bookmark_borderOne Problem with Swinburne’s Case for God

In The Existence of God (2nd edition, hereafter: EOG), Richard Swinburne lays out a systematic cumulative case for the claim that it is more likely than not that God exists.
I have a specific objection to the third argument in this case, but I believe this objection throws a monkey wrench into the works, and creates a serious problem for the case as a whole.
To understand my objection, it is important to understand the general logical structure of Swinburne’s case for the existence of God. It is always natural and tempting to immediately focus in on the question of the truth of the premises of an argument for God, so in order to get a clear grasp on the logical structure of Swinburne’s case, it may be best to FIRST consider that structure apart from the specific content of the premises of the arguments in his case. The content of the premises will be important to make my objection, so we will get to the specific content at a later point.
One key idea in Swinburne’s logic is that we begin from a state of ignorance in which we are to imagine that we know ZERO empirical claims (both facts and theories). Swinburne thus controls the flow of empirical data, introducing one fact at a time, and arguing that in each case (with the exception of the problem of evil)  that the added fact increases the probability of the hypothesis that God exists.
The basic strategy is to (1) put forward an empirical fact, (2) show that the empirical fact is more likely to be the case if God were to exist than if there were no God, (3) conclude that the fact increases the probability of the hypothesis that God exists above the a priori probability that God exists (i.e. the probability based on ZERO empirical facts), then (4) introduce a second fact, (5) show that the second fact is more likely to be the case if God exists (and the first fact is the case) than if God does not exist (and the first fact is the case), (6) conclude that the second fact in conjunction with the first fact increases the probability that God exists above the probability based on the first fact by itself, (7) put forward a third fact, (8) show that the third fact is more likely to be the case if God exists (and the first two facts are the case) than if God does not exist (and the first two facts are the case), (9) conclude that the third fact in conjunction with the previous two facts increases the probability of the hypothesis that God exists above the probability based on just the previous two facts, and so on…slowly increasing the probability of God’s existence with each new fact.
Swinburne changes the strategy a bit when he gets to the argument from religious experience (in Chapter 13 of EOG), but the above pattern of reasoning is supposed to hold up until that point, and the above pattern of reasoning, filled in with the empirical facts that Swinburne has selected, is supposed to get us to the point where the probability of the existence of God is about .5 (meaning there is about a 50/50 chance that God exists).
Swinburne uses Bayes’ theorem to justify key inferences in his reasoning, so I will reformulate the above description of the logical structure of Swinburne’s case in terms of conditional probability statements.  Let’s use the letter e for evidence, plus a number to indicate which empirical claim we are talking about in the sequence of empirical claims introduced by Swinburne.  Thus, e1 represents the first empirical  claim in Swinburne’s case, and e2 the second empirical claim, and so on.
g: God exists.
k: [tautological background knowledge – analytic truths, truths of logic, math, and conceptual truths]
The probability of e1 being the case given that God exists is written this way:
P(e1|g & k) 
Here is how we represent the idea that the first factual claim is more likely to be the case if God exists (and we have only tautological truths as background knowledge) than if God does not exist (and we have only tautological truths as background knowledge):
P(e1|g & k) > P(e1|~g & k)
From this Swinburne makes use of Bayes’ theorem and infers that e1 provides evidence that increases the probability that God exists, over the a priori probability that God exists (the probability based on ZERO empirical facts):
P(g| e1 & k) > P(g| k)
Then Swinburne introduces a second factual claim e2. Again Swinburne argues that this factual claim is more likely to be the case if God exists than if God does not exist (now assuming e1 as part of our background knowledge, for after consideration of the first argument we are no longer completely ignorant of all empirical facts):
P(e2|g & e1 & k) > P(e2|~g & e1 & k)
From this Swinburne makes use of Bayes’ theorem and infers that the addition of this second empirical fact to the first empirical fact has again increased the probability of the existence of God, over what it was based on just the first fact by itself:
P(g| e2 & e1 & k) > P(g| e1 & k)
Then Swinburne introduces a third factual claim: e3. Again Swinburne argues that this factual claim is more likely to be the case if God exists than if God does not exist (now assuming both e1 and e2 as part of our background knowledge):
P(e3|g & e2 & e1 & k) > P(e3|~g & e2 & e1 & k)
From this Swinburne makes use of Bayes’ theorem and infers that the addition of this third empirical fact to the first empirical fact has yet again increased the probability of the existence of God, over what it was based on just the first two facts:
P(g| e3 & e2 & e1 & k) > P(g| e2 & e1 & k)
There are problems and objections that can be raised against each of the particular arguments that Swinburne uses to get up to the point where the probability of the existence of God supposedly reaches the halfway mark, but this post will focus on the third argument in the systematic cumulative case that Swinburne presents: The Teleological Argument from Spatial Order (hereafter: TASO).
TASO can be stated fairly briefly:
