Faith, Knowledge, Belief and Stochastic Theory Part 3: Putting It All Together

jmb275 faith, religion, testimony, thought 14 Comments

In part one I introduced the problem I see with our current understanding of faith, introduced some basic statistics, and weakly drew a comparison to faith. In part two I introduced deductive and inductive reasoning, and showed how Bayesian inference leads to good inductive reasoning. I also gave a brief example of how this might work in real life. In this post I would like to put all these concepts together into at least one way of viewing faith, knowledge, and belief. I will do this by examining the plausible reasoning of three individuals: a stereotypical believing Mormon, a Mormon convert, and a disaffected Mormon. As a disclaimer my intent is not to say this is how all such individuals think or act, only how they might think or act. I also want to clearly state that I do not think one is better than the others – rather, I think they all follow the same model.

The Convert

John is a member of another Christian denomination and he was raised as a believer. He has had one discussion with the LDS missionaries and plans to continue these discussions. In the first discussion the missionaries built on common beliefs with John and challenged him to read a few verses in The Book of Mormon and to pray over them. They read Moroni 10:3-5 in which the Lord, through his prophet, provides a recipe for confirmation of the truthfulness of the message taught. John takes this seriously and reads the verses and prays over them. He also has a strong spiritual manifestation. He feels peace, warmth, and what he interprets as an assurance from the Holy Spirit that the message is true.

For John, he has had a number of spiritual manifestations and hence accepts this form of gaining knowledge. He has not had one quite this powerful before so he takes this manifestation as evidence that the LDS church is true. In Bayesian terms, we might claim that John had a confidence distribution with a mean of “my Christian denomination is true” with a fairly large standard deviation (since he was open to other religious possibilities). When he received this new piece of information (a spiritual manifestation of the truthfulness of the LDS message) he incorporated it into his confidence distribution. This, along with further discussions from the missionaries is enough to shift his distribution to one with a mean of “the LDS church is the true church” with a fairly small standard deviation.

In this scenario there are some interesting things going on with regard to faith, knowledge, and belief. John had “belief” enough to take a leap of “faith.” In essence, he was testing the “tail ends” of his confidence distribution by examining a foreign concept. In a Monte Carlo sense, his random walk was probing “less probable” areas of his distribution. For John, he found some valuable information that he then used to modify that distribution. It is easy to characterize his actions as “faith” as he probed heretofore untested waters. His experience exemplifies the allegory of faith given in Alma 32.

The Stereotypical Mormon

Bill is a lifelong member of the LDS church. He was raised in Salt Lake City and has been an obedient member of the church for all of his 39 years. Bill has a strong testimony of the truthfulness of the Gospel and all of its core principles and doctrines.

Bill has had many experiences which he interprets as support for his view of the Gospel. He has a successful career, a great family, good health, and an abundance of opportunities to serve which he attributes to his adherence to tithing, prayer, fasting, righteous living, and heeding the counsel of prophets. Bill has so much confirming evidence of his life choices and beliefs that his confidence distribution has a mean of “the LDS church is the true church” with a very small standard deviation. Bill acknowledges that others have some pieces of truth, but is grateful that he has the blessing of knowing the fulness. Indeed, Bill claims he “knows” the Gospel is true. He would live and die by this, and admits that nothing could persuade him otherwise.

In this scenario, faith, belief, and knowledge take on a bit different meaning. Bill hasn’t really taken the same kind of “leap of faith” that John did. He has put his beliefs to the test and received verification that they were correct. While he has somewhat probed the less probable regions of his confidence (the tails of his distribution) he interprets the information as confirming his beliefs. His confidence in his mean is so great it would be easy to classify Bill’s “faith” or “belief” as “knowledge” (which of course he does regularly at testimony meetings). Each successive spiritual experience or life event, properly interpreted, only adds more information which confirms Bill’s knowledge.

The Disaffected Mormon

Fred is in the same boat as Bill. He is a lifelong member of the LDS church, grew up in Salt Lake City, and did all he was asked to do. However, about a year ago he encountered some individuals that posed challenging questions to his worldview. Initially, Fred’s response was much like Bill’s, that is, he interpreted information to confirm his knowledge. But eventually the information became so overwhelming that Fred had to concede he might not have it quite right.

Fred has also had many spiritual manifestations, but his probing into psychology convinces him that much of it can be explained by regular, well understood psychological phenomena. Fred has also been richly “blessed” with a good career, great family, etc. but has to acknowledge that many non-Mormons have also been similarly blessed. For Fred, his confidence distribution is beginning to change. Each new piece of information, incorporated loosely via a built-in Bayesian inference calculator, shifts the distribution away from his mean of “the LDS church is the true church.” Initially, the information only increases his standard deviation as he acknowledges truth in other places, but eventually his mean starts to shift as well when he examines what he considers to be the lack of evidence for the historicity of The Book of Mormon, the myriad conundrums in Church history, etc. Most alarming for Fred is the feeling of betrayal by not realizing these things earlier in life which he attributes to white-washing by the LDS church.

