Using Bayes Theorem to Support Theism?

[_EAllusion]

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.

[_Analytics]

The official way you are supposed to figure out the truth of Mormonism is jaw-droopingly circular: the way to find out that the Book of Mormon is true is to pray about it. Why do we know this is the correct way to figure it out? Because the Book of Mormon says so.

A Bayesian approach to the problem is devastating because it provides an honest and valid way to break out of the circle.

But is it really that devastating? True believers are gunna believe--even if they are a whiz at Statistics.

[_Water Dog]

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.

Because in these theological situations Bayes is being misapplied. It is a tool for incomplete information problems that are deterministic, the proper use of which relies on appropriate assumptions and controls. Induction should be equally applied to hypothesis that we do not believe and/or know to be false in order to learn these competing results and compare against them. For Bayes to be correctly applied to a question in Mormonism, for instance, it would have to be applied to the same question in the non-Mormon context. Applied to all other faiths, including the atheistic ones, etc. And when that is done, Mormonism loses. Moreover, for many questions it becomes infeasible to the point of being impossible because of claims about a one true church, etc. The starting assumptions don't allow for Baysean comparisons. In order to test a theory with Bayes, lip service must be paid to alternative theories in order to suss out what the data most likely predicts. Apologists move the goal posts by testing their theories in a vacuum against an infinite number of possibilities. That isn't how it works. Induction doesn't tell us what is right, it tells us what is most strongly indicated by the current set of data.

Harold Jeffreys described it like this, "A common argument for induction is that induction has always worked in the past and therefore may be expected to hold in the future. It has been objected that this is itself an inductive argument and cannot be used in support of induction. What is hardly ever mentioned is that induction has often failed in the past and that progress in science is very largely the consequence of direct attention to instances where the inductive method has led to incorrect predictions."

ET Jaynes, responding to this quote said, "Put more strongly, it is only when our inductive inferences are wrong that we learn new things about the real world. For a scientist, therefore, the quickest path to discovery is to examine those situations where it appears most likely that induction from our present knowledge will fail. But those inferences must be our best inferences, which make full use of all the knowledge we have. One can always make inductive inferences that are wrong in a useless way, merely by ignoring cogent information."

[Guest]

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.

Because in these theological situations Bayes is being misapplied. It is a tool for incomplete information problems that are deterministic, the proper use of which relies on appropriate assumptions and controls. Induction should be equally applied to hypothesis that we do not believe and/or know to be false in order to learn these competing results and compare against them. For Bayes to be correctly applied to a question in Mormonism, for instance, it would have to be applied to the same question in the non-Mormon context. Applied to all other faiths, including the atheistic ones, etc. And when that is done, Mormonism loses. Moreover, for many questions it becomes infeasible to the point of being impossible because of claims about a one true church, etc. The starting assumptions don't allow for Baysean comparisons. In order to test a theory with Bayes, lip service must be paid to alternative theories in order to suss out what the data most likely predicts. Apologists move the goal posts by testing their theories in a vacuum against an infinite number of possibilities. That isn't how it works. Induction doesn't tell us what is right, it tells us what is most strongly indicated by the current set of data.

Harold Jeffreys described it like this, "A common argument for induction is that induction has always worked in the past and therefore may be expected to hold in the future. It has been objected that this is itself an inductive argument and cannot be used in support of induction. What is hardly ever mentioned is that induction has often failed in the past and that progress in science is very largely the consequence of direct attention to instances where the inductive method has led to incorrect predictions."

ET Jaynes, responding to this quote said, "Put more strongly, it is only when our inductive inferences are wrong that we learn new things about the real world. For a scientist, therefore, the quickest path to discovery is to examine those situations where it appears most likely that induction from our present knowledge will fail. But those inferences must be our best inferences, which make full use of all the knowledge we have. One can always make inductive inferences that are wrong in a useless way, merely by ignoring cogent information."

looking at your quotes,

Bayes...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.

But...

Because in these theological situations Bayes is being misapplied. It is a tool for incomplete information problems that are deterministic, the proper use of which relies on appropriate assumptions and controls.

So which is it, Water Dog? Is it unkind to Mormonism to apply Bayesian theory, or is Bayesian theory being misapplied to Mormonism?

And just a clarification based on your second quote above, are you suggesting that Bayesian theory can only be used to evaluate deterministic systems?

For Bayes to be correctly applied to a question in Mormonism, for instance, it would have to be applied to the same question in the non-Mormon context.

Or are you suggesting that various concepts of religion can be formulated as a deterministic model?

[_Gadianton]

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.

Hold up there, cowboy. There are a few possible claims about Bayesian analysis being made.

1) How does Mormonism fare in a Bayesian weighing of evidence?

2) How does Mormonism fare in a Bayesian weighing of evidence vs. other frameworks?

3) How does Mormonism fare in a Bayesian weighing of evidence, within a framework as advanced by the Church or an apologist?