(e3) There is a complex physical universe that is governed by simple natural laws and the values of the constants of the laws and of the variables of the universe’s initial conditions make it probable that human bodies will evolve in that universe.
(g) God exists.
Remember, this is NOT a deductive proof for the existence of God.  (e3) is put forward NOT as a conclusive reason for (g), but merely as evidence for (g); (e3) is an empirical claim that is supposed to increase the probability of (g) relative to the probability of (g) based on just the two previous empirical claims:
(e1) There is a complex physical universe.
(e2) There is a complex physical universe that is governed by simple natural laws.
One problem is that it is not clear to me that (e3) is in fact true.  The fact that human bodies evolved once in this universe does NOT imply (by itself) that it was probable that human bodies would evolve in this universe.  I think a good deal of argumentation and evidence would be required to establish the truth of (e3).
Another more important problem with (e3) is one that Swinburne himself mentions and briefly discusses: “What reason would God have for taking an evolutionary route?” (EOG, p.188).  Swinburne goes on to talk about the beauty of the long cosmological “evolution” of the universe, and the beauty of plants and animals that resulted from the long history of biological evolution.  But this is all beside the point. God, being omnipotent and omniscient, could have brought about all of the beautiful plants and animals on earth including human beings in the blink of an eye.
God had no need to use the natural biological process of evolution, and no need to build such a process into the fabric of the universe.  The story in Genesis makes much more sense than evolution as the way that God would create animals and humans.  If there really was an omnipotent and omniscient person, then that person could have brought about all life on earth in an instant.  Most importantly, doing so would have bypassed hundreds of millions of years of animals suffering and dying from disease and parasites and predation and injury.  A huge amount of animal suffering was involved in the natural process of evolution, so a perfectly morally good person clearly would NOT have used evolution to produce human bodies when there was a much better solution ready at hand: create plants, animals, and humans instantly, as in the book of Genesis. So, it seems clear to me that contrary to Swinburne’s view, (e3) does not provide evidence in support of the existence of God, even assuming (e3) to be true.
But there is a deeper problem here than just the inductive inference from (e3) to (g).  What do we need to know in order to determine that (e3) is true?  I think we have to know, or have good reasons to believe, that the theory of evolution is true, and I think we have to know, or have good reasons to believe that the Big Bang theory of the universe is true.  What do we need to know in order to determine that the theory of evolution is true and that the Big Bang theory is true?  I think we need to know at least a little about: chemistry, biology, physics, paleontology, geology, cosmology, and astronomy.  We might not need to be experts in any of these scientific fields, but we need to have some grasp of some key facts, concepts, and theories in these areas of knowledge.
Furthermore, since the theory of evolution has been generally opposed by many Christian and Muslim religious believers, we need to have given some consideration to the problem of the apparent conflict between science and religion.  For example, if the Pope were to declare that evolution is a false theory, would that be a sufficient reason to reject this theory, even given all of the scientific evidence we have supports the theory?  What if the Bible clearly teaches that God created the world 6,000 years ago, is that sufficient reason to reject the theories and findings of geology and astronomy that indicate the age of the earth to be billions of years?  Unless one has done some thinking about science vs. religion, I don’t see how one can be fully justified in believing the theory of evolution. In sum, to have a justified belief in the theory of evolution and the Big Bang theory, one must have a bit of knowledge about the history and philosophy of science, in addition to knowing a good deal of scientific facts, concepts, and theories from several scientific disciplines.
OK.  Here is the big problem.  In order to know that (e3) is true, one must have a good deal of knowledge about science and about a number of important scientific disciplines, including a good deal of basic facts, concepts, and theories from a variety of scientific disciplines.  This means that the background knowledge that is in play in evaluating this third argument has grown exponentially.  A large portion of human knowledge has been pulled back into the picture, and Swinbure has completely lost control of the flow of data.  Because of the significant amount of empirical facts, concepts, and theories that are required to determine whether (e3) is true,  it is difficult to distinguish between such a sizable collection of information and knowledge and our normal everyday background knowledge.
One very important implication of this is that the problem of evil has itself been pulled back into the picture.  Knowing that the theory of evolution is true involves knowing that there has been hundreds of millions of years of animal suffering from disease, injury, parasites, and predation.  Swinburne’s strategy was to put off the problem of evil until after several empirical facts that favor the existence of God had been put forward one at a time, and the probability of the existence of God had been bumped upward several times.  But since the problem of evil has come rushing back in with just the third argument, it is no longer clear whether his logical strategy can work.  At any rate, the problem of evil cannot be dealt with after three or four more factual claims have been put forward in support of God’s existence.  The problem of evil must be faced as part of the consideration of the significance of (e3).