In this scenario it would be easy to claim that “faith” is being destroyed. I think this is erroneous. Rather, I would say that “faith” is shifting. Fred now has faith in other things, though admittedly less faith in the LDS church being the true church. After a year of struggling, Fred admits he no longer has any confidence that the LDS church is the true church.

Contrasting the Scenarios

The commonalities between the scenarios are interesting. Each individual is doing what he thinks is most probable. John and Fred actually took a “leap of faith” to probe the less probable regions of their confidence distribution which turned up valuable information. Additionally, since some previous experiences had modified their distribution, their built-in Bayesian inference calculator was perhaps more able to objectively incorporate the new information. While Bill did occassionally probe the less probable regions of his distribution, the new information was interpreted to add more evidence to his beliefs.

This leads me to conclude that the biggest argument over “faith,” “belief,” and “knowledge,” actually has nothing to do with one’s “faithfulness” and everything to do with the quantity, types of, and weighting given to different types of evidence. For John and Bill, spiritual manifestations are a perfectly valid form of evidence, perhaps even the most important kind, which they weight appropriately. For Fred, this used to be the case, but as he discovered new information he had to modify his weightings, and began to reject some forms of evidence (spiritual manifestations) previously acceptable to him.

I subscribe to the “confidence distribution” model for understanding people’s beliefs, motivations, actions etc. because I believe it drives to the real issues which is what types of evidence are accepted by people, and what importance they place on that evidence.

This kind of reasoning also brings a different perspective to the word “doubt.” We could say that Fred is “doubting” and couch this in negative terms, but I think a more appropriate characterization would be to admit that Fred now accepts other forms of evidence and hence his faith has shifted. For Fred, he is being intellectually honest, as is Bill and John. This doesn’t make one more faithful, or more spiritual than the others, just different!

Comments

comments

Comments 14

  1. I know you’re forced to keep this simple, but I think we need to think about the internal calculator working on multiple hypotheses at once. For example, John above also has another parallel hypothesis: “my denomination is true” is paired with “only one denomination can be true”. His new evidence conflicts with the first, but does not provide much input to the second, so he shifts the first, but probably holds the second just as strongly. If he is presented with challenges to the second hypothesis before reading the BofM, he evolves into a different belief system.

  2. Dagnabbit, what’s the fun of religion if you can’t burn heretics? And how in Odin’s name can you possibly feel good about burning heretics when it’s all a matter of how people monkey differently around with statistics?

  3. Bravo, jmb.

    So, could you say that each person has a sample of experience to draw confidence on truth, and ultimate truth is the entire population of experience?

    Fred and Bill have different interpretations of the ultimate truth, but neither of them totally describes the whole population characteristics (or ultimate truth), only bits and pieces of it as represented in their sample of experiences?

    Even if they claim to “know” truth, their sample could be off. Fred could have an alpha (type I) error or Bill could have a beta (type II) error.

  4. Nice analysis, jmb! This stuff is right up my alley.

    #1: An inference method like this (presumably some kind of MCMC sampler, jmb?) leaps about in *hypothesis* space already. The idea is to test various hypotheses one at a time, somewhat randomly and somewhat directed, to see how well they fit the evidence. Those that fit best, or that the inference method spends the most time in, have highest probability. Every hypothesis’s weight is stored and kept track of.

    Keeping things simple might have made this hard to spot: jmb characterized beliefs as having a “mean” around “the Church is true” with a tight standard deviation. I put “mean” in quotes because it’s very unlikely that the hypotheses live in a tidy Euclidean space and that the area of high probability is symmetric. It’s really more like “the Church is true” and *related explanations* (perhaps with different combinations of sticky subjects on the back burner) collectively have high probability.

    Maybe there’s another bump around “my old Church is true”, but it’s lower. It could start higher and go lower, even with the “only one is true” constraint. Some inference methods allow only one bump, period – and that’s a problem with the inference method – but not the one it sounds like jmb is talking about.

    (FWIW, the “only one is true/right” constraint is very interesting. I have a friend who removed that constraint from Bayesian ensembles (basically committees of artificial statistical learners) and came up with something that kicks everything else’s butt in terms of prediction accuracy. It’s more complicated that way, but it has much more representational power. I think usually one committee member gets the most say, but the others chime in a little – just enough to learn something complex but still generalize well.)

    jmb, I’ve found that a lot of people who “lose their testimonies” because of new information do so because they had previously assumed something was infallible. (It’s basically a delta conditional distribution on some evidence, which often amounts to a logical connective like equivalence.) But nothing at all is infallible! When they discover that the few bits of evidence that keep their belief tight are doing too much (i.e. they should have wider conditional distributions), they update their model and the previous tightness goes flatter. They start exploring other hypotheses rather than spending their time in the small group clustered around “the Church is true”… and they turn into Fred.

