Thursday, August 28, 2008

Doctor Logic's Humean Objection

You can also criticize the argument by maintaining, in a broadly Humean way, that the claim that Jesus is God is an extraordinary claim that requires extraordinary evidence. Hence if you have some evidence that Jesus claimed to be God, and that Jesus possessed the character of a great moral teacher, and that it is highly improbable that Jesus could have had the character of a great moral teacher while at the same time falsely claiming to be God, you still can't get to the conclusion that Jesus was God if the claim that Jesus is God is so antecedently improbable that the evidence for the other propostions can't get the claim anywhere near probability .5. I can lay this all out with Bayes'theorem:

p (h/e) (The consequent probability of the claim Jesus is God after the evidence concerning Jesus' claim to be God and his being a great moral teacher is considered) = P (h) (the antecedent probability that Jesus is God) X P (e/h), (how probable the evidence would be if Jesus were God) over P (e) (how probable the evidence would be whether or not Jesus is God.

Doctor Logic's claim is that the claim "Jesus is God" is so antecedently improbable that the even if historical evidence provides some confirmation of the claim, and if all the naturalistic scenarios have plausibility problems, the argument still fails.

I addressed this issue in my essay replying to Hume on miracles, and C. S. Lewis addressed in in chapter 13 of Miracles. I link to my own essay here.


Doctor Logic said...


Let's zoom in on your fundamental complaint. You claim the frequentist approach leaves one in ambiguous situations. Specifically, you give an example based on baseball statistics. You say:

Have these batters faced Williams too few times for this last statistic to count? And can this be straightforwardly determined from experience?

I'll answer that. Yes. We can get statistics about statistics. Scientists do this constantly. They evaluate whatever they can, including the likelihood of bias in selecting the relevant statistical measure or reference class.

You want to make the decision about opening up a new reference class one of personal "judgment". Well, I think your use of the term "judgment" is misleading. "Bias" is the word you're looking for. And there's lots of statistical evidence about human bias.

Let's look at your argument as applied to the Resurrection.

What we know is that if Jesus belongs to any historical reference class, and if the Christian cult belongs to the class of similar cults, then the Resurrection is almost certainly false.

Your argument, applied by analogy, is that Jesus might not be a member of the set of normal humans, and the Christian cult was not a typical of such cults, so maybe our statistics are useless.

But we both know that there is a mountain of statistics that help us decide whether we ought to create new reference classes for such claims. There are (and have been) many claimants to superhuman abilities out there. Benny Hinn is one of them. John Edwards (the psychic) is another. Statistics show that such people are frauds. In every case that has been resolved. By your logic, if I am a Hinn-believer I am justified in creating a new reference class just for Hinn and his crowd.

[Note: These cases could be resolved by statistics in the favor of the claimant. If Uri Geller repeats his feats with enough statistics, we can easily be convinced of his powers in a frequentist picture. However, paranormal claimaints have NEVER have been vindicated so!]

So your attack on frequentism only stands if you disallow frequentism about frequentism. Actually, I don't think you said that. You just tried to make the situation look horribly complex to the reader, as if to suggest that it could not be resolved in a frequentist approach.

To sum up, if you devise a method of inventing new reference classes, we will simply find general statistics about the validity of your method.

Another of your attacks, the one on the "anything goes" objection, is analogically broken. You said that a Gremlinist theory of the Christian myth is not as plausible as the Christian theory of the Christian myth. Do you see the flaw in this? Your analogue is not a gremlin theory of the Christian myth, but a gremlin theory of a Gremlin myth. You're assuming throughout your defense that the stories in the Bible are true facts, and that the Christian testimony explains the facts well (if it does). But they are not true facts that are being "explained". The so-called facts are themselves examples of Christian testimony. So what you have is a case of Christian testimony being "explained" by Christian testimony.

Finally, I want to answer the following philosophical argument:

But this attempt to go from a statistical "is" to an epistemological "ought" seems to suffer from with the same (or worse) difficulties that getting "ought" from "is" suffers from in ethics, and here again Hume's empiricist/foundationalist assumptions impose an impossible burden on probability theory.

You are right that there is, at philosophical root, an epistemological "ought" that won't be justified by statistics alone. It can only be justified by a desire. By a bias, if you will. And what is this "bias"? It is whether or not you are biased for or against your own biases. Do you want a belief system in which every experience confirms what your bias says, or do you want a belief system in which your biases can be wrong about the world? Do you want the guarantee of your bias proving out in the end? It's there for the taking if you want it.

This is an ought question. A moral question. Personally, I don't believe in objective morality. As in any moral debate, I can only appeal to your own moral bias. We ought not be biased towards our own bias in matters of what is. That means the personal bias to create a new reference class (and an untestable one at that) is immoral. It's a case of believing what you want to believe.

Anonymous said...

Doctor Logic, you say that Uri Geller's abilities could be established if he demonstrated his powers with enough statistics. If the Humean count is correct, how would this occur? Just as testimony occasionally fails us, so do our eyes, our scientific instruments, and our interpretations of experimental data. If you're advocating a strictly Humean approach, it would seem like a hundred demonstrations of Geller's magical powers is no better than one. In each case, it's more likely that our eyes, or our instruments, or our interpretations are failing us than it is that Nature's laws have been violated.

Maybe I'm missing something, but it seems to me that you could never justify the supernatural on the basis of many confirmed cases if your analytical method essentially forbids you from ever granting that a single instance happened, regardless of the evidence for it. (After all, it's more likely that the evidence has been forged, or misinterpreted, or misrepresented, or "pick your alternative to supernaturalism here".)

You end your response by saying it's morally imperative that we have a belief system that can confront our biases about the world. Can you, then, tell us how your method would confirm a miracle, should one occur?

Doctor Logic said...


Highly improbable events can be shown to have occurred. You just need to acquire comparable statistics or leverage the statistics you already have.

I'll use the Geller example.