bookmark_borderThe Carrier-Barnes Exchange on Fine-Tuning

Reader GGDFan77 asked me for my thoughts on the exchange between Dr. Richard Carrier, who I respect and consider a friend, and Dr. Luke Barnes regarding fine-tuning arguments. I initially responded in a series of comments in the combox for my post about Hugh Ross’s estimates for the probability of life-permitting prebiotic conditions. But those turned out to be so lengthy that I think the topic deserves its own dedicated post.
Here’s some brief context for readers not familiar with the exchanges between Dr. Richard Carrier and Dr. Luke Barnes:
* Dr. Carrier wrote an essay, “Neither Life Nor the Universe Appear Intelligently Designed,” in The End of Christianity (ed. John Loftus, Buffalo: Prometheus Books, 2011), pp. 279-304.
* Dr. Barnes wrote a four part series on his blog critiquing that essay by Carrier.
* Dr. Carrier and Dr. Barnes had an extensive back-and-forth exchange in the combox on Carrier’s blog.
Let me preface my comments by saying that I have a lot of empathy for any writer, including Dr. Carrier, who is trying to use the formal apparatus of Bayes’ theorem in a way that is accessible to a beginning-to-intermediate audience, which I take to be the target audience of The End of Christianity. If you go for too much precision and formalism, you risk losing your audience. If you focus too much on accessibility, you risk misunderstandings, oversimplifications, and outright errors. Finding the right balance isn’t easy.

Part 1

With all due respect to Dr. Carrier, I find part 1 of Dr. Barnes’ critique to be very persuasive and, in fact, to be a prima facie devastating critique. (I quickly skimmed the combox on Dr. Carrier’s site to see if they debated anything relevant to part 1, but I didn’t find anything, so it appears that the points in part 1 of Dr. Barnes’ series have gone unchallenged by Dr. Carrier.)
In particular, I agree with the following points by Dr. Barnes.

  • “Bayes’ theorem, as the name suggests, is a theorem, not an argument, and certainly not a definition.”
  • “Also, Carrier seems to be saying that P(h|b), P(~h|b), P(e|h.b), and P(e|~h.b) are the premises from which one formally proves Bayes’ theorem. This fails to understand the difference between the derivation of a theorem and the terms in an equation.”
  • “Crucial to this approach is the idea of a reference class – exactly what things should we group together as A-like? This is the Achilles heel of finite frequentism.”
  • “It gets even worse if our reference class is too narrow.”
  • “This is related to the ‘problem of the single case’. The restriction to known, actual events creates an obvious problem for the study of unique events.”
  • “Carrier completely abandons finite frequentism when he comes to discuss the multiverse.”
  • “Whatever interpretation of probability that Carrier is applying to the multiverse, it isn’t the same one that he applies to fine-tuning.”
  • “If we are using Bayes’ theorem, the likelihood of each hypothesis is extremely relevant.”

In addition, I would add the following comment.

  • In his essay, Carrier writes: “Probability measures frequency (whether of things happening or of things being true).” Not exactly. The frequentist interpretation of probability measures relative frequency, but the frequentist interpretation of probability isn’t the only interpretation of probability. There are “many other games in town” besides that one; there is also the epistemic interpretation of probability (aka “subjective” aka “personal” aka “Bayesian”), which measures degree of belief. Thus, to say that probability just is relative frequency is to beg the question against all the rival interpretations of probability. (And, for the record, I’m actually a pluralist when it comes to probability; following Gillies, I think different interpretations can be used in different situations.)

Part 2

Here are my thoughts on Part 2 of Dr. Barnes’ reply.

This simulation tells us nothing about how actual cars are produced.

I strongly agree.

The fact that we can imagine every possible arrangement of metal and plastic does not mean that every actual car is constructed merely at random.

I agree.

Note a few leaps that Carrier makes. He leaps from bits in a computer to actual universes that contain conscious observers. He leaps from simulating every possible universe to producing universes “merely at random”.

