting blog was a mistake. Proper application of Bayesian analysis as a decision making tool regarding the foundational truth claims and unique teachings of Mormonism can never end well for the testimonies of the faithful.

Anyone who does even a minimal amount of reading on the subject of Bayesian inference and religion soon realizes (or should soon realize) that religion in general, and Mormonism in particular, do not fare well. Bloggers focused on the faith promoting content need read no further than the pages of MormonDiscussions.com to recognize the power of Bayesian analysis as a destroyer of unfounded belief.

On this board a great example of the utility of Reverend Bayes' theorem was its application to the oft heard apologetic claim that 'absence of evidence is not evidence of absence' when it comes to the abject lack physical evidence for the Book of Mormon. The OP for this thread was based on the formal analysis of the claim as shown in http://oyhus.no/AbsenceOfEvidence.html. There are other variations on this basic proof, one of the best illustrated being from RationalWiki https://rationalwiki.org/wiki/Absence_of_evidence.

Dean Robber's thread entitled Moroni Challenge Mathematically Incoherent - Bayes (in which Lemmie provides another of her now famous math tutorials), and Analytics' Bayesian Moroni Calculator at http://www.lds4u.com/lesson1/bayesian.htm are two more examples from MormonDiscussions.com authors of how toxic Bayesian inference can be to Mormonism.

One feature of Bayesian analysis that I find to be of great value is that it favors simple (and therefore more elegant) models. In this respect, it can be thought of as incorporating an 'Occam's razor' module.

It is a given, for example, that the simpler the model, the more precise its predictions. The corollary here is that the more complex the model (or the more claims it makes) the less utility it has, and the less likely its predictions are to be valid in general. In probability speak, more complex models, or hypotheses if you will, must spread their allotted probability (=1) over more data space, and thus lend less credence to each possible prediction or outcome.

Here is an example: Gordon B. Hinckley made the following statement about the truthfulness of Mormonsim's foundational claims in an interview conducted for FRONTLINE in January of 2007.
Gorden B. Hinkley on PBS FRONTLINE wrote:
Well, it's either true or false. If it's false, we're engaged in a great fraud. If it's true, it's the most important thing in the world. Now, that's the whole picture. It is either right or wrong, true or false, fraudulent or true. And that's exactly where we stand, with a conviction in our hearts that it is true --.
There was also this:
Gordon B. Hinckley also wrote:
Each of us has to face the matter — either the Church is true, or it is a fraud. There is no middle ground. It is the church and kingdom of God, or it is nothing. (Bolding mine.)

In an application of a Bayesian like approach to evaluating whether Mormonism is true or a fraud, as Hinkley indicates, one can simply start with a unbiased prior (say 50%) and then adjust the posterior probability in an iterative manner as they run through the truth claims of the Church. Here are a few truth claims to run through the process. If the LDS Church is as Hinkley states, then the following (and many more) must all be true.

(1) The LDS Church must be the restoration, by divine revelation, of the church that Jesus Christ established upon the Earth during his ministry.

(2) The Book of Mormon, which must contains the fullness of the gospel of Jesus Christ, must also be a record of several small groups of Semites who traveled to the New World starting around 2,500 BCE.

(3) The Book of Abraham must be a true translation of extant Egyptian papyri as claimed by Joseph Smith.

You get the point.

The main point I wish to make, however, is the utility and value of a Bayesian approach (or at least Bayesian-like approach) to building one's worldview. The continual process of validating new information and then reasonably and logically determining the consequences of this information, if any, on ones belief system is fundamental to building a life based on objective truth and reality rather than on falsehoods and fantasy.

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 Post subject: Re: Using Bayes Theorem to Support Theism?
PostPosted: Sun Jan 14, 2018 2:40 pm 
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Why use "Bayesian" as a label for "the continual process of validating new information and then ... determining [its] consequences"?