Experience shows that familiar metals do not bend or break with the application of thought power. Rather, they bend or break due to applied energy that breaks bonds. There have been thousands of experiments that have established this. Indeed, we now rely on this fact, e.g., to build airplanes. We would, for example, discount a theory that said that an airplane crash was caused by a passenger dreaming about bending rivets in the skin of the fuselage.

Now Geller comes along claiming to bend metal forks with his thoughts. For his claim to be true, we need to establish that no energy is getting into the metal from conventional sources, and that the metal is normal, familiar metal. If we can establish this, we will know that Geller is not a normal person.

So we set up multiple instruments that measure conventional energy sources. Suppose the instruments have been tested in thousands of experiments, and their accuracy and reliability have been well-established. Suppose we use 20 instruments and each is reliable to 1 part in 10^5. And suppose the experiment is blind so that the experimentalists don't know which instruments are connected to the Geller fork versus the control fork. Suppose that the metal is consistently found to be normal, and no conventional source of energy can be found entering the fork. In the end, we will have a situation in which it is too improbable that ALL the instruments and experimentalists failed simultaneously. If it is 1 in a 10 billion that Geller was telling the truth based on background, we can repeat the experiment with sufficient controls and reliability that we can show Geller to be an exception to the general rules established by past experience. Eventually, our past experience (with instrumentation and composition) is leveraged in Geller's favor. Further, the statistics are cumulative if the event can be repeated.

However, we cannot do any of this without controls and statistics. If we let Geller run the experiment, and supply the equipment, and write the lab report, then the result isn't worth the paper it's printed on.

Thus, it is quite straightforward to justify new claims that are highly improbable based on background knowledge, but we require experience that is leveraged by statistics.

However, if the new claim implicitly or explicitly denies the possibility of obtaining experience backed by statistics, then the claim can be junked immediately. It will never accumulate statistics in its favor.

Anonymous said...

So, you disagree with Hume, then? In the situation you describe, you think it more likely that Geller has magical powers than it is that all the instruments failed at the same time?

Doctor Logic said...


The experiment would clearly show that Geller has a power, and that this power is peculiar in the universe. (Though it doesn't show that it is "magical" per se.)

The question is whether the experimental validation renders Geller's abilities non-miraculous. If it does, then Hume is right. Otherwise, I am disagreeing with Hume.

Anonymous said...

But the question at issue is how you would identify SUPERNATURAL powers via your method. If the most your experiment can prove is that Geller's power is "peculiar", then your method of investigation fails to live up to your stated standards.

It seems to me that, outside of simultaneous equipment failure, if Geller seems to pass the tests you give him, you have two options.

1. Geller has supernatural powers.

2. Geller's powers are the result of some presently unknown but completely natural phenomenon.

What would it take for someone using your method to conclude that 1. was more probable than 2.?

Anonymous said...

Let me be more explicit.

I'm assuming you're advocating a strictly frequentist approach. And I'm assuming that you hold that supernatural abilities have never previously been experimentally verified, while there have been many instances where phenomena that haven't been explainable under contemporary scientific pictures of the world were subsequently fully explained by later scientific pictures of the world. Thus, I assume that under a frequentist account, the supernatural explanation will always be far less probable than the unknown natural explanation. And what I'm asking is, what experimental or statistical method could possibly tip the scales in favor of a supernatural explanation?

Doctor Logic said...


What is the definition of supernatural?

I have put forward my own definition of natural versus supernatural. Natural means predictable and deterministic (even if only probabilistically). That's why physicalism is a subset of naturalism.

The opposite of naturalism is something wholly unpredictable and non-deterministic.

But explanations require predictive theories. There's simply no such thing as a supernatural explanation. For example, "fate" is not an explanation for anything. It is a circular reference to what happened. Consequently, there never can be evidence for the supernatural because supernatural events aren't the best explanation for anything. God is no more predictive than fate, no more predictive than a theory we have yet to discover.

On the other hand, this might not be a problem for you. Supernatural is not the same thing as non-physical.

Anonymous said...

So, why are you pretending that you can use a frequentist Bayesian approach to methodologically exclude the supernatural when all you are really doing is ruling it out by definition?

In your view, if a supernatural claim fails the test, that proves that the event in question wasn't supernatural. However, if a supernatural claim passes the test, that ALSO proves that the event in question wasn't supernatural!

You said it was morally imperative that our methods be able to overcome our biases and show us we are wrong about the world. It seems obvious that your method can't do that.

Even if the skies split open, and all of humanity saw a terrifying giant being of majestic power, with lightning bolts for eyes, a countenance as bright as a thousand suns, and a voice like thunder, and this being pointed right in your face and said "Be assured, Dr. Logic, I exist", you would still stick to your refrain that "the supernatural can't explain anything".

I don't see how a method that could yield such an absurd result could be considered a rational approach.

Doctor Logic said...


So your definition of the supernatural is the same as mine?

If so, our inability to accept supernatural explanations is like our inability to accept square circles. Ought I change my epistemology to accept square circles because I think they'll give me eternal life, universal justice, etc?

Besides, the question was whether the Resurrection occurred, not whether Jesus is supernatural in the sense I have outlined.

"Be assured, Dr. Logic, I exist", you would still stick to your refrain that "the supernatural can't explain anything".

So is the voice a natural effect or a supernatural one? How will you tell the difference? Do you even have a definition of the supernatural? I suspect you don't.

Anonymous said...

I think there are any number of definitions of the supernatural available which aren't so nakedly question-begging and deck-stacking. I seriously doubt you'll find a religious person who defines supernatural as something utterly random, which is what you suggest. Nearly all religious people believe the supernatural works in ways that are, in some sense, regular. Christians believe that God can be reliably counted on to answer prayers that are in accord with His will. Even the superstitious don't believe in random attacks of bad luck, they believe it happens regularly in accord with certain acts (breaking a mirror, walking under a ladder, etc.)