I agree.

 This is a textbook example of affirming the consequent, a “training wheels” level logical fallacy.”

I think this is an uncharitable interpretation of Carrier’s statements by Barnes.

False. Obviously False.

I disagree with Barnes. Here is the passage by Carrier which Barnes is referring to.

It simply follows that if we exist and the universe is entirely a product of random chance (and not NID), then the probability that we would observe the kind of universe we do is 100 percent expected.

Let’s abbreviate the statement “we exist” as B (for our background knowledge); the statement “the universe is entirely a product of random chance (and not NID)” as C (for chance); and the statement “we observe the kind of universe we do” as E (for evidence). Then we can abbreviate the paragraph just quoted as:

Pr-L(E | B & C) = 1, where Pr-L represents a logical probability.

It seems to me that Carrier is correct. Contrary to what Barnes writes, however, it doesn’t follow that we can’t conclude it is highly probable someone was cheating in a game of poker. It just means that the correct way to show that cheating took place is not to use an argument analogous to the argument Carrier is refuting.
Aside: Reading the exchange between Carrier and Barnes reminds me of one of my wishes for people who use Bayes’ Theorem in this way: I really wish people would explicitly state the propositions they are including in their background knowledge. It avoids misunderstandings and misinterpretations.

Carrier says that “if the evidence looks exactly the same on either hypothesis, there is no logical sense in which we can say the evidence is more likely on either hypothesis”. Nope. Repeat after me: the probability of what is observed varies as a function of the hypothesis. That’s the whole point of Bayes theorem.”

I think Barnes is being uncharitable to Carrier. When Carrier writes, “the evidence looks the same,” I interpret him to mean “when the evidence is equally likely on either hypothesis.”

All that follows from the anthropic principle…

I need to study this section in detail, but I think agree with Barnes.
I would add the following. In his essay, Carrier writes this:

Would any of those conscious observers be right in concluding that their universe was intelligently designed to produce them? No. Not even one of them would be.

It would be most helpful if Carrier would explicitly defend this statement: “No. Not even one of them would be.” Unless I’ve misunderstood his argument, I think this is false. If we include in our background knowledge the fact that Carrier’s hypothetical conscious observers exist in a universe we know is the result of a random simulation, then we already know their universe is the result of a random simulation. Facts about the relative frequency aren’t even needed: we know the universe is the result of a random simulation.
If, however, we exclude that from our background knowledge, so that we are in the same epistemic situation as the hypothetical observers, then things are not so easy. Again, it would be helpful if Carrier could spell out his reasoning here.

Part 3

Let’s move onto Part 3 of Barnes’s reply.

“Refuted by scientists again and again”. What, in the peer-reviewed scientific literature? I’ve published a review of the scientific literature, 200+ papers, and I can only think of a handful that oppose this conclusion, and piles and piles that support it.

I think Dr. Carrier absolutely has to respond to this point by Dr. Barnes or publicly issue a retraction.

With regards to the claim that “the fundamental constants and quantities of nature must fall into an incomprehensibly narrow life-permitting range”, the weight of the peer-reviewed scientific literature is overwhelmingly with Craig. (If you disagree, start citing papers).

This strikes me as a devastating reply. Like the last point, I think Dr. Carrier absolutely has to respond or else issue a retraction.

He can only get his “narrow range” by varying one single constant”. Wrong. The very thing that got this field started was physicists noting coincidences between a number of constants and the requirements of life. Only a handful of the 200+ scientific papers in this field vary only one variable. Read this.

Ouch. Same as the last two points.

“1 in 8 and 1 in 4: see Victor Stenger”. If Carrier is referring to Stenger’s program MonkeyGod, then he’s kidding himself.

I haven’t studied MonkeyGod enough to have an opinion, so I have no comment on this one.

In all the possible universes we have explored, we have found that a tiny fraction would permit the existence of intelligent life. There are other possible universes,that we haven’t explored. This is only relevant if we have some reason to believe that the trend we have observed until now will be miraculously reversed just beyond the horizon of what we have explored.

If I understand Dr. Barnes’ point correctly here, then I think he is making a simple appeal to induction by enumeration and I think his argument is logically correct.

In fact, by beginning in our universe, known to be life-permitting, we have biased our search in favour of finding life-permitting universes.

I find this point very interesting. I hadn’t even thought of it that way, but I think he’s right.

Nope. For a given possible universe, we specify the physics. So we know that there are no other constants and variables. A universe with other constants would be a different universe.

think I agree with this.

