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. 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. 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.” 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.”
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. 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). 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.
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.
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. 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). 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.
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.
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)
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.
 Douglas W. Hubbard, The Failure of Risk Management (New York: Wiley, 2009), kindle reference: 2296. Italics are mine.
 Hubbard 2009, Kindle location 3950-1.
 Richard Swinburne, The Existence of God (2nd ed., New York: Oxford University Press, 2004).
 Brian Skyrms, Choice & Chance: An Introduction to Inductive Logic (4th ed., Belmont: Wadsworth, 2000), 23.
 Paul Draper, “A New Theory of Intrinsic Probability,” unpublished manuscript.
 Paul Draper, “Theism, Naturalism, and the Burden of Proof,” 2009 Presidential Address to the Society for the Philosophy of Religion.