That's kind of like using "Haagen-Dazs" as a label for the entire beef and dairy industry. I mean, you seem to be practically using "Bayes" as a synonym for "reason". That's confusing. I'd rather use Bayes's name only to refer to his actual theorem, which is just one little tool in the box.

A more technical point in Bayesian model selection: simple models don't usually make more precise predictions than complex ones. The whole reason for developing complex models, after all, is usually to increase precision. The more complex model usually fits the data more closely, just because it has more parameters to tune, and hence is usually preferred by Bayesian criteria.

The question is whether the more complex model's extra parameters are providing enough increase in precision to be worthwhile. People comparing simple and complex models typically give the simpler models a chance by penalizing the number of parameters, but there's no really well-defined way to do this. "Worthwhile" is not a concept in logic.

So I don't understand your apparent view that Bayesian analysis automatically incorporates Ockham's Razor. On the contrary, Bayes's Theorem and Ockham's Razor seem to me to be mainly opposed, with Bayes preferring accuracy regardless of complexity cost, and the Razor having to be added by hand, as a kludge.


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 Post subject: Re: Using Bayes Theorem to Support Theism?
PostPosted: Sun Jan 14, 2018 3:20 pm 
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Physics Guy wrote:
Why use "Bayesian" as a label for "the continual process of validating new information and then ... determining [its] consequences"?

That's kind of like using "Haagen-Dazs" as a label for the entire beef and dairy industry. I mean, you seem to be practically using "Bayes" as a synonym for "reason". That's confusing. I'd rather use Bayes's name only to refer to his actual theorem, which is just one little tool in the box.

A more technical point in Bayesian model selection: simple models don't usually make more precise predictions than complex ones. The whole reason for developing complex models, after all, is usually to increase precision. The more complex model usually fits the data more closely, just because it has more parameters to tune, and hence is usually preferred by Bayesian criteria.

The question is whether the more complex model's extra parameters are providing enough increase in precision to be worthwhile. People comparing simple and complex models typically give the simpler models a chance by penalizing the number of parameters, but there's no really well-defined way to do this. "Worthwhile" is not a concept in logic.

So I don't understand your apparent view that Bayesian analysis automatically incorporates Ockham's Razor. On the contrary, Bayes's Theorem and Ockham's Razor seem to me to be mainly opposed, with Bayes preferring accuracy regardless of complexity cost, and the Razor having to be added by hand, as a kludge.

Please note that I used the term 'Bayesian-like' for a couple of the examples. In any case, there are literature references for both of the assertions with which you seem uncomfortable. Since you apparently have not come across them, when I have some time I will provide them for you as I did with the graphic from Rovelli's book on a previous thread.

In the meantime, perhaps you might wish to consider Lemmie's suggestion and read a bit more in the relevant subject matter area before you go on the attack. This kind of intolerant 'my way or the highway' behavior seems to be a pattern with you. It becomes a bit annoying after a while.

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 Post subject: Re: Using Bayes Theorem to Support Theism?
PostPosted: Sun Jan 14, 2018 7:03 pm 
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If Philo (or anyone else) has a link to a summary by Sean Carroll I'd be interested in a summary of his Bayes argument for naturalism. So far in what I've seen from Carroll, I like his arguments better than other atheists who go on the debate circuit with Christian opponents.

Mormonism to me seems to be a totally different animal than belief in God generally -- well, maybe not really in everyday practice, but in the advertised belief commitments about what Mormons are doing as Mormons, it's very different in that they perceive themselves as "testing the word in a lab" to discover truth. It's entirely empirical. The way they set the stage themselves begs for a Bayesian analysis. They start by encountering the word and "not casting it out"; seeming to say giving it a fair 50-50 chance (as a "prior", and then "test" it through prayer (Moroni's promise). IIRC, I found this funny in a Bayes context because an answer in the affirmative allegedly imbues certainty for Mormons, which is not congruent with Bayes. But this doesn't extend to other Christians.