How does a historian come to think that he can crown a theory “the most popular going theory in cosmological physics today” without giving a reference? He has no authority on cosmology – no training, to expertise, no publications, and a growing pile of physics blunders.


In any case, the claim is wrong…

I don’t have the physics expertise to evaluate this paragraph.

By what criteria is that the simplest entity imaginable? If the point is lawless, why does it evolve into something else? How does it evolve? What evolves? What defines the state space? If it is a singular point, how are there now many spacetime points? Why are they arranged in a smooth manifold? Why spacetime? What if space and time aren’t fundamental? It’s not clear that a lawless physical state makes any sense. Even if it does, if it’s lawless, why do we observe a law-like universe?

Good questions.

Fine-tuning doesn’t claim that this universe has the maximum amount of life per unit volume (or baryon, or whatever). So this argument is irrelevant.

Dr. Barnes is, of course, correct that fine-tuning doesn’t logically entail that this universe has the maximum amount of life per unit volume, in the sense that “fine-tuning” is logically compatible with “the universe NOT having the maximum amount of life per unit volume.” But I disagree with Dr. Barnes that the hostility of life is irrelevant. In fact, as I’ve argued before, focusing only on facts about “fine-tuning” while ignoring facts about “course-tuning” (i.e., the hostility of the universe to life) commits the logical fallacy of understated evidence.

Part 4

Let’s move onto part 4 of Dr. Barnes’ reply. Barnes writes:

What is Carrier’s main argument in response to fine-tuning, in his article “Neither Life nor the Universe Appear Intelligently Designed”? He kept accusing me of misrepresenting him, but never clarified his argument.

I agree.

Bayes’ theorem follows from Cox’s theorem, which assumes only some reasonable desiderata of reasoning.

I haven’t studied Cox’s theorem, so I can’t comment on that directly. Instead, I want to point out that Bayes’s theorem also follows from the Kolmogorov axioms of the probability calculus plus the definition of conditional probability.

A given proposition Ki can play the role of “background” or “evidence”, depending on the term.

I agree.

Talking about “the prior” or “the likelihood” in such a context is ambiguous. Better to use notation.

I strongly agree.

Look closely at p(o | ~NID.b’). This is the probability that a universe with intelligent observers exists, given that there is no intelligent cause of their universe, and given background information b’ that does not imply o. This is exactly the probability that Carrier is afraid of, the one that could equal an “ungodly percentage” (pg. 293). It is the probability that “the universe we observe would exist by chance” (pg. 293). Carrier argues that this term is irrelevant because ignores o. It does, but rightly so. The posterior does not ignore o. Look at Bayes’ theorem: p(H|EB) = p(E|HB) p(H|B) /p(E|B).  Both E and B are known, and yet the likelihood p(E|HB) just ignores the fact that we know E! Rightly so! This is the whole point of Bayes’ theorem.

1. Here I think Dr. Barnes is being just a tad snarky (“This is exactly the probability that Carrier is afraid of”).
2. This may be a nitpick, but I wouldn’t word things the way Dr. Barnes does, when he writes that p(o | ~NID.b’) is “the probability that ‘the universe we observe would exist by chance.'” Instead, I would define that probability in plain English as “the probability that intelligent observers exist conditional upon our background knowledge conjoined with the hypothesis that a non-terrestrial intelligent designer did NOT design the universe.” The key difference here is that the latter phrasing keeps the distinction between “the universe we observe” and “intelligent observers exist.”
3. I strongly agree with this: “Carrier argues that this term is irrelevant because ignores o. It does, but rightly so. The posterior does not ignore o. Look at Bayes’ theorem: p(H|EB) = p(E|HB) p(H|B) /p(E|B).  Both E and B are known, and yet the likelihood p(E|HB) just ignores the fact that we know E! Rightly so! “
4. Again, this may be another nitpick but I agree and disagree with this statement: “This is the whole point of Bayes’ theorem.” Not exactly; here I think Dr. Barnes is unwittingly presupposing the epistemic interpretation of Bayes’s theorem. Based on that interpretation, he’s correct. On rival interpretations–such as the frequency interpretation–we wouldn’t talk about knowledge at all, but the relative frequency among some reference class.

Here’s the problem with the argument above. What (3) shows is that, since f follows from o, I need not condition the posterior on f. There is a redundancy in our description of what we know. But that does not mean that the posterior p(NID|f.b) is independent of the “ungodly percentage” p(o | ~NID.b’). The surprising fact on ~NID, that a life-permitting universe universe exists at all, cannot hide in the background. We can draw it out. It’s right there in equation (7).

