bookmark_borderScientific Evidence Against God’s Existence: A Reply to Joe Hinman

In response to my recent blog post, “Six Findings from Experimental Science that Disconfirm Theism,” Joe Hinman (aka Metacrock) recently posted a rebuttal on his blog ‘AtheistWatch.’
1. His post begins with a graphic which shows two pie charts, one showing the distribution of different religious beliefs among the general public and one showing that same distribution among scientists. There are many things which could be said about that topic, but I’m going to pass over that since (1) Hinman doesn’t appeal to the graphic in the text of his post; and (2) the (un)popularity of religious belief among the general public (or among scientists) is not, by itself, of obvious relevance to God’s existence. The popularity of theism among the general public is no better evidence for God’s existence than is the widespread lack of theistic belief among scientists as evidence against God’s existence: neither fact provides any evidence at all for or against God’s existence.
2. Hinman next proceeds to make some preliminary comments about my abductive arguments (or, as I prefer to call them, “evidential” or “explanatory” arguments) against theism. As I read him, his first point is this:

But we must weigh the value of those concepts that are best explained by naturalism against the value of those best explained by theism.

If we are trying to arrive at a final estimate of the probability of naturalism or theism by considering all of the evidence, then I agree with Hinman. (I would replace “the value of those concepts” with “the evidential force of those facts” in that sentence of his.) This isn’t of obvious relevance to my blog post, however, since I wasn’t trying to do that. Rather, my claim was more modest: I simply claimed that six findings from experimental science are more probable on the assumption that naturalism is true than on the assumption that theism is true.
3. Hinman’s next point seems to be that:

there is a difference in “disconfirm theism” and “best explained by naturalism.” The latter is not proof, it’s a form of inference used when proof is not forthcoming. The former implies actual disproof of theism. My argument will be that neither is the case, except maybe in some instances where we understand the naturalistic reasons better, but they don’t out weigh the instances where theism is the better explanation.

First, we can quickly dispatch Hinman’s point about “proof.” Whereas I have offered a detailed, explicit explanation of what I mean by evidence (see here), he doesn’t explicitly say what he means by “proof.” He seems (?) to have in mind something stronger than evidence, perhaps such as the kind of “proof” one reads in a mathematics textbook, where the conclusion is absolutely certain. I don’t claim to “disprove” God’s existence in that sense. I think a charitable reading of my post (and the other posts linked from it) is that by “disconfirm” I mean “provide evidence against.”
Second, I didn’t claim that naturalism is the “best” explanation for these six facts, although I suspect it is. Rather, I claimed that naturalism is a “better” explanation than theism for those six facts. I trust the importance of this distinction will be obvious to the reader.
Third, all of my explanatory arguments follow the same pattern or have the same logical form.

1. F is known to be true, i.e., Pr(F) is close to 1.

2. Theism is not intrinsically much more probable than naturalism, i.e., Pr(|T|) is not much more than Pr(|N|).

3. Pr(F | N & B) > Pr(F | T & B).

4. Other evidence held equal, theism is probably false, i.e., Pr(T | B & F) < 0.5.

So when I say that some finding from experimental science “disconfirms” theism, I mean that there is an argument, of the form listed above, where F represents that finding from experimental science.
In response to arguments of this form, it is irrelevant to make objections of the form, “But F is logically compatible with T!” Indeed, to make such an objection is to miss the point. The whole point of evidential or explanatory arguments is to grant, at least for the sake of argument if not in fact, that F is logically compatible with rival hypotheses but more probable on one than on the other. And yet Hinman makes this fundamental blunder in his reply to some of my arguments.
In reply to my first argument, he asks, “Why can’t God create the universe with time as opposed to in time?” But that argument doesn’t claim that God cannot create the universe with time. Rather, it simply claims that the universe’s beginning with time is more probable on naturalism than on theism.
Similarly, in response to the argument from biological evolution, he writes, “No reason why God could not use evolution as a mechanism.” Again, Hinman points out that a finding from experimental science is logically compatible with theism and, again, I reply that he’s missed the point of explanatory arguments in general and this argument in particular. Yes, God could have used evolution. God also could have used other methods to create life besides evolution, methods which are logically incompatible with naturalism. Prior to examining the scientific evidence for evolution, theists had good reason to predict that evolution is false. In contrast, if naturalism is true, evolution pretty much has to be true. (I’ll say a little bit more about this in a moment.)
4. Hinman seems to misunderstand what I mean by “theism.” He writes:

One other preliminary point. This is not an attack on Jeff. The assumptions he seems to makes behind each of these points is that theism us [sic] represented by fundamentalism of the YEC kind. I’, [sic] basic liberal or perhaps neo-Orthodox, so these things don’t pertain to what I think of as theism. I understand he was answering a creationist so of course he makes that assumption. Not a criticism. 