The apologists have often invoked Kuhn, for instance, and in response, some of us point out why Kuhn is a bad pick, and possibly worse than picking another empiricist. For instance, science was advanced by Richard Feynman as the belief in the ignorance of experts. Feynman took the anti-establishment angle to highlight the commitment to evidence; let the evidence speak for itself! This is a far friendlier basic position to apologetics than Kuhn's theory, which is fanatically pro-establishment. Kooks love Feynman because he makes it appear as if they might have a chance of being right if only the holier-than-thous of the establishment would listen. And at least with Feynman, they have a chance. Kuhn wouldn't even allow for Book of Mormon apologetics to exist. There is no archaeological data that has trouble being accounted for and requires the Book of Mormon to be advanced as an alternative theory where a second paradigm can rise that challenges the reigning paradigm. This point is explicit in Brandt's personal "paradigm shift" of looking for mesoamerica in the Book of Mormon rather than the Book of Mormon in mesoamerica. Well, you can see the point in any Book of Mormon theory that opts for consistency with evidence rather than uniquely supported by the evidence.

So it could be the case also that Bayes is damaging to Mormonism (or religion) beyond what some other philosophy of science might say.

What I think Analytics was referring to in this thread is that Bayes forces you to consider the chances of observing your outcome if your theory is false, which may be outright heresy for most Chapel Mormons. Other frameworks could be heretical too -- falsification may be worse. But hypothetico-induction? At least in principle it seems pretty good. You might not get your rope around a steer when proper controls are put into place, but at least you can get your horse out of the gate.

Think of the comments recently quoted by IHAQ from Hinckley, that Mormonism is either the truth or a great fraud. if it's a "great" fraud, then we ought to consider either the cunning of man or Satanic forces would do pretty well in getting a person a positive answer to prayer over the Book of Mormon. And so Bayes pretty much "F"s the entire Mormon epistemology of getting confirmation. (and in a really entertaining way)

These comments of course are taking an approach of evaluating internal consistency rather than a more objective external evaluation of the evidence for Mormonism. Whether or not Bayes fares poorly here I don't know, I'd have to read Carroll's book first, as that seems to be where Dr. W is coming from.

[_DrW]

These comments of course are taking an approach of evaluating internal consistency rather than a more objective external evaluation of the evidence for Mormonism. Whether or not Bayes fares poorly here I don't know, I'd have to read Carroll's book first, as that seems to be where Dr. W is coming from.

I would agree with Gadianton that my comments do "come from Carroll's book" - not because they were first encountered there, but because Bayesian reasoning, as he describes it, has always served me well and because Carroll provides far and away the most convincing case I've seen for its use in everyday life.

The process of model testing and evaluation described in Chapter 28 of the MacKay textbook, as mentioned upthread, pretty much describes the scientific method as currently practiced, as well as the method I have endeavored to use to build a worldview.

What I found in Carroll's book, after striving to practice this general approach both professionally and personally for some 50 years, was probably the best justified and articulated description of Bayesian reasoning one could imagine. Indeed, Carroll states that this approach is the framework from which he tends to view the world and continually re-evaluate and update his personal "planet of belief".

As a final comment in response to EA, I see Mormonism as being more susceptible to negation by Bayesian reasoning because Mormonism makes (many) more falsifiable (and falsified) truth claims than does traditional Christianity in general.

[_Gadianton]

as a brief add-on point: the various proposed models for how science work probably overlap significantly when articulated properly, i mean, nobody is going to let Book of Mormon apologetics slide through the door as how science should be done no matter what their model is.

[_Philo Sofee]

as a brief add-on point: the various proposed models for how science work probably overlap significantly when articulated properly, i mean, nobody is going to let Book of Mormon apologetics slide through the door as how science should be done no matter what their model is.

For some odd reason, this post triggered a memory of mine when I was doing apologetics. It was in my beginning of the enterprise, and I found out through the grapevine that John Gee was writing Egyptological articles for serious scholarly journals, and I was thrilled, and drove down to the BYU library to look them up and photocopy them all. Here was LDS Egyptological materials on Joseph Smith's translations being shared with the world's scholars in their own journals! This is great man!

I didn't even read them first, I simply photocopied them so I possessed them in person so I could savor the discussions of a real Egyptologist showing the scholars how well Joseph Smith's translation jibe with their knowledge of ancient Egyptian hypocaphali, and facsimiles, and religion, once I got back home.

I was sooooooooooooo disappointed that Gee apparently dwelt on all manner of trivialities (to my mind then anyway), since he never brought up Joseph Smith at all. He never examined and showed (as Hugh Nibley had done in his research) how well Joseph Smith's translations and interpretations in the Book of Abraham fit.

This was one of the first introductions to my mind that LDS scholars were, in point of fact, publishing in non-Mormon scholarly journals. All well and good. But Joseph Smith's translations never got any air time. It was only later that I discovered why, and hence why I am where I am now in my life.

LDS scholars simply cannot get published in valid scholar venues using Joseph Smith's materials. And they ad hoc with the excuse that the journals are biased, not us!