I agree. Dr. Barnes is making a very similar point to the one I make below, where I talk about pushing the problem back a step.

There a couple of different versions of NID floating around Carrier’s essay….

I agree with pretty much this entire section of Dr. Barnes’s essay.

Question 5: What mathematician should I read to learn about reference classes and why probabilities measure frequencies? Is Carrier a frequentist or a Bayesian?

Actually, this is a question not best suited for a mathematician, but a philosopher. In my opinion, the “go-to” reference books for this question are (1) Choice & Chance by Brian Skyrms and (2) Philosophical Interpretations of Probability by Gillies.

Question 9: Moving on to Carrier’s scientific claims, there’s some explaining to do.

I think Dr. Carrier must directly answer the questions in the bulleted list that follows.

This time could have been spent showing that I am wrong. More time is spent attacking me than defending, or even explaining, his case. Take the comment on January 7, 2014 at 8:43 am. Of 14 sentences: 1 clarification of a previous comment, 2 repetitions of points from his article that I agreed with, 2 claims contrary to mine (hurray! interaction!), and 9 that merely accuse of error and incompetence.

I strongly agree. I hope that Dr. Carrier will directly respond to Dr. Barnes without the personal attacks.

Carrier’s Endnote 23

GGDFan777 also asked me to parse endnote 23 of Dr. Carrier’s essay. Unless otherwise indicated, the quotations are from that endnote.

This is undeniable: if only a finely tuned universe can produce life, then by defintion P(FINELY TUNED UNIVERSE | INTELLIGENT OBSERVERS EXIST) = 1, because of (a) the logical fact that “if and only if A, then B” entails “if B, then A” (hence (“if and only if a finely tuned universe, then intelligent observers” entails “if intelligent observers, then a finely tuned universe,” which is strict entailment, hence true regardless of how that fine-tuning came about; by analogy with “if and only if colors exist, then orange is a color” entails “if orange is a color, then colors exist”; note that this is not the fallacy of affirming the consequent because it properly derives from a biconditional), and because of (b) the fact in conditional probability that P(INTELLIGENT OBSERVERS EXIST)=1 (the probability that we are mistaken about intelligent observers existing is zero, a la Descartes, therefore the probability that they exist is 100 percent) and P(A and B) = P(A|B) x Pr(B), and 1 x 1 =1.

I agree.

Collins concedes that if we include in b “everything we know about the world, including our existence,” then P(L | ~God & A LIFE-BEARING UNIVERSE IS OBSERVED) = 100 percent (Collins, “The Teleological Argument,” 207).

I don’t have access to the material by Collins, but I don’t have any reason to doubt that what Carrier says here is correct.

He thus desperately needs to somehow “not count” such known facts. That’s irrational, and he ought to know it’s irrational.

Sigh. I think the statement “desperately needs” is snarky and off-putting. I think these two sentences are uncharitable to Collins, for reasons I will explain below.

He tries anyway (e.g., 241-44), by putting “a life-bearing universe is observed” (his LPU) in e instead of b. But then b still contains “observers exist,” which still entails “a life-bearing universe exists,” and anything entailed by a 100 percent probability has itself a probability of 100 percent (as proven above). In other words, since the probability of observing ~LPU if ~LPU is zero (since if ~LPU, observers won’t exist), it can never be the case that P(LPU|~God.b) < 100 percent as Collins claims (on 207), because if the probability of ~LPU is zero the probability of LPU is 1 (being the converse), and b contains “observers exist,” which entails the probability of ~LPU is zero.

I agree with his analysis, but — you knew there was a “but” coming — I think this misses the point, which seems to be a restatement of the anthropic principle dressed up in the formalism of probability notation. Yes, if we include “(embodied) intelligent observers exist” in our background knowledge (B), then it follows that a life-permitting universe (LPU) exists. But that isn’t very interesting. In one sense, this move simply pushes the problem back a step.
To see why, we can (in a sense) do a Bayesian analysis in reverse. Abstract away everything we know, including our own existence, and include in our background knowledge only the fact that our universe exists. Based on that fact alone, the prior (epistemic) probability of “(embodied) intelligent observers exist” is not 1 on naturalism and it is not 1 on theism.
In the jargon of academic philosophy of religion, the proponent of a fine-tuning argument for theism is asking us to compare the epistemic probability–not relative frequency–of a life-existing universe conditional upon theism to the epistemic probability of a life-existing universe conditional upon naturalism. To respond to that argument with “But we exist” misses the point.
The proponent of the fine-tuning argument can, should, and will respond, “No shit, Sherlock. Everyone agrees that we exist. The question is whether the life-permitting preconditions of our universe is evidence relevant to theism and naturalism.”