    How do we fix it? Lots of evidence! My faith is built on mounds and mounds of weak evidence, with just two or three very strong points. Now, I admit that this makes me less certain of things than I was in my late teens. But I can also handle noise in the evidence a *lot* better, and better relate to people who come to different conclusions.

    To get to this point, though, I had to have a few crises in which those darned conditional distributions either widened or went almost flat. Looking back, I think it was unavoidable. It was either that or start with the distributions that way – but I don’t think I would have accumulated enough evidence to sustain me through a two-year mission.

    Also, kids and teenagers don’t really handle wide conditionals well. In plain English: everything is so black-and-white to them! (It has to be. Otherwise, real life is pretty much intractable at first.)

    I like thinking like this. It has explanatory power.

  5. JMB and Right Trousers:

    An interesting speculation on this is whether God’s mind also incorporates this same mode of “inference” operation.

    “An inference method like this (presumably some kind of MCMC sampler, jmb?) leaps about in *hypothesis* space already. The idea is to test various hypotheses one at a time, somewhat randomly and somewhat directed, to see how well they fit the evidence.”

    Maybe we’re ways God explores Himself. There’s an old child’s question: “Can God create a rock so heavy God Himself can’t lift it?” Maybe an equivalent is “Is God so great, even God Himself can’t figure Him out?”

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    Sorry, was busy last night, so I couldn’t respond.
    Re #1 Firetag
    You’re right. I’m definitely simplifying it. It is much more complex than I have indicated. However, the pure Bayesian inference (complete with random processes, not just random variables) would still provide the correct prediction if modeled just right. More on this below.

    Re #2 Thomas
    I know, I know, it’s no fun if you can’t disparage those who disagree with you. After all, if we recognize them as just as good, intelligent, faithful as we are then we’d be following a more pure Gospel 😉 !

    Re #3 Heber
    Yes, you’re getting very close. It’s not so much about what is or is not truth (objectively), but what people believe is the truth based on their experiences and information. Fred and Bill may or may not have all the truth (in other words there is no reason to assume initially that Bill is not 100% correct). This analysis is more about the perception of truth. If we compare this to science, the reason most of us have VERY similar beliefs when it comes to science is that there is a more rigorous standard for acceptable types of evidence and how much weight we should give to that evidence.

    Almost everyone believes that electromagnetics is “true.” Why? Even if they don’t know anything about it, they would readily accept Maxwell’s equations because they know that engineers have been using these equations to provide radio signals to their radio, information to their cell phones, etc. etc.

    But in the religious realm there it is much more ambiguous as to what constitutes “evidence” and how it should be weighted. Furthermore, this “evidence” is often contrasted (perhaps erroneously) with scientific standards. This doesn’t make the evidence wrong, or invalid, just different. Some will find it compelling, others will not.

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    Re #4 The Right Trousers

    #1: An inference method like this (presumably some kind of MCMC sampler, jmb?)

    Yes, an MCMC sampler is a good visualization, though not necessary. In reality, as you know, you can’t solve Bayes equation in PDF form analytically so we resort to such sampling methods. But that’s more of an implementation detail.

    Keeping things simple might have made this hard to spot: jmb characterized beliefs as having a “mean” around “the Church is true” with a tight standard deviation. I put “mean” in quotes because it’s very unlikely that the hypotheses live in a tidy Euclidean space and that the area of high probability is symmetric. It’s really more like “the Church is true” and *related explanations* (perhaps with different combinations of sticky subjects on the back burner) collectively have high probability.

    You’re exactly right! This is similar to what FireTag is pointing out – I’ve grossly over simplified it. In reality the distribution is a random process in some other sort of manifold (likely not even Euclidean). Very good analysis!

    (FWIW, the “only one is true/right” constraint is very interesting. I have a friend who removed that constraint from Bayesian ensembles (basically committees of artificial statistical learners) and came up with something that kicks everything else’s butt in terms of prediction accuracy. It’s more complicated that way, but it has much more representational power. I think usually one committee member gets the most say, but the others chime in a little – just enough to learn something complex but still generalize well.)

    Very cool. This sounds similar to what I did for my MS thesis work. I incorporated a particle filter to map fires from an unmanned aircraft, but rather than constraining it to “one hump” or one location of fire, allowed for multiple fire spots. In other words, in my work the posterior distribution WAS the answer rather than the mean.

    jmb, I’ve found that a lot of people who “lose their testimonies” because of new information do so because they had previously assumed something was infallible. (It’s basically a delta conditional distribution on some evidence, which often amounts to a logical connective like equivalence.) But nothing at all is infallible! When they discover that the few bits of evidence that keep their belief tight are doing too much (i.e. they should have wider conditional distributions), they update their model and the previous tightness goes flatter. They start exploring other hypotheses rather than spending their time in the small group clustered around “the Church is true”… and they turn into Fred.

