Is It a Crock to Use Bayes’ Theorem to Measure Evidence about God? Part 2

I want to continue where I left off in part 1 of my response to Metacrock on the use of Bayes’ Theorem (BT) to measure evidence about God.

Here is Metacrock:

Bayes’ theorem was introduced first as an argument against Hume’s argument on miracles, that is to say, a proof of the probability of miracles. The theorem was learned by Richard Price from Bayes papers after the death of the latter, and was first communicated to the Royal society in 1763.[6] The major difference in the version Bayes and Price used and modern (especially skeptical versions) is that Laplace worked out how to introduce differentiation in prior distributions. The original version gave 50-50 probability to the prior distribution.[7] The problem with using principles such as Bayes theorem is that they can’t tell us what we need to know to make the calculations of probability accurate in dealing with issues where our knowledge is fragmentary and sparse. The theorem is good for dealing with concrete things like tests for cancer, developing spam filters, and military applications but not for determining the answer to questions about reality that are philosophical by nature and that would require an understanding of realms beyond, realms of which we know nothing. (Italics are mine.)

1. Again, Metacrock claims that we can’t use BT to measure the probability of God’s existence. Why? Because BT is not good

for determining the answer to questions about reality that are philosophical by nature and that would require an understanding of realms beyond, realms of which we know nothing.

In other words, Metacrock seems to embrace a kind of so-called “skeptical theism,” according to which we don’t have sufficient knowledge in order to measure the probability of certain items of evidence on theism (such as, but not limited to, evil). That position is a double-edged sword, however, for it implies that we also don’t have sufficient knowledge to conclude that certain items of evidence (such as, say, fine-tuning) are more probable on theism than on naturalism.

2. But is Metacrock correct that we cannot use BT to assess the probability of God’s existence? No. As Doug Hubbard writes, “We use probabilistic methods because we lack perfect data, not in spite of lacking it. If we had perfect data, probabilities would not be required.”[1] Furthermore, “It is a fallacy that when a variable is highly uncertain, we need a lot of data to reduce the uncertainty. The fact is that when there is a lot of uncertainty, less data is needed to yield a large reduction in uncertainty.”[2]

Bayes conquered the problem of what level of chance or probability to assign the prior estimate by guessing. This worked because the precept was that future information would come in that would tell him if his guesses were in the ball park or not. Then he could correct them and guess again. As new information came in he would narrow the field to the point where eventually he’s not just in the park but rounding the right base so to speak.

The problem is that doesn’t work as well when no new information comes in, which is what happens when dealing with things beyond human understanding. We don’t have an incoming flood of empirical evidence clarifying the situation with God because God is not the subject of empirical observation.

Again, Metacrock argues that we don’t have empirical evidence about God and, again, Bayesian philosophers of religion (including theists, agnostics, and atheists) must disagree with him. Metacrock needs to study Richard Swinburne’s classic, The Existence of God.[3] Although I disagree with his conclusions, I largely agree with his overall Bayesian approach.

Where we set the prior, which is crucial to the outcome of the whole thing, is always going to be a matter of ideological assumption.

With all due respect to Metacrock, this statement reveals that he simply doesn’t know what he is talking about. He needs to study the philosophy of science and specifically confirmation theory. According to the epistemic interpretation of probability, the probability of a statement is a measure of the probability that a statement is true, given some stock of knowledge.  In other words, epistemic probability measures a person’s degree of belief in a statement, given some body of evidence. The epistemic probability of a statement can vary from person to person and from time to time (based upon what knowledge a given person had at a given time).[4] For example, the epistemic personal probability that a factory worker Joe will get a pay raise might be different for Joe than it is for Joe’s supervisor, due to differences in their knowledge.

When we are comparing two rival explanations or hypotheses (such as theism and naturalism), we can compare their intrinsic epistemic probabilities by considering (1) their modesty and (2) their degree of coherence. Regarding (1), as Paul Draper explains,

The degree of modesty of a hypothesis depends inversely on how much it asserts (that we do not know by rational intuition to be true). Other things being equal, hypotheses that are narrower in scope or less specific assert less and so are more modest than hypotheses that are broader in scope or more specific.[5]

As for (2), I will again quote Draper.

The degree of coherence of a hypothesis depends on how well its parts (i.e. its logical implications) fit together. To the extent that the various claims entailed by a hypothesis support each other (relative only to what we know by rational intuition), the hypothesis is more coherent. To the extent that they count against each other, the hypothesis is less coherent. Hypotheses that postulate objective uniformity are, other things being equal, more coherent than hypotheses that postulate variety, either at a time or over time.[6]

The upshot is that the intrinsic epistemic probability of a hypothesis is entirely objective, not “a matter of ideological assumption” as Metacrock claims.