Contrary to what Hinman claims, however, I don’t think theism is “represented by fundamentalism of the YEC kind.” The idea that Hinman brings YEC into the discussion strikes me as odd, since nowhere in my post did I even mention the age of the universe. I think it’s charitable to assume that what Hinman really means is that I think theism is “represented by fundamentalism of the anti-evolution kind,” i.e., the kind of theist who denies what Purdue University philosopher Paul Draper calls the “genealogical” and “genetic” theses (see here for definitions and references). This interpretation would be more understandable since I do appeal to evolution against theism. He’s wrong to conclude, however, that my appeal to evolution presupposes that theism = fundamentalist, anti-evolution theism. (More on that in just a moment.)
In fact, following Draper (see references here), I define theism as follows:

supernatural person: a person that is not part of nature but can affect natureExamples of supernatural persons include God, angels, Satan, demons, ghosts, etc.
theism: the hypothesis that there exists an omnipotent, omniscient, and morally perfect person (God) who created the universe. 

Since my definition of theism is so generic, it is obviously logically compatible with a belief in theistic evolution. So why, then, do I argue that evolution is evidence against theism? Hinman needs to read the section, “Evaluating Auxiliary Hypotheses,” in my essay, “Basic Structure of My Evidential Arguments.” If both God and life exist, then God either directly created life (aka so-called “special creationism”) or He indirectly created life (through either guided evolution [“theistic evolution”] or unguided evolution [“Darwinism”]). These options are auxiliary hypotheses to theism. As Draper has shown, the auxiliary hypothesis of special creationism is antecedently much more probable on theism than either the auxiliary hypothesis of theistic evolution or the auxiliary hypothesis of Darwinism. (Skip down to the section “Draper’s Defense of A” in this post.)
5. I’m going to stop my reply to Hinman here, at least for now. I’ve left some of his objections unaddressed, but for now I’ll just say this. I think that if you follow the links in my original post to my other posts which defend these arguments in much greater length, you’ll find that I’ve already addressed most, if not all, of his remaining objections.

bookmark_borderIs 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.


[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.

bookmark_borderIs It a Crock to Use Bayes’ Theorem to Measure Evidence about God? Part 1

Over at the Christian Cadre, “Metacrock” has written a post entitled, “Bayes Theorum [sic] and Probability of God: No Dice!” Metacrock makes a number of points regarding the use of Bayes’ Theorem (BT) with evidence about God’s existence. I want to comment on many of those points.

It is understandable that naturalistic thinkers are uneasy with the concept of miracles.

I think I understand the point that Metacrock is trying to get across, but I disagree with this sentence as written. Metaphysical naturalists are not literally “uneasy” with the concept of miracles any more than they are “uneasy” with, say, the concept that the evil lord Sauron is a threat to Middle Earth. The point is that calling both things concepts means just that: they are concepts. Nothing more, nothing less. Being a “concept” is neutral about whether the concept is about something real (as theists believe God is) or something fictional (which everyone knows Sauron is).

I think the point that Metacrock is trying to make is that, if we define “miracle” as an event which requires a supernatural explanation, then by definition a miracle is logically incompatible with metaphysical naturalism, which denies the existence of all supernatural beings, including God. So naturalists can’t remain naturalists and believe a miracle has occurred. The options seem to be: (1) give up naturalism, (2) deny the event took place at all, or (3) agree the event did take place, but deny it has a supernatural explanation.

So should we all be watchful not to believe too quickly because its easy to get caught up in private reasons and ignore reason itself. Thus has more than one intelligent person been taken by both scams and honest mistakes. By the the same token it is equally a danger that one will remain too long in the skeptical place and become overly committed to doubting everything. From that position the circular reasoning of the naturalist seems so reasonable. There’s never been any proof of miracles before so we can’t accept that there is any now. But that’s only because we keep making the same assumption and thus have always dismissed the evidence that was valid.

I agree with everything Metacrock writes here, with two important exceptions. First, that metaphysical naturalists do, in fact, reason in the way he describes. Second, that metaphysical naturalists rely upon “circular reasoning” to avoid the conclusion that a miracle has occurred. It is true, of course, that some individual metaphysical naturalists have made fallacious inferences about miracles. The same could be said about some individual theists. But so what? Metacrock presents absolutely no evidence to justify the assumption that such individuals are representative of the position they represent. Metacrock is attacking a straw man of his own creation.

At this point most atheists will interject the ECREE issue (or ECREP—extraordinary claims require extraordinary evidence, or “proof”). That would justify the notion of remaining skeptical about miracle evidence even when its [sic] good.

With all due respect to Metacrock, this statement suggests he does not understand ECREE. As I have explained elsewhere, the best interpretation of ECREE is the Bayesian interpretation. According to BT, the final probability of a hypothesis is determined by two other values: the prior probability of a hypothesis and the hypothesis’s explanatory power. Now explanatory power is, by definition, a measure of how well a hypothesis “predicts” (i.e., make probable) the data.