Christianity in general either seems to just assume the Bible is true by its own authority or by inner light they've been given to recognize the Bible is already true, or there are a priori theology arguments, but none of this really has any relevance to Bayesian analysis. So where would it come in? I'm thinking once you get to Christian apologists who invoke the design arguments and so on, then perhaps that's where a guy like Carroll steps in to weigh the evidence for or against God using Bayes. But most Christians aren't going to just put it all on the line and say that if Bayes doesn't validate rising from the tomb and the earth's distance from the sun then they'll concede to atheism.


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 Post subject: Re: Using Bayes Theorem to Support Theism?
PostPosted: Sun Jan 14, 2018 9:51 pm 
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Gadianton wrote:
If Philo (or anyone else) has a link to a summary by Sean Carroll I'd be interested in a summary of his Bayes argument for naturalism. So far in what I've seen from Carroll, I like his arguments better than other atheists who go on the debate circuit with Christian opponents.

Dean Robbers,

Sean Carroll has indeed written clearly and convincingly regarding what he terms a Bayesian argument for his poetic naturalism.

In his book entitled, "The Big Picture", he contrasts inductive reasoning with deductive reasoning and then describes the technique of abductive reasoning, which he recommends when confronted with questions about belief. He contrasts abductive reasoning with deductive and inductive reasoning as follows.
Sean Carroll wrote:
With abduction, by contrast, we take all of our background knowledge about how the world works, and perhaps some preference for simple explanations over complex ones (Occams Razor) and decide what possible explanation provides the best account of all the facts we have.

He terms this approach "inference to the best explanation". He describes the various probabilities involved in terms of "credences" and shows how these credences can be increased or decreased in value by proper evaluation and analysis of available factual information. He terms this approach, in general, to be Bayesian reasoning, and provides a simple equation for making such determinations based on Bayes' theorem.

He goes on to describe a 'good Bayesian' approach to considering issues of science vs. religion and woo woo, and provides examples. This theme is introduced in Chapters 9 and 10 of the book and revisited often thereafter. Not sure where it might be available in summary form other than in his book, which is definitely worth reading.

I happen to agree that Carroll's approach to debate with theologians is more effective than that of Richard Dawkins, for example. Arguments born of physics just seem more fundamental and clear cut than those arising from evolution and biology in general, and Carroll does physics a lot better than, say, Larry Krauss.

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 Post subject: Re: Using Bayes Theorem to Support Theism?
PostPosted: Mon Jan 15, 2018 6:50 am 
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Physics Guy,

In further response to Gadianton's question upthread regarding a 'Bayesian approach' to decisions regarding belief, the graphic mentioned below provides a good overview. The references mentioned, or referred to, below also address both of the assertions with which you were uncomfortable in my earlier post.

The 'good Bayesian' approach that Carroll describes in "The Big Picture" is well illustrated by the graphic on page 356 in Chapter 28 of a Cambridge University text book (McKay, 2003).

A PDF of Chapter 28 (titled,Model Comparison and Occam’s Razor) is available here: http://www.inference.org.uk/mackay/itprnn/ps/343.355.pdf . This reference has been cited before on MormonDiscussions.com when discussing Bayesian inference.

Carroll's book, as described upthread, and "Model Comparisons and Occam's Razor"are two references among several I have come across that deal with Bayesian inference in combination with Occam's razor as a decision making tool. Here is a passage from McKay's text.

Quote:
How does this relate to Occam's razor, when H1 is a simpler model than H2? The first ratio [(P(H1)=P (H2)) term] gives us the opportunity, if we wish, to insert a prior bias in favour of H1 on aesthetic grounds, or on the basis of experience. This would correspond to the aesthetic and empirical motivations for Occam's razor mentioned earlier.

But such a prior bias is not necessary: the second ratio, the data-dependent factor, embodies Occam's razor automatically.

For at least half a dozen more credible references on the subject, all one need do is type in < Bayesian inference and Occam's razor > as a Google search string.