For example we could put the prior at 50-50 (either God exists or not) and that would yield a high probability of God.[8] Or the atheist can argue that the odds of God are low because God is not given in the sense data, which is in itself is an ideological assumption. It assumes that the only valid form of knowledge is empirical data. It also ignores several sources of empirical data that can be argued as evidence for God (such as the universal nature of mystical experience).[9] It assumes that God can’t be understood as reality based upon other means of deciding such as personal experience or logic, and it assumes the probability of God is low based upon unbelief because the it could just as easily be assumed as high based upon it’s properly basic nature or some form of elegance (parsimony). In other words this is all a matter of how e chooses to see things. Perspective matters. There is no fortress of facts giving the day to atheism, there is only the prior assumptions one chooses to make and the paradigm under which one chooses to operate; that means the perception one chooses to filter the data through.

This is refuted by Draper’s objective criteria explained above. Since metaphysical naturalism and (metaphysical) supernaturalism are equally modest and equally coherent, it follows that they have equal intrinsic epistemic probabilities. Since there are other options besides naturalism and supernaturalism, however, it follows that the intrinsic probabilities of both naturalism and supernaturalism are less than 1/2.[7]

Unlike naturalism and supernaturalism, however, naturalism and theism are not symmetrical claims. Theism entails supernaturalism but is not entailed by it; theism is one of many variants or more specific versions of supernaturalism. Thus, theism is less modest than supernaturalism. Furthermore, theism is not epistemically certain given supernaturalism. So metaphysical naturalism has a higher intrinsic epistemic probability than theism.[8]

Moving on:

Stephen Unwin tries to produce a simple analysis that would prove the ultimate truth of God using Bayes. The calculations he gives for the priors are as such:

Recognition of goodness (D = 10)

Existence of moral evil (D = 0.5)

Existence of natural evil (D = 0.1)

Intra-natural miracles (e.g., a friend recovers from an illness after you have prayed for him) (D = 2)

Extra-natural miracles (e.g., someone who is dead is brought back to life) (D = 1)

Religious experiences (D = 2)[10]

Metacrock’s article reminds me that I need to add Unwin’s book to my list of books to read. Since I haven’t read it, I cannot yet comment on how he justifies these values. I do, however, have one nitpick. Metacrock refers to these values as “priors,” but that is obviously wrong for the simple reason that probability values, regardless of one’s philosophical interpretation of probability, are by definition always real numbers between 0 and 1 inclusive. It would appear that the D values quoted by Metacrock are what is known as “Bayes’ factors.”

This is admittedly subjective, and all one need do is examine it to see this. Why give recognition of moral evil 0.5? If you read C.S. Lewis its obvious if you read B.F. Skinner there’s no such thing. That’s not scientific fact but opinon. [sic]

Misleading. While epistemic final probabilities and estimates of explanatory power are subjective, it doesn’t follow that they are entirely arbitrary in the way that Metacrock suggests.

When NASA does analysis of gas pockets on moons of Jupiter they don’t start out by saying “now let’s discuss the value system that would allow us to posit the existence of gas.” They are dealing with observable things that must be proved regardless of one’s value system. These questions (setting the prior for God) are matters for theology. The existence of moral evil for example this is not a done deal. [sic] This is not a proof or disproof of God. It’s a job for a theologian, not a scientist, to decide why God allows moral evil, or in fact if moral evil exists. These issues are all too touchy to just blithely plug in the conclusions in assessing the prior probability of God. That makes the process of obtaining a probability of God fairly presumptive.

Again, Metacrock seems to assume that theism makes no empirical predictions and, again, Bayesians disagree. To cite just one example of so-called “natural evil,” theism does not predict the observations we do, in fact, make regarding the biological role of pain and pleasure. Those observations are antecedently very much more probable on naturalism than on theism and hence are strong evidence against theism.

Notes

[1] Douglas W. Hubbard, The Failure of Risk Management (New York: Wiley, 2009), kindle reference: 2296. Italics are mine.

[2] Hubbard 2009, Kindle location 3950-1.

[3] Richard Swinburne, The Existence of God (2nd ed., New York: Oxford University Press, 2004).

[4] Brian Skyrms, Choice & Chance: An Introduction to Inductive Logic (4th ed., Belmont: Wadsworth, 2000), 23.