Metacrock’s statement, “That would justify the notion of remaining skeptical about miracle evidence even when its [sic] good,” is ambiguous. “Good evidence for a miracle” could mean one of two things. First, it could mean the miracle hypothesis has high explanatory power with respect to the relevant data. Second, it could mean that, compared to rival explanations, the miracle hypothesis has the greatest overall balance of prior probability and explanatory power (and so the miracle hypothesis is probably true).

Depending on the miracle claim, metaphysical naturalists may agree with the first interpretation. It may indeed be the case that a particular hypothesis about miracles may have strong explanatory power but such low prior probability that the resulting final probability is low. (In other words, the miracle probably never happened.)

But, as pointed out earlier, as long as a person remains a metaphysical naturalist, the second interpretation is not an option. This seems to be what Metacrock has in mind. But notice that to write as if there is “good” evidence for one or more miracles is to beg the question. In fact, he writes in an unnecessarily partisan manner, as if it were only “atheists” who assign a low prior probability to miracles. That is, of course, false. Many theists can and do assign low prior probabilities to all sorts of miracles, such as miracles which are seen as “competing” with the claims of their own faith tradition or religious community. (For example, orthodox Christians don’t hesitate to assign a low prior probability to the Mormon claim that the angel Moroni revealed the Book of Mormon to Joseph Smith on golden tablets.) Even no less an authority than Christian philosopher Stephen T. Davis has written about the “shocking” nature of the Resurrection.

Moving on:

There are many refutations of this phrase, which was popularized by Karl [sic] Sagan. One of the major problems with this idea is that atheists rarely get around to defining “extraordinary” either in terms of the claim [sic]

Irrelevant. The fact that many atheists do not define “extraordinary” does not in any way “refute” ECREE.

(why would belief in God be extraordinary? 90% of humanity believe in some form of God) [1]

Again, with all due respect to Metacrock, this statement shows that Metacrock doesn’t understand ECREE. We don’t determine whether a belief is extraordinary by measuring the percentage of people who hold that belief. Rather, ECREE is epistemic in nature; it has to do with what we would expect to be the case based upon our background knowledge.

The slogan ECREE is usually said to be based upon the Bayes [sic] completeness theorem.

No, this isn’t true. ECREE is often said to be best interpreted by BT, not “Bayes [sic] completeness theorem.”

Sagan popularized the slogan ECREE but the mathematical formula that it is often linked to (but not identical to) was invented by the man whose name it bears, working in the seventeen forties but then he abandoned it, perhaps because mathematicians didn’t like it. It was picked up by the great scientist and atheist Laplace and improved upon.[2] This method affords new atheism the claim of a “scientific/mathematical” procedure that disproves God by demonstrating that God is totally improbable. It is also used to supposedly disprove supernatural effects as well as they are rendered totally improbable.[3]

It is often assumed that the theorem was developed to back up Hume’s argument against miracles. Bayes was trying to argue against Hume and to find a
mathematical way to prove that there must be a first cause to the universe.[4] Mathematicians have disapproved of the theorem for most of its existence. It has been rejected on the grounds that it’s based upon guesswork. It was regarded as a parlor trick until World War II then it was regarded as a useful parlor trick. This explains why it was strangely absent from my younger days and early education as a student of the existence of God. I used to pour through philosophy anthologies with God articles in them and never came across it. It was just part of the discussion on the existence of God until about the year 2000 suddenly it’s all over the net. It’s resurgence is primarily due to it’s use by skeptics in trying to argue that God is improbable. It was not taught in math from the end fo [sic] the war to the early 90s.[5]

There are several problems with this account, but I will mention just the two most important.

First, this history of BT is misleading insofar as it suggests that BT is in doubt. It isn’t. BT follows from the Kolmogorov axioms of the probability calculus. To be sure, there are disagreements over the proper interpretation of probability (such as frequency vs. epistemic), but those issues do nothing to undermine the truth of BT.

Second, if someone read nothing about BT except the paragraphs quoted above, they would get the impression that BT is used solely by atheists and skeptics. That is nonsense! BT is used around the world every day on a variety of statistical problems that have nothing whatsoever to do with God, miracles, or the philosophy of religion. Furthermore, even within the philosophy of religion, it’s not just atheists who employ BT.

To cite the most obvious counter-example, has Metacrock never heard of Richard Swinburne or read any of his numerous books which use BT to defend Christian theism? (See here, here, here, here, here, here, and here.) Or seen Tim and Lydia McGrew’s impressive use of BT to argue for the Resurrection in The Blackwell Companion to Natural Theology? (See here.)

Metacrock is simply “barking up the wrong tree” on this one. I cannot think of any way to salvage his point.

(to be continued)