If (in even greater desperation) Collins tried putting “I think, therefore I am” in e, his conclusion would only be true for people who aren’t observers (since b then contains no observers), and since the probability of there being people who aren’t observers is zero, his calculation would be irrelevant

Again, I find the snark (“greater desperation”) off-putting, but let’s put that aside. At the risk of repeating myself, the fact that each of us knows that we exist doesn’t make fine-tuning arguments go away. Yes, we know that our universe is life-permitting because we know that we exist. But why is our universe life-permitting? Some philosophers (including both theists and atheists like Paul Draper) argue that that is evidence favoring theism over naturalism. If they are right, then so be it. But if they are wrong, they are NOT wrong because we exist. That objection just doesn’t work.

(it would be true only for people who don’t exist, i.e., any conclusion that is conditional on “there are no observers” is of no interest to observers).

Dr. Carrier doesn’t speak for all observers. I’m an observer and find the question of interest. So does Paul Draper. So do many atheist philosophers who don’t think fine-tuning arguments work, including Bradley Monton, Keith Parsons, Graham Oppy, Quentin Smith, and so forth. So do many (but not all) theist philosophers. So do many non-philosophers of all stripes. If he doesn’t find the question of interest, that’s fine. But, at risk of stating the obvious, his lack of interest in the argument isn’t a defeater for the argument.

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)

bookmark_borderVictor on Weird Stuff

Victor Reppert has been kind enough to reply on his Dangerous Idea blog to my comments on his earlier posting. I’m replying to his reply, which will evoke a counter-reply, which will get a counter-counter-reply…until one or the other of us has some real work to do and has to break it off. Sigh. That is the damn problem with these discussions. They could go on for lifetimes, but we academics have to work them in between grading papers, committee meetings, publishers’ deadlines, etc.

Anyway, here is what he says:

“I have trouble seeing why people are so sure that he [the supposedly clairvoyant violin teacher] didn’t know, even if they are naturalists. Does he really know that this is naturalistically impossible? It might be less likely given naturalism than given supernaturalism, and thus the evidence might probabilistically support supernaturalism via Bayes’ theorem. (OK, OK, people accuse me of abusing Bayesian probability theory on a daily basis, so I’m already bracing myself). But the most we can say, I think, if my teacher knew that my rival had gone down and been upset, this might be difficult to explain naturalistically based on what we know about nature at this point. Why do we have to assume it was a guess that turned into an appearance of knowledge because of confirmation bias.

A few more details about the incident are relevant here. First, he said he had this “perception” just at the time when the rival went down. Second, my violin teacher never reported anything like this in the three years when he was my teacher. It’s not as if he brought up a bunch of them, and this one just happened to fit. He did mention other clairvoyant incidents, but didn’t claim to have a whole lot of them. Third, although spellers, like all competitors, experience the agony of defeat, nobody ever was quite as demonstrative as this guy. So I’m just not sure you can chalk it all up to guesswork and confirmation bias. In fact, in the absence of some good reasons to believe that he couldn’t have known something that was going on a couple of miles away in that school auditorium, I think the reasonable thing to say would be that he did know.

But, of course, we have to consider the not only the probability of the event given naturalism, but we must also consider the laws of supernature. How probable is the event given supernatural involvement. Is it the sort of thing God is likely to do, or not, if we suspect God? Of course, Keith and I disagree as to whether it is possible to consider the laws of supernature, but people who have beliefs about supernature have probabilistic expectations concerning what to expect from supernature. If you say that’s not enough for a law, well guess what. In quantum mechanics all you get are probabilities also. Are we worried that God isn’t observable? Well, science commits to unobservables all the time.

In considering miracles claims like the Resurrection, we can formulate a theory about what kinds of miracles God is likely to perform, and why he would perform them. Given this theory, we can ask whether the historical evidence is more likely to be the sort thing we should expect if the theistic theory is true, or whether it is more like the sort of thing we should expect if the theistic theory is false. There is a very large trail of historical evidence to look at.

Of course, you can end up deciding that yes, the historical evidence confirms the theistic story, but the atheistic account is more probable based on the total evidence, or relative to your priors.