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 Post subject: Re: Using Bayes Theorem to Support Theism?
PostPosted: Mon Jan 15, 2018 12:24 pm 
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I agree with Physics's Guy here. I don't see what about Bayesian analysis is uniquely so difficult for the reasonableness of Mormonism. The answers so far just seem to reduce into "Reasoning with observational evidence is not kind to Mormonism." Well, of course. Also, one can expect and LDS apologist not to agree with that. But this is true regardless of what tools we use to measure how confident we should be in accepting or rejecting propositions given what is known. It doesn't matter if we translate those judgments into Bayesian analysis or not. What does Bayes do on top of this?

Sure, Analytics' Bayesian formulation might help someone think about Moroni's Promise in a way they haven't before, but it doesn't change the evidence. And while Bayes may be illuminating for people there, Swinburne's use of Bayes for the proposition God exists might just as easily confuse. The underlying mathematical reasoning isn't adding anything to the mix, as best I can tell.


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 Post subject: Re: Using Bayes Theorem to Support Theism?
PostPosted: Mon Jan 15, 2018 12:47 pm 
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EAllusion wrote:
I agree with Physics's Guy here. I don't see what about Bayesian analysis is uniquely so difficult for the reasonableness of Mormonism. The answers so far just seem to reduce into "Reasoning with observational evidence is not kind to Mormonism." Well, of course. Also, one can expect and LDS apologist not to agree with that. But this is true regardless of what tools we use to measure how confident we should be in accepting or rejecting propositions given what is known. It doesn't matter if we translate those judgments into Bayesian analysis or not. What does Bayes do on top of this?
I'm not seeing in this thread the argument with which you and PG are ostensibly disagreeing.

The argument so far has not been unique to Mormonism, but rather holds for religion in general. Additionally, the focus on Bayes was a result of its recent use by an apologist, not because Bayesian analysis necessarily brings about a different or qualitatively superior result than other reasonable evaluation methods. As DrW noted:
DrW wrote:
As Philo indicated in the OP, I suggested on another thread that the mention of Bayesian analysis on a supposedly faith promoting blog was a mistake. Proper application of Bayesian analysis as a decision making tool regarding the foundational truth claims and unique teachings of Mormonism can never end well for the testimonies of the faithful.

Anyone who does even a minimal amount of reading on the subject of Bayesian inference and religion soon realizes (or should soon realize) that religion in general, and Mormonism in particular, do not fare well. Bloggers focused on the faith promoting content need read no further than the pages of MormonDiscussions.com to recognize the power of Bayesian analysis as a destroyer of unfounded belief.
[bolding added]


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 Post subject: Re: Using Bayes Theorem to Support Theism?
PostPosted: Mon Jan 15, 2018 1:03 pm 
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The way I would phrase it is that Bayes, as opposed to other probabilistic frameworks like the frequentist, is uniquely unkind to Mormonism because it is the only logically consistent way to approach incomplete information problems. And Mormonism is an incomplete information problem.


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 Post subject: Re: Using Bayes Theorem to Support Theism?
PostPosted: Mon Jan 15, 2018 1:32 pm 
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Lemmie -

What I'm having a hard time with here is understanding why Bayesian analysis is especially bad for Mormonism. So a blogger brings up Bayes in the context of supporting Mormonism. DrW takes great exception because Bayes is actually bad for Mormonism. Why is this any different than a Mormon apologist asserting any approach to evidence is good for Mormons and DrW saying, "Omg. No it isn't." ? What specifically about Bayes is so egregious that this just doesn't reduce into a proxy disagreement about the state of evidence regarding Mormon or religious truth claims?

Oddly, since what little there is in the way of positive evidential argument in favor of theistic justification in phil of religion these days often gets expressed in Bayesian notation, my instinct is to think that's the best the got. (Partially helped by sophisticated ways of cheating in favorable probability estimates in the priors). But really, it's the same disagreements just expressed in a novel mathematical way.


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