NO ONE believes in supernaturalism as you define it. It's a straw man.

Here's an attempt to define the supernatural. A being is supernatural if that being's activities are not restrained by or subject to a complete and accurate account of the laws of nature.

Thus, if a being could suspend the laws of gravity simply by an act of will, with this act not being caused by any intermediary force other than his will, that being would have supernatural powers. And this would be the case even if this being could reliably and repeatedly suspend these laws on command.

I don't think mere repeatability or consistency makes a power natural. If a complete and accurate picture of the world tells us that causal powers are only exerted through forces or particles, and a person is able to suspend these laws simply by an act of their will, with no particles or forces intervening, then that act is supernatural, regardless of how reliably the being could be counted on to perform it.

You might take the track of suggesting that anything that is regular and even slightly predictable is natural. Thus, if a purportedly supernatural being like God could reliably suspend any natural law He wanted at will, then He would be natural.

If that definition is accurate, then no one is, nor has ever been, a supernaturalist. So even if you deny my definition, yours is certainly out of the question. Whatever religious people mean by supernatural, it's certainly not that.

Anonymous said...

It occurs to me, though, that we don't need to get bogged down into definitions of the supernatural. It's a semantic issue. Let's assume that if God acts regularly, then He is natural, and a completely accurate scientific picture of the world includes His will as the most fundamental law of the world. Thus, any true scientific counterfactual statement of the form "if x, then y" is actually shorthand for the more accurate "if x, then y, unless God wills otherwise".

How would a frequentist approach allow to to conclude that an event was best (naturally) explained by God, rather than by some unknown law other than God? In a frequentist approach, it would still be the case that (in your view) nothing has ever been accurately explained by reference to the direct action a being whose will was the fundamental (natural) law of the universe.

So let's say Geller claimed to be this being. Is there any test available within your method which could yield the result that it's more probable that Geller's will is the supreme natural law of the universe than it is that all the instruments simultaneously failed? Won't the probability that all the instruments failed simultaneously always be orders of magnitude more likely than the idea that any being's will is the most fundamental natural law of the universe?

Steve Lovell said...

Doctor Logic,

I think the question of biased samples is a really interesting one to raise in this connection.

Suppose that we have lots of cases where dead people of stayed dead. In all those cases we agree that no miracle occurred, and that God wasn't specially active. Why can't I claim that generalising from this to the probablility of the resurrection is based on a biased sample? After all, in the case of the resurrection I think that God was specially active. Why should I expect the same result in both cases? Surely to avoid the accusation that you are reasoning from a biased sample, you need to have already argued that it is unlikely that God would be specially active.

Have I missed something?


Doctor Logic said...


You are identifying supernaturalism with non-physicalism. I have no philosophical objections to there being non-physical, natural stuff. (Although, there are good a posteriori reasons to think there's nothing more than physical reality.)

But for purposes of this discussion, your God is natural by my definition (i.e., statistically lawful and predictable).

And I will assume that you agree that the supernatural as I have defined it (i.e., non-lawful, non-predictable) is incapable of explaining anything.

How would a frequentist approach allow to to conclude that an event was best (naturally) explained by God, rather than by some unknown law other than God?

The frequentist answer is that even if God exists and can interfere, it's something he's very unlikely to do. Hume seems to understand this when he says:

Though the being to whom the miracle is ascribed be almighty, it does not, upon this account become a whit more probable; since it is impossible for us to know the attributes or actions of such a being, otherwise than from the experience we have of his productions, in the usual course of nature.

Suppose I form a physicalist Christian splinter group. This group says that there is a physical (and as-yet undiscovered) Theory of Everything (ToE) that explains why Jesus was resurrected. We say that, if had the initial conditions, and we had the ToE, we could predict the Resurrection.

There are two potential problems.

First, if I don't actually know what the ToE says (i.e., I don't have a formulation of the theory), I'm not doing any explaining. I can't explain an event with a theory I do not have. And I cannot be circular and say that the ToE is "that which caused the Resurrection." I have to be able to predict something else with my theory before it becomes explanatory.

Second, and related to the first, we have to be able to say something about the frequency with which the ToE would actually cause a resurrection. If we assume the known physical laws are approximations to the ToE, then the ToE very rarely (if ever) causes resurrections.

Of course, if I knew my ToE with enough precision to make predictions and test them, then I can begin to accumulate frequentist evidence for belief in my ToE.

Now just substitute my ToE for God. God is not explanatory of the Resurrection story unless you know the mind of God, which you don't. The only way you know the mind of God is by what he did in the past, but (conveniently) not well enough to predict any other events. That's circular, and not explanatory unless events automatically explain themselves.

If you knew God's mind and could make testable predictions with that information, then you could begin to accumulate evidence for belief. Such a god would be natural, if non-physical, and explanatory.

Is there any test available within your method which could yield the result that it's more probable that Geller's will is the supreme natural law of the universe than it is that all the instruments simultaneously failed?


Suppose the reliability of our instruments is 99%. That is, in 1% of cases, the instrument, or the person reading the instrument, fails. Suppose also that we are confident in physical laws to 1 part in a trillion. Then we would only need to use 6 instruments in a well-designed experiment to rule out instrument failure. I say well-designed experiment because they have to be operated by independent parties an in a blind testing fashion. After all, 100 instruments would be inadequate if Geller's manager was the one placed in charge of the experiment.

As to whether "Geller's will is the supreme law of the universe" that might be harder to establish. The universe is a big place. However, we could easily show that Geller's will is the dominant law of our neighborhood. We'll just configure one physically imnpossible/improbable task after the other, determine Geller's will, and see that he defeats each task in accordance with his will. Should be child's play.

The problem with the Resurrection is that there was no instrumentation, no control, and there was biased, untrustworthy reporting. It's not like Jesus took on 5 legions of Romans, slaying them with his bare hands. At least then we might have found urgent communiques between Palestine and Rome warning the Senate about Jesus and asking for more legions to defeat this monster. The only reports of the Resurrection are from Jesus's own organization.