[5] Paul Draper, “A New Theory of Intrinsic Probability,” unpublished manuscript.

[6] Ibid.

[7] Paul Draper, “Theism, Naturalism, and the Burden of Proof,” 2009 Presidential Address to the Society for the Philosophy of Religion.

[8] Ibid.

About Jeffery Jay Lowder

Jeffery Jay Lowder is President Emeritus of Internet Infidels, Inc., which he co-founded in 1995. He is also co-editor of the book, The Empty Tomb: Jesus Beyond the Grave.

  • Sebastian

    “That position is a double-edged sword, however, for it implies that we also don’t have sufficient knowledge to conclude that certain items of evidence (such as, say, fine-tuning) are more probable on theism than on naturalism.” Agreed. A skeptical theist can’t assign a probablity to P(FTU | T) as they can’t know what world God is more likely to create. The theist can take two positions, either adhere to skeptical theism and not use the fine-tuning argument or disgard skeptical theism and suffer the conclusion of the evidential problem of evil.

    • Sebastian

      discard*

    • Metacrock

      “That position is a double-edged sword, however, for it implies that we
      also don’t have sufficient knowledge to conclude that certain items of
      evidence (such as, say, fine-tuning) are more probable on theism than on
      naturalism.” Agreed. A skeptical theist can’t assign a probablity to
      P(FTU | T) as they can’t know what world God is more likely to create.
      The theist can take two positions, either adhere to skeptical theism and
      not use the fine-tuning argument or discard skeptical theism and suffer
      the conclusion of the evidential problem of evil.

      no because fine tuning is indirect. It doesn’t’ claim to be direct observation of God but part of evidence of God’s doings.”

      • Sebastian

        And how is this relevant? P(FTU | T) is inscrutable if one adheres to skeptical theism.

        • Metacrock

          We can have indications of God’s reality in the form of justification arguments, that is, warrants for belief, rather than “proof.” If we not claiming it as proof but merely “reason to believe” then we are not trying to claim direct knowledge of God.

          I still object to the term “skeptical theism.” I prefer to think of my position as “Jamesian” or “mystical.” (as in William James).

          • Sebastian

            But given skeptical theism, we have no reason to believe, (i.e. no warrant) anything about what world God is more likely to create. And given this, P(FTU | T) is inscrutable and cannot count as evidence for Theism.

            And Bayesian arguments are not considered to be a conclusive proof (as the word ‘proof’ is used in mathematics). They merely give us warrant to rationally believe some hypothesis.

          • Metacrock

            “But
            given skeptical theism, we have no reason to believe, (i.e. no warrant)
            anything about what world God is more likely to create. And given this,
            P(FTU | T) is inscrutable and cannot count as evidence for Theism. ”

            >>>I’m not a skeptical theist. God created this world. The kind of thinking that uses possible worlds to determine the divine essence is mixed up. they have it backwards.

            “And Bayesian arguments are not considered to be a conclusive proof
            (as the word ‘proof’ is used in mathematics). They merely give us
            warrant to rationally believe some hypothesis.”

            >>>But when it comes to reality of God they don’t. They don’t apply, as I pointed discussed in my arguments.

  • JohnH

    The priors do make a huge difference, in particular how much weight or certainty one places on the prior.

    Not all theistic positions entail supernaturalism.

    The argument in regards to pain and pleasure appears to largely be post-fitting to observed data, and completely dependent on a certain type of theism.

    • http://secularoutpost.infidels.org/ Jeffery Jay Lowder

      The priors do make a huge difference, in particular how much weight or certainty one places on the prior.

      It’s not clear to me which portion of my article, if any, you are disputing.

      Not all theistic positions entail supernaturalism.

      If you claim that not all theistic positions entail supernaturalism, then I think we are speaking different languages. On my terminology, theism entails supernaturalism by definition.

      The argument in regards to pain and pleasure appears to largely be
      post-fitting to observed data, and completely dependent on a certain
      type of theism.

      I’d be happy to discuss that argument further in the comments section on the relevant page (not here). That argument is simply an example.

  • Metacrock
    • http://secularoutpost.infidels.org/ Jeffery Jay Lowder

      Before getting into specifics I think
      it’s important to understand the basic difference between the
      orientation of a believer and a skeptic. The kind of skeptics that tend
      to make up most of the atheist ranks on the net are scientifically
      inclined people who view the world through the lens of some kind of
      scientific orientation.