Have the laws of nature been established by a firm and unalterable experience, as Hume suggests? I don’t think so. My experience is far from establishing the laws of nature on a firm and unalterable basis. What about yours?”


Is clairvoyance impossible given naturalism? I certainly see no reason to think so. We currently have no idea, given what we know about the natural world, how clairvoyance, ESP, etc. could possibly work, and no scientific (as opposed to anecdotal) evidence that it does work. However, it strikes me as dogmatic to say that such events could not someday be verified and scientifically explained. No, my point is that skepticism about anecdotal reports of clairvoyance or other paranormal occurrences is abundantly justified, to the point that we can very reasonably dismiss such stories without further ado.

Consider what we know about memory. I hope I do not embarrass Victor when I reveal that he is within a year or two of my age (58). This means that for him, as for me, seventh grade was a looooong time ago. Memory is not a recording device. It is a story teller. In telling stories to ourselves and others repeatedly, what gets locked in our memories is not what happens, but the stories we tell. It is far too easy to think that the foibles of memory only happen to other people while our memories are clear. So, Victor may–in all honesty, of course–be reporting details that did not happen. The plasticity of memory is naturally a problem with all reports of extraordinary occurrences (Let’s see, was that one angel, or two men in dazzling apparel, or just a young man dressed in white at the empty tomb?).

A principle of rationality that I endorse is this: “When you hear hoofbeats in the distance, think ‘Aha, horses!’ not ‘Aha, unicorns!'” In other words, try hard to give something an ordinary explanation before resorting to a weird one. What I have from Victor is not the original event but a report of an event that allegedly occurred 40+ years ago. That report is the “hoofbeats” here. How best to explain the occurrence of such a report? Even supposing that the event happened exactly as Victor reports it, it would be credulous in the extreme to conclude that this was a genuine case of clairvoyance. Humans have a strong tendency to underestimate the prevalence of coincidence, and paranormalists thrive in that lacuna of human rationality.

Let me illustrate with my own anecdote. Needless to say, World War II seriously disrupted relationships and friendships, sending people for years to distant locales. During the War, my father lost track of an old friend. One day, a couple of years after the War, he was walking down the streets of Atlanta and thought he saw the old friend walking down the block ahead of him. He increased his pace, moving to catch up. Just as he was about to catch up, he blunders into a man who just stepped out of a shop. He steps back to apologize and sees that the man he blundered into was the old friend he thought he was pursuing. Something paranormal? Nope. Coincidence? Yep. Of course, such events are so striking and surprising when they occur, that we have a hard time accepting that they are “just coincidence.” Yet, over the course of a normal lifetime, highly improbable events of some sort or another are almost certain to occur. On a given day, an event like that might be most unlikely, but at some point in the approximately 30,000 days of an 80 year life, it very well could happen.

Victor also notes, correctly, that in estimating the probabilities of miracles, we have to recognize that these estimates will rationally differ given people’s priors. Therefore, the degree of credulity or incredulity with which we approach a miracle report can be rationally different for different people. OK, but I am interested in miracle claims adduced for apologetic purposes. As I see it there are two kinds of religious apologetic–soft apologetic and hard apologetic. Soft apologetic endeavors to reassure the faithful that their beliefs are, for them, reasonable. Thus if a Sam Harris or Richard Dawkins type says that religious believers are all fools or knaves, a soft apologist would show that believers need be neither. Hard apologists, on the other hand, try to bludgeon people like me into belief. But if you are going to try to convince me, you have to work with MY priors, not yours. Soft apologetic is easy to do; hard apologetic is hard.

Is it reasonable for Victor to believe in some miracles, the Resurrection, say? Sure. Why not? Is it reasonable for me to disbelieve it? I defy anyone and everyone to show me that it is not.

Finally, Victor says that his experience is far from establishing the laws of nature on a firm and unalterable basis. Two questions here: (1) If so, does not this make the task of the apologist much harder in trying to convince the well-girded skeptic? If we really don’t have any firm basis for regarding certain things as physical impossible, and I am given evidence that someone rose from the dead, I could just pass this off as something that happens from time to time. No miracle is needed if no natural law had to be violated. (2) OK, well what then is wrong with the following?: A man applied to a welfare agency for public assistance and got back the following bureaucratic missive: “Dear Sir, Our records indicate that you are presently deceased, and therefore ineligible for public assistance. Should your condition have changed, please notify this office within the next thirty days.” Well, holy mackerel. Something is wrong here. If “firm and unalterable experience” have not shown us that the dead remain dead, what has gone wrong???