Anonymous said...

I do agree that the supernatural as you define it wouldn't explain anything. However, it being that literally no one who believes in the supernatural defines it the way you do, I hardly see how that's relevant.

I don't know if you intended it or not, but most of your response just sounded to me like a capitulation. The point I was trying to make was that your method couldn't discover God or attribute the Resurrection to Him, even if He existed and caused the Resurrection. You seem to concede this in your last response. Q.E.D.

Thus, if it's really a moral imperative that our method be able to tell us we're wrong about the world, as you claimed previously, then you should adopt another method (assuming your moral code includes prohibitions against hypocrisy and special pleading).

Yes, I agree that God would make a bad scientific explanation of the Resurrection, and He'd probably make an even worse T.O.E. Luckily, those unhappy facts have nothing to do with what we're discussing, unless you think all true explanations are scientific explanations. God might fail to be a prediction-yielding scientific explanation (particularly concerning one-time, historic events) but might still be a good personal or historic explanation. After all, historians can't make predictions, but that doesn't prevent them from giving reasonable explanations of their data. Last I heard, Bayesian analysis wasn't limited to analyzing scientific theories.

And I'm not going to get bogged down here, but I don't agree that Christians don't make predictions about what God will do. They very obviously do this sort of thing all the time. I'm not specifically talking about the resurrection and I see no reason to focus our conversation on that. The topic at hand is whether your method meets the requirements you set for other methods.

On that note, I don't see how it could ever be easy, or even possible, to conclude that Geller's will was the supreme law of the universe on a frequentist account. You know that there is a 1% chance that any one of your instruments will fail. So, I don't know the math, but that means the odds that all 6 will fail at once will be astronomically high. But how do you set the prior probability that Geller's will is the ultimate law of the universe? We have no indication that anyone in history can suspend natural laws with their wills. Thus, on the frequentist account, wouldn't the prior probability that Geller's will is law have to be zero? And once it's zero, it can't get above zero, regardless of the evidence, correct?

Further, I believe I asked you how you'd be able to rule out that some other presently unknown natural law was at work, rather than Geller's will, since that would also be much more likely than Geller's will being the supreme natural law. You didn't respond to that.

Let me rephrase it using our current terminology.

Assume that Geller passes all the neighborhood tests you give him. The options you have left are:

1. Geller passed the test because his will is the supreme natural law in the universe.

2. Geller passed the test because some previously unknown natural law other than his will was at work.

How could you use YOUR METHOD, not a common sense account, to show that 1. was more probable than 2.?

What you gave us was a common sense account of how Geller would go about proving his powers. I agree that a common sense method could work, the whole point was that on this particular issue your method contradicts common sense.

Doctor Logic said...

Steve Lovell,

Why can't I claim that generalizing from this to the probability of the resurrection is based on a biased sample?

There are several reasons.

First of all, you can use that argument to destroy even the most basic belief. Your belief that 1+1=2 could fall for the same reason. Maybe you added wrong every other time, and you misheard people when they told you 1+1=2. It's theoretically possible.

Second, if the sample is biased, then we know something about the bias itself. For example, we might suppose that resurrection is commonplace, but that our bias causes resurrected people to be invisible to us. But if we do this, then we are stipulating that our bias is such that we cannot see resurrected people. The bias is so strong that someone seeing a resurrected person is itself super improbable. (Sort of like someone being able to see in infrared.)

Third, every physical law comes with an associated domain. For example, Hooke's Law about the force exerted by a spring assumes the displacement is small. The acceleration due to gravity assumes friction is small. Newton's Laws are still true, assuming relative speed is small, and so on.

Similarly, the conclusion is that the Law of Non-Resurrection applies within some limited domain, the boundaries of which have yet to be discovered.

However, in all these cases, experiment can tell us where the laws are valid. Newton's laws are used to build cars and bridges because Newton's laws have been verified in those domains. If we're not in a quantum or relativistic domain, Newton's laws are still effective. The Law of Non-Resurrection holds for physical humans who lack high technology.

So the burden on believers is to show that the Resurrection was not in the domain of the known Law of Non-Resurrection. And you cannot circularly say Jesus wasn't human because he was resurrected.

Steve Lovell said...

Doctor Logic,

Your examples don't persuade (me):
(1) I don't see the relevance of the mathematical example. 1+1=2 is not an inductively reached generalisation. If it were one, then there would be no problem, epistemologically speaking, with it having exceptions. Not sure why we need to worry about "getting it wrong" or "mishearing". Such things don't generally distroy knowledge, and I'm not asserting that they do, am I?
(2) Okay, I assert that the sample is biased. What do we actually know about that bias? We know that in every non-disputed case God wasn't specially active and that no resurrection occurred. How do you get from that to any sceptical conclusion? Your invisible resurrection example is interesting, but again, I don't see the relevance.
(3) I couldn't agree more about applicable domains. However, laws not only have a "domain" but also have an implicit or explicit "cetaris paribus" (other things being equal) clause. Even within the relevant domain, the expected outcome may not obtain, and indeed won't obtain if something we had not accounted for in our initial conditions "interferes". But God's special action is just such a "something".

I think the sample is biased. I don't want to say that you should deduce a different law from the sample (or from some other sample), but the law should have a cetaris paribus clause. And the presence of that clause means you can't actually predict anything at all without asserting "and other things are equal", but whether or not other things were equal in the case of the (alleged) resurrection of Jesus is one of the things at issue. I think that in that case other things weren't equal; God was specially active. If you pile up evidence saying, in effect, when God is not specially active resurrections don't occur, then I can agree and say you've missed the point. None of that evidence has any bearing at all on what actually happened in the case at hand. The interesting question is "how likely is it that God would be specially active?" Now I'm happy to say that the probability of this, in any individual case, is low. But I don't see why it should be so low as to make it impossible or near impossible to overcome with evidence we are likely to possess.