    Again, you’re spot on. Just your explanation is brilliant because you are pointing out the flaw in their distribution rather than merely attacking them for lacking faith (which is what I’m really after). I agree this problem is a big one, and one that most religions face. I think there are a few issues at play here:
    1. Some people are prone to insist on certainty (more specifically a probability of nearly 1 with an infinitesimal standard deviation). Whatever they decide on has this distribution. They are the black and white thinkers.
    2. In the church we encourage this too much. Our culture, our vernacular, etc. (IMHO) lead one to make this mistake. How would an individual know if his distribution was too “delta like”? Someone would have to point out to him a world outside his distribution, one that had truths he didn’t realize before, or perhaps show him that some parts of our culture may not be right. But this type of tactic is discouraged and often referred to as “destroying faith.” However, I think we’re making progress in the church now by encouraging good history like RSR, etc.
    3. Neo-atheists (as I call them) don’t help. They often have as tragically flawed arguments as many apologists, but they win many over in the fight against religion, all while ignoring the benefits that religion/spirituality has.

    How do we fix it? Lots of evidence! My faith is built on mounds and mounds of weak evidence, with just two or three very strong points. Now, I admit that this makes me less certain of things than I was in my late teens. But I can also handle noise in the evidence a *lot* better, and better relate to people who come to different conclusions.

    Yep! I don’t view being less certain as a bad thing. In fact, I worry about the Bills in the world (of which I know many) as they have set themselves up for failure in a myriad ways.

    To get to this point, though, I had to have a few crises in which those darned conditional distributions either widened or went almost flat. Looking back, I think it was unavoidable. It was either that or start with the distributions that way – but I don’t think I would have accumulated enough evidence to sustain me through a two-year mission.

    I’m in the same boat, and have gone through similar crises. Though they were painful for me, I would not trade them. I think my nuanced testimony is far healthier than it was otherwise, and I’m able to appreciate the Gospel much more now.

    Also, kids and teenagers don’t really handle wide conditionals well. In plain English: everything is so black-and-white to them! (It has to be. Otherwise, real life is pretty much intractable at first.)

    It’s true. I think a careful program of “inoculation” is appropriate. I know many would disagree, but my current bishop has a program like this. He is well read in church history and slowly tries to expose his children to the best information we have available so they don’t get the wrong idea.

    I like thinking like this. It has explanatory power.

    Thanks!

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    Re #5 FireTag

    Maybe we’re ways God explores Himself. There’s an old child’s question: “Can God create a rock so heavy God Himself can’t lift it?” Maybe an equivalent is “Is God so great, even God Himself can’t figure Him out?”

    Very interesting idea. As a corrolary, I have also wondered whether or not many of the religions in the world are God’s way of providing the truth in a plethora of ways. Perhaps we focus too much on the correct organization, correct authority, correct ordinances, etc. and not enough on living good lives (the common thread amongst most religions). Perhaps the important truths are found in most religions and God has put them here, tailored for many different kinds of people, to maximize his ability to “bring to pass the immortality and eternal life of man.”

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    Re #9 FireTag

    So there are routes to evolve our beliefs toward truth no matter where we start or whatever the order of our search algorithm?

    Absolutely (at least in my book)! Though certainly some search algorithms are definitely worse than others and some starting places better than others! Otherwise what prayer in the world do we have (unless you’re absolutely certain that YOU’VE got it right, but I sure don’t)? I view my religion/spirituality as a compass that (I hope) points me in a good direction. My hope is that if/when the absolute truth is made manifest to me I will be humble enough (and my definition of humble is “openness to the truth”) to recognize it because/in spite of my current confidence distribution.

    However, this really opens another can of worms – namely, what is truth? My explanation thus far has been about our perception of truth which may or may not correlate with objective or absolute truth. To argue over whether or not our perception of truth is objective truth is to argue over what forms of evidence are acceptable and what weight we should apply to that evidence (which is the conclusion of this post and is an argument with no victor).

  11. JMB:

    I think this kind of modeling is very valuable to increasing our understanding of ourselves and each other’s frameworks of belief. I’ve spent a lot of time figuring out what kind of evidence I weight most heavily, and, more importantly, why I weight the evidence that way, and how the resulting complex of beliefs lead me to respond the way I do.

    I always have a lot more work to do in these areas, so thanks for some new ideas and techniques to consider in going forward.

  12. JMB,

    I had avoided this post for a few days, because judging from your last 2, I knew it was going to take a lot of energy to digest. I waited to read until I had some time to sit down and really digest it, but I love this!!!! I think this is the best, easiest to understand of all 3 parts! I love the analogy, and it makes perfect sense to me.

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