      Note: one may question whether Metacrock has the sort of data which would justify such a statistical generalization, but the claim itself seems reasonable, so let’s see what he does with it.

      Believers tend to be more “liberal arts”oriented in that their top concerns are not scientific proof.

      I don’t think there is such a thing as “proof” per se in science, but let’s put that to the side.

      I have observed time after time the atheist constantly [sic] a mistake in thinking that the reason to believe in God is because one needs to explain that [sic] world. That is catered to by God argument, but God arguments are attempts to reach out to others so they embody the concerns of non believers. The reason for belief in God is not to explain the world. Atheist think this so they always oriented [sic] things in those terms. This is [sic] will be important in the discussion below becuase Mr. Lowder is constantly saying things about hypothesis. one of my major arguments is that belief is not an hypothesis. It’ snot [sic] an attempt to explain the world, at least not in the same kind of scientific terms. Thus the arguments he makes taht [sic] embody the idea of competing explanatory power are non [sic] applicable.

      The expression, “The reason for belief in God …,” is ambiguous. It could mean “Among those people who believe in God, the reason why they believe in God is …” It could also mean, “The proper reason for belief in God is…” It may also mean something else. It’s not entirely clear what Metacrock means. He seems to have the second interpretation in mind, but I’m not really sure.

      In any case, what can be said about the idea of treating God’s existence as an explanation? First, as Metacrock himself acknowledges, many people who have defended arguments for God which do use God as an explanation. In the dialectical context of debates about such arguments, it’s entirely appropriate for critics of those arguments to meet the argument on its own terms and critique it as such.

      Second, the proposition, “God exists,” where “God” is defined in a traditional or classical way, makes testable predictions. In a similar vein, metaphysical naturalism also makes testable predictions. We can “test” both theism and naturalism by comparing their predictions to what we actually find in the world. This is what I have in mind when I refer to theism as a “hypothesis.” I am not claiming that theism is literally a scientific hypothesis. I am using the word “hypothesis” simply to emphasize the fact that the proposition, “God exists,” does make testable predictions and so, at least in theory, is capable of serving as an “explanation.”

      So when Metacrock writes:

      one of my major arguments is that belief is not an hypothesis.

      My response is a question: do you agree that the sentence, “God exists,” is a proposition? If yes, do you believe that proposition makes testable predictions? If your answer to both questions is “yes,” then we agree! Again, I’m not claiming that most theists view their belief as an explanatory “hypothesis.” (I’m well aware that they do not.) Nor am I even arguing that theists should frame their own beliefs about God as a “hypothesis.” All I am arguing is that the proposition, “God exists,” can function as a hypothesis in the sense I’ve defined above.

      • Metacrock

        “My response is a question: do you agree that the sentence, “God exists,”
        is a proposition?”

        Meta>>>>It’s a proposition but it’s also a mistake in theology. AT least if you believe Tillich. existence is for contingent things. That’s part of the problem; you want to treat God like a contingent thing. That’s why you want to examine him scientifically and see if he is another thing that can be found in the universe, which he is not. So when you don’ find him out there among the flotsam, jetsam of the universe you assume there’s no god. There’s no reason why he should among that stuff becuase that’s contingent stuff.

        “If yes, do you believe that proposition makes
        testable predictions?”

        Meta>>>Depends. this one doesn’t.

        “If your answer to both questions is “yes,” then we
        agree! Again, I’m not claiming that most theists view their belief as
        an explanatory “hypothesis.” (I’m well aware that they do not.) Nor am I
        even arguing that theists should frame their own beliefs about God as a “hypothesis.” All I am arguing is that the proposition, “God exists,” can function as a hypothesis in the sense I’ve defined above.”

        Meta>>> Yes, that’s a mistake. It’s not consistent with the basis of Christian theology. the problem is the enlightenment thinking reduces everything to quantifiable results and makes it all into objects of our subjectivity. In placing human consciousness at the center of reality and causing the physical world to orbit around it, it transforms reality into the sea of contingency I mentioned above and leaves out that which is not quantifiable as theoretical construct floating about on the margins that is soon dismissed by a reductionist view point.

  • Michael Borland

    I recently wrote an app that allows anyone to carry out these calculations. It guides the user through a series of observations and assessments of the consistency of the observation with the god hypothesis and its negation. In the end, it assesses the likelihood of god existing based on the users responses. If nothing else, it will give god-believers a good dose of cognitive dissonance.

    http://play.google.com/store/apps/details?id=borland.doesgodexist


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