I short I just don't see how to get from any of your three points (or any combination of them) to the conclusion that your sample isn't biased. Perhaps you need to repeat you points more slowly and draw out the inferences explicitly. I evidently need more help than your last post provides.



Doctor Logic said...


The point I was trying to make was that your method couldn't discover God or attribute the Resurrection to Him, even if He existed and caused the Resurrection.

I explained how, using Bayesian reasoning, we could show that Geller's will was the law of the neighborhood. To say his will was the law of the universe would be like saying that all ravens are black. Now I think that passing these tests would establish Geller as a deity. Is that not enough? It seems like a small point to quibble about.

Thus, if it's really a moral imperative that our method be able to tell us we're wrong about the world, as you claimed previously, then you should adopt another method (assuming your moral code includes prohibitions against hypocrisy and special pleading).

You're just trying to bounce my criticism of your pro-bias views back to me, but with no justification. Geller can pass the tests and be a deity. That there's no possible experience that could tell us whether he is the deity of deities is not my problem. It's a problem with reality.

If an epistemology prevents me from distinguishing two identical protons, does that mean there's a problem with my epistemology? I don't think so. It's not a matter of me being biased against distinguishable protons, but of me being unable to find evidence that they're different.

You want us to introduce new axioms into our epistemology just so you can say Geller is god of gods. You have no basis for making such a claim, apart from personal bias.

After all, historians can't make predictions, but that doesn't prevent them from giving reasonable explanations of their data.

This is incorrect. Suppose a historian theorizes that Stonehenge is a wooden facade. Or that Stonehenge is made of rock from Easter Island. Do you think these sorts of claims make no predictions? How about a theory that Elizabeth I was Nigerian? Predictionless? Of course not.

The only proper explanations are predictive.

If explanations don't have to have predictions, then I can explain everything with my undiscovered ToE. There's a perfect analogy here between undiscovered ToE and God. Both "theories" are in principle capable of generating what we observe. And in each experiment, we can say "My theory can do that." In neither theory can we say that "My theory must do that!" Why? Because these are theories we do not have. God is explanatory when you know the mind of God, and you don't know it.

When you say "Thank God for saving me in that car crash," God is not explanatory of your survival because your God theory never predicted you would survive. You run your theory in reverse, fine-tuning it, but never yielding a prediction. Would that be acceptable for my ToE? Can I do experiments and take results from daily life (e.g., election results or the weather) and say "It's the ToE that accounts for the data"? Well, sure, if there is a ToE, and I knew what it said, then it would certainly account for what I have seen. But I haven't explained anything yet.

So don't pretend your God is different from an undiscovered ToE. If non-predictive theories count as explanations, then I am justified in explaining stuff with a non-predictive naturalistic theory too.

1. Geller passed the test because his will is the supreme natural law in the universe.

2. Geller passed the test because some previously unknown natural law other than his will was at work.

I've been clear in my past comments, so are you asking something new here?

You are testing Arthur C. Clarke's maxim: sufficiently high technology is indistinguishable from magic? If so, then by all means, tell me how you do distinguish them.

Or are you suggesting that Geller by chance coiincides with irrelevant physics? I think I've been clear that we could easily rule this out.

Doctor Logic said...

Steve Lovell,

Deductive inferences are justified by inductive inferences. To say that they're not is to assume that we know deductions incorrigibly, which is an unnecessary axiom. But let's skip this tangent because it opens another can of worms.

I thought I was pretty clear that there is a cetaris paribus clause in the method. The experiments do not say that there are no conditions under which a person will be resurrected. It says that the conditions under which we observe someone resurrected are extremely rare.

It seems as if you want to exempt acts of God from Bayesian analysis. There are two reasons that this cannot be done.

First, there's the issue of identifying an act of God. What tests need to be passed before an event is said to be an act of God versus an act stemming from non-conscious laws or from undiscovered non-conscious laws?

Second, a personality is statistically deterministic. This is why one can say things like "he was not himself." Thus, Bayesian reasoning is used on people too. So even if God does exist and can resurrect people at will, we can say that God has never done so before, and that God doesn't resurrect people at rates detectably higher than nature does. (The mere fact that God can resurrect a person is irrelevant, because physics can do so also if the conditions are right.)

I short I just don't see how to get from any of your three points (or any combination of them) to the conclusion that your sample isn't biased.

I've been agreeing that, generally, samples are biased, but if our samples are all so biased, then we ought to expect them to be biased at similarly high rates in the future. If you want to say that our bias should be ignored in some scenario, you need to produce extraordinary evidence that the new scenario isn't biased like your previous trillion samples were.

I can always devise a just-so story in which all previous samples were biased, but the my next sample will be unbiased. For example, I could devise a story in which my leap from the roof of my building will not result in an uncomfortable fall despite all our past experience of physics. Does my ability to devise a just-so story in any way alter my expectation that I will fall? No. Not unless I can point to extraordinary evidence that my past samples were biased in this particular pattern. For I can always devise a just-so story that will defeat any inductive inference.

Anonymous said...

Doctor Logic,

Lots of non-sequitors, there.

I asked you about how your frequentist interpretation would assess the Resurrection, and you respond by referring to a non-Bayesian, non-frequentist, common-sense account of how you'd believe Geller was a deity if he showed up in your neighborhood and pulled off a few magic tricks.

Let's separate out the two questions. There's the question of whether or not your method could be used to find out whether an event in the past was caused by God. It seems obvious it could not. You can't avoid that by distracting us to the separate question of Geller. In the section you quote, I wasn't asking you whether you could separate Geller from Yahweh. I was asking if your method could attribute causal activity God, even if God was causally active.

Now, I'm not the one who claimed that if our method of finding the truth can't tell us we're wrong about the world, we should abandon it. That was you. And it's pretty obvious from your sudden lack of specifics that when it comes to cases with no precedent, you abandon your method and hope no one will notice.

Let's ask some simple questions here.

1. What's the prior probability that God raised Jesus from the dead?

2. If you believe that there have never been any resurrections, then how on a frequentist account do you give this a live prior probability?

3. If you can't give the ressurection a live prior probability, then isn't it the case that your method can't correct your view about the world?

Your comments about Geller again just prove my point. What it amounts to is your saying you wouldn't believe an entity was God no matter what He did. If he demonstrated control of everything in the world, you'd say He was just in control of the world. If He demonstrated control of everything in the solar system, you'd just say He was in control of the solar system. Thus, you could never discover God even if God existed and was constantly doing miracles to prove Himself to you.


And by the way, it wouldn't take a new axiom of epistemology to establish a being was God. It would take a very old axiom called an inductive inference. If this being demonstrated total control over every natural law we saw Him encounter for a sufficient amount of time, at some point it would be reasonable to suppose this being was in control of all laws. Certainly, this couldn't be accomplished by just watching this being at work for an afternoon in a neighborhood, but it's also certainly not impossible, as you suggest.

You are the one suggesting a new law of epistemology, one that suggests we can't trust inductive reasoning. Sure, we could be wrong about a being's being God, but that applies to almost all our knowledge, and doesn't make it any less secure.

It just seems obvious that in every way you're stacking the deck against the possibility of your ever having to admit that God exists and your worldview is wrong. Which is your right, of course, I only wonder why you so stridently chastise others for doing the same.

Steve Lovell said...

Doctor Logic,

I don't think I'm wanting to exempt God's action from Bayesian analysis. I just don't think you can get at the "priors" the way you are suggesting.

I've been agreeing that, generally, samples are biased, but if our samples are all so biased, then we ought to expect them to be biased at similarly high rates in the future. If you want to say that our bias should be ignored in some scenario, you need to produce extraordinary evidence that the new scenario isn't biased like your previous trillion samples were.

Hmm. I guess this is correct as far as it goes (apart from the "extraordinary evidence" bit), but the chances of a sample being biased are surely not determined merely by the size of the sample or the number of samples, it depends on the nature of the sample. Does the law of gravity really become more certain every time I drop my pencil? I don't believe it. Certainly it doesn't matter how many times I drop a pencil on Earth, if I then try to say the exact same thing will happen on the Moon. The increase in the size of the sample on Earth is irrelevant, so doesn't alter the priors relating to what happens on the moon. (Obviously I've oversimplified here, but the basic point it right, I think.)

Moreover, the samples in question deliberately exclude the cases where other miracles may have occurred, the bias is self-perpetuating.

We cannot simply project the current sample onto the event in question and get out a prediction or a prior probability. That is to assume that the sample is representative, when the question at issue is whether it is representative or not. Rather we need some other handle on the prior probabilities. I'm not entirely happy to suggest that these are simply subjective, but I don't think a frequentist account works here. At some point we reach epistemological foundations and the frequentist account can't apply. Why can't we say whatever we say about those foundational "priors" about the priors for special acts of God? Interestingly (to me at least) C.S. Lewis thought that we needed a different way to assess these probabilities. Chapter 13 of Miracles is devoted to his account. As good a Miracles chapter 3 is, it isn't actually about miracles. I think Lewis's best stuff on miracles is in chapter 13.

I'm starting so see some cross-over between my points and those of anonymous.


Doctor Logic said...


It's obvious now that what you want is to be justified in concluding that Jesus was resurrected by God. And you're willing to twist your epistemology into knots to get there.

I've already explained that we can justify any testable conclusion based on statistics. But since the statistics for the resurrection don't exist, that's not good enough for you. You have to be able to justify something even when the statistics don't exist.

You essentially believe that it is impossible for history to cover its tracks. If evidence is destroyed, that is intolerable for you. You have to be able to infer the truth (or your preferred version of it) despite the loss of data.

Moreover, for you, it's not good enough to conclude that Geller is a god. He has to be the god of gods. Something that is fundamentally impossible to test. So you fallaciously argue that you're using induction to prove an impossible thing. It's like you think that white ravens are impossible anywhere in the cosmos because none have been observed here on Earth.

So, please, don't pretend to be the unbiased one in this conversation.

What's the prior probability that God raised Jesus from the dead?

Set your priors at 50%. See if it makes any difference.

Your initial belief is 50% that God resurrected Jesus. Then you notice that 10 billion people failed to get resurrected, and adjust your prior. Now your belief is about 5x10^-9%

2. If you believe that there have never been any resurrections, then how on a frequentist account do you give this a live prior probability?

Ahem. I assumed the rate of resurrection was on the order of 1 in 10 billion. I can increase the rate if you allow me to include vampires, but I doubt you'll gain an entire order of magnitude. On this world, resurrections are extremely rare.

In contrast, reports of magic are commonplace. And in EVERY case where reports of magic have been investigated to conclusion, the report has been found to be false, frequently fraudulent.

Could God/Jesus pumped their resurrection signal above the noise? In principle, sure. But they didn't.

You are the one suggesting a new law of epistemology, one that suggests we can't trust inductive reasoning. Sure, we could be wrong about a being's being God, but that applies to almost all our knowledge, and doesn't make it any less secure.

Well, I've got you pegged now. You don't see that the claim that God is the supreme god is a strong negative claim (like "all ravens are black"). It's the exact opposite of what Steve Lovell has been arguing for.

Steve has been saying that just because no resurrections have been observed, that ought not imply (with any degree of certainty) that resurrection is impossible under all conditions everywhere. It only means that resurrection is very unlikely in our neighborhood or under familiar conditions.

I assume you agree with Steve. So do I on this point.

But then you turn it around and argue the exact opposite. You argue that if God appears to be locally godlike, then we ought to conclude God is godlike everywhere and above all other gods.

Make up your mind.

Doctor Logic said...

Stevel Lovell,

Does the law of gravity really become more certain every time I drop my pencil? I don't believe it. Certainly it doesn't matter how many times I drop a pencil on Earth, if I then try to say the exact same thing will happen on the Moon.

This is fair. The law of gravity on Earth relates to drops through some small fraction of the Earth's radius. There's a huge extrapolation taking place when we try to translate this to the Moon.

But that's not what is happening with the Resurrection. Here's the analogy with gravity. We've taken trillions of readings all round the Earth in almost every place an time. Suppose a man claims that the law of gravity failed in Krakatoa last year, but that it has since returned to normal. Can you argue that Krakatoa last year should be afforded any special classification, or be seen as an extrapolation of the trillions of other places and times when samples were taken? I don't see it.

Here's how the analogy plays out. The person who claims gravity failed in Krakatoa last year starts The Anti-Gravity Cult of Krakatoa. Members of the AGCK claim that because of the miraculous events there last year, Krakatoa (last year) ought not be considered part of the usual sample of places and times where gravity has been found to apply.

I'm sure you can see that this is circular. Members would only believe that gravity was in retreat there if Krakatoa is special. And they believe Krakatoa is special because gravity was in retreat.

Moreover, the samples in question deliberately exclude the cases where other miracles may have occurred, the bias is self-perpetuating.

As I suggested to Anonymous, set the rate of resurrection to 1 in 10 million instead of less than 1 in 10 billion. Assume 10 resurrections per 10 billion people if you like. It won't substantially alter the numbers. Also, feel free to set priors at 50%. Again, it is pretty inconsequential. I wouldn't consider priors of 50% to be biased for binary (yes/no) scenarios.

Anonymous said...

I'll just clear up some of your misconceptions here. I am a Christian, but I am not really interested in whether or not the Resurrection can be proven via Bayesian analysis. My guess is, probably not. On that issue either something like Plantinga's properly basic beliefs are in effect or all Christians are ultimately fideists. There may be good arguments that clear out some objections to the Resurrection, but I don't think anyone believes in the Resurrection on the basis of them. To me, this is an academic exercise.

I obviously don't care if you can prove that Geller is God, since I don't believe that Geller is God. I don't even care that you, personally, wouldn't accept God as God, even if He were constantly performing miracles on a local, global, and galactic scale. I'm merely pointing out that you are the one complaining that we shouldn't have epistemlogies that can't self-correct and you are the only one promoting a non-self-correcting epistemology.

I assume that you believe everything that has all the macroscopic properties of water also has the property of being composed of two parts hydrogen and one parts oxygen. And you are rational in believing this because, as far as you know, this has been true of all water you've ever encountered. You don't need to do chemistry experiments on all water everywhere to be justified in this belief. By the same token, if not Geller, but God, demonstrated total control over every supposed law of nature, not just on a neighborhood, but on a global and galactic scale, AT SOME POINT it would be reasonable to believe that God was God. Note, I'm not saying that at any point this will have been proven. I'm saying at some point it will pass the threshold of reasonable belief. Do you grant this much, or will you try to special plead your way out of this one as well?

I think Lowell's questions get to the heart of the issue. Do the number of people not ressurected when God was not specially active reduce the probability that Jesus was raised when God was specially active? And does the unique fact of Jesus's ministry and works make him more likely to be the type of person God would resurrect if He did that sort of thing?

Does the question of whether normal people are resurrected when God is not specially active at all impact the question of whether sages who claimed the authority of God in teaching a revolutionary theory of ethics are resurrected when God is specially active? The former claim does not reduce to "a claim of magic". Your bias here influences to exclude the relative category. You consider only normal people and magic-claiming charlatans. Whether or not Jesus belongs in either category or a more accurate third is hotly debated, and presuming to put him in any of them biases the assessment tremendously.

Contrary to your statement, I don't claim to lack bias. I just don't care whether or not Bayesianism can tell us if God raised Jesus from the dead. God can provide that belief for those who need it and are willing to accept if He needs to. I'm not trying to prove anything to you, I'm just pointing out your more or less obvious hypocrisy.

There is no inconsistency between my position on the Resurrection and the Geller example. The problem in each situation is the sample. In the case of the Resurrection, I don't think you have the right sample. If the only sample we had in your Geller example was a handful of neighborhood tricks, I fully agree with you that we wouldn't be justified in thinking he was the deity (or even a deity). But I stipulated in my last response that if Geller (or God) demonstrated himself not only on a neighborhood, but on a global, galactic, and universal scale, then AT SOME POINT you would be justified in believing that this being was God. I'm sure that if every Christian was resurrected, the probability for you that God raised Jesus from the dead would continue to rise for you, until at some point it was rational to believe. The same principle is in play here.

I'm not claiming you're being irrational in not accepting the Resurrection based on the available evidence. I'm saying you're a hypocrite for chiding other people for having epistemolgies that can't correct themselves when yours can't.

Steve Lovell said...

Doctor Logic,

The Krakatoa example is interesting. It helps me see the issue from your side. However, my overriding feeling is this: the members of the cult know that things like that don't normally happen. That is why they are so interested in this particular case.

It's unfair to then argue against them on the basis that what they are claiming is unlikely in the ordinary course of events. They agree that it's unlikely in the ordinary course of events. They think this wasn't part of the ordinary course of events.

The question isn't how likely a certain outcome is "in the ordinary course of events". The question is how likely is it that the "ordinary course of events" be suspended. But that latter probability isn't one which we can decide by examining what happens in the ordinary course of events.

I can see some of your earlier answers (about expecting future samples to be as biased as past samples) coming back at this point. But those answers didn't seem entirely right the first time around. Remember I'm not hugely convinced that the size of samples is particularly important. The first few instances of type give much more support to a generalisation than do latter ones, so the relatively small number of alleged miracles doesn't worry me. Moreover, the sample size isn't the only thing of relevance. The first member of any sample cannot be allowed into the sample on the basis of it's conformity with the sample. I repeat priors can't all be assessed on the frequentist account.

Hope this makes my position clearer. I'm not sure we are going to agree, but I think we might be getting to understand each other better.


Darek Barefoot said...


It would be a mistake to isolate the resurrection of Jesus from the course of Israelite history and the nature of biblical revelation. If there are features of written revelation which, within its historical-spiritual context, are hard to account for naturalistically, then the resurrection of Jesus becomes more likely.

The trouble is that it could take much study to bring those factors into the picture. I give a brief example here, but there are many more that could be considered.

The point is that the resurrection of Jesus cannot be severed from a multitude of factors that affect probability judgments.

Doctor Logic said...


I am totally unconvinced by this line of argument. It looks very much like numerology to me.

You also assume that because the writers of different parts of the Bible are different people, they represent random statistical samples. They are not. The writers of the NT were well-aware of the OT, and wanted to leverage it where they could.

Indeed, we can make similar arguments in almost any other case of the paranormal. Recently, there was a case where a couple of guys faked the carcass of a dead Sasquatch. (Okay, never thought I would write those words!) Why didn't they fake a completely different kind of creature?

Answer: because latching onto an existing myth carries weight (albeit fallacious) in the minds of the general public. Average people start to ask themselves "What's more likely? That these guys would fake a Sasquatch, or that thousands of Sasquatch witnesses would be wrong?" To the careless observer, it looks like the odds of the Sasquatch corpse being real might be 50%, if they estimate the odds at all.

But of course, the Sasquatch fraud fits a common pattern. There aren't thousands of witnesses. The samples are biased, and the solid witnesses only appear when the Sasquatch industry tells its own story. When scientists examine the results, they find only fraud and self-deception.

Yet people gain folk credibility when they make reference to existing myths and paranormal beliefs. That's why the Mormons were successful in converting Christians to their plainly-fake religion. And in claims of the paranormal, fraud and self-deception are widespread and well-documented.

You can't substantiate your case on the basis of a story written by the founders of your cult. It doesn't count for the purposes of statistical analysis because the authors are not unbiased. They are cherry-pickers. They tell the parts of their story they believe are relevant, or that will be the most convincing. They are not dispassionate investigators, or people who see Jesus as an enemy.

Just for kicks, take a quick look at the LDS FAQ here and here.

It's often said that if you delve into the details of Christianity, go through the volumes of "scholarship", you can account for the contradictions and find compelling evidence. Well, I don't buy it. The only reason the LDS has amassed a slightly less intimidating volume of "scholarship" that Christianity is that they've had less time to amass it.

Darek Barefoot said...


Obviously, readers will have to take a look at my article for themselves to decide whether your analysis is credible. The specifics are what count.

Your theory is apparently that the authors of all four New Testament Gospels conspired to create a complex inter-gospel pattern related to the resurrection of Jesus--a pattern that is not apparent from any Gospel in isolation.

Are you aware of the historical and literary obstacles to such a theory? Not the obstacles in the minds of Christians, but in the minds of secular critics and historians who are academically qualified. If not, do a bit of research into the Gospels as ancient literature, the nature of their differences and dependencies. The idea that the four Gospels were composed as the result of a conspiracy among the authors is so manifestly implausible that I have never seen it seriously propounded.

You would be much better off trying to attribute the pattern I identify to pure chance. But that would be no cake walk, either.

Doctor Logic said...


I don't think the coincidence you cite is significant. You can always go and find some coincidence in a complex story and then cook up a conspiracy theory around it. And that's what you present in your paper. If it weren't stages of death, it would have been stages of life, e.g., child-child-adult. Or geographic location, southerner-southerner-northerner. Or by alphabetic order of the parent's name. Or whatever else you can find.

You're finding patterns in noise and attributing them to causes. It's like the Bible Code pseudoscientists that claim that if you traverse letters in the Bible by skipping every Nth character, the Bible will spell out "relevant" words. And they do this on the KJV Bible!! Their reasoning being that God didn't just guide the original authors, but also the subsequent scribes who compiled and translated the books. Yet, if you run the same tests in War and Peace, you'll see similarly "stunning" coincidences.

So I don't think it's a conspiracy theory of the authors. I'm just saying that we cannot check one author against the other as if they were independent witnesses. They were not. They were almost certainly collaborators who shared each other's stories before they wrote or dictated their preferred storylines.

Darek Barefoot said...


Here is your first take on the thesis of my article:

>>The writers of the NT were well-aware of the OT, and wanted to leverage it where they could.

Indeed, we can make similar arguments in almost any other case of the paranormal. Recently, there was a case where a couple of guys faked the carcass of a dead Sasquatch.<<

Surely I can't be blamed for seeing this as an invocation of a conspiracy among the Gospel writers to fake the pattern I described.

In other words, you didn't immediately incline to seeing it as "statistical noise." Now, apparently, you understand that a conspiratorial collaboration among the authors of the four Gospels is simply untenable.

So your current tack is:

>>You can always go and find some coincidence in a complex story and then cook up a conspiracy theory around it.<<

First of all, mine is a theory of providence and inspiration. Yours was the conspiracy theory.

Second, I did not identify simply any pattern, did I? There is an understandable rationale and a clear connection to the question of the credibility of Jesus' resurrection. It's not just any kind of pattern.

The ELS Bible codes are indeed nothing but results sifted from random string generation.

Here's a way to distinguish the two types of patterns. If someone chanced across the pattern I identify (and, by the way, I can produce more such evidence) in my article, but they did so in a novel written by a single author, would we reasonably conclude that the pattern was deliberately created by the author? Or rather that we were simply injecting it into the novel via our imaginations?

To be even more specific, in novel in which the spiritual significance of the number seven and the superiority of the seventh were clearly exhibited, would we conclude that it was by pure chance that the resurrection of the protagonist of the entire novel--and the hinge of the novel's plot--were placed as the seventh resurrection by the author?