Wednesday, September 13, 2006

Turning, twisting in the wind

JC: I understand that Steve is not saying that we must know the resurrection with absolute certainty with no possibility for being wrong.

Several clarifications are in order:

1.There’s a difference between knowing something and proving it. Likewise, there’s a difference between the relative certainty of the raw evidence, and the relative certainty of an argument that attempts to capture and formalize the evidence.

2.I have never said that we cannot “know” that Jesus rose from the dead. But in making a case for what we know, we may resort to probabilistic arguments.

3.The case for the Resurrection is a many-layered affair with direct and indirect arguments.

As I’ve said many times before, probability is a comparative concept. Everything cannot be uncertain. Degrees of certainty are relative to some fixed frame of reference.

So the fact that varirous arguments, taken in isolation, may fall short of certainty, does automatically mean that the overall case for the Resurrection is uncertain.

4.Jason will have to speak for himself, but I believe that when Jason gets into these debates, he brackets the argument from religious experience, since that is inaccessible to an outsider, and confines himself to common ground arguments.

But if you were to ask Jason why he is a Christian, the argument from religious experience would figure in his answer.

So his personal reasons are broader than the reasons he chooses to give in apologetic dialogue. He limits himself for discussion purposes.

And I agree with this basic distinction. So when we talk about degrees of certainty, we must also distinguish between a Christian’s individual level of certainty, which is intransmissible, and the degree of certainty which his arguments attain.

JC: What he and you would say is that the resurrection hypothesis must exceed the 50% threshold, with the sum total of the other naturalistic alternatives being less than that. So what I mean by "certain" is that it is head and shoulders above the other alternatives. Maybe 5 other plausible alternatives are at 10%.

SH:

1.I don’t think that either Jason or I would say this. To my knowledge, Jason is noncommittal on BT.

As for me, I regard the attempt to quantify historical evidence as fatuous. For the most part, historical evidence is a question of psychological probabilities—the probability that the witness is telling the truth.

That is not something we can attach a number to. Rather, it’s an intuitive judgment. Is the reader a good judge of character? How does the author come across?

So I reject the way in which Curry’s attempts to frame the issue.

Sure, the resurrection has to be more probable than not, but the mathematical apparatus is misguided.

2.I also don’t regard the resurrection as a hypothesis.

3.In addition, one can evaluate the naturalistic alternatives on two different grounds:

i) We can evaluate each naturalistic alternative on its distinctive merits, or lack thereof.

ii) And/or we can evaluate the naturalistic worldview which underwrites any naturalistic alternative.

Indeed (ii) is directly germane to the assignment of prior probabilities.

JC: For me, I'm comfortable not being certain what really happened. Maybe I'd assign a .0001% chance that the resurrection occurred, 1% chance of a stolen body, 1% for twin, 10% for real man with a lot of legendary growth, 20% for Early Doherty style myth, 20% chance the facts are unknown to us because the relevant evidence has been lost, etc. Not knowing what actually happened is an acceptable state of affairs for me. Not so for Steve.

SH: This is disingenuous. He is comfortable with how it didn’t happen as long as it didn’t happen. He can afford to be indifferent to the various ways in which it might not have happened because he doesn’t believe that it ever happened, so that, assuming the resurrection as a nonevent, it isn’t terribly important how you account for a nonevent.

But his nonchalance is not transferable to the operating assumption, or his naturalistic outlook on life.

JC: Murders are rare, but resurrections are even more rare. Orders of magnitude more rare. We are all aware that murders happen every day. Some of us know people that have been murdered. None of us know anyone that has been resurrected. None of us have ever heard a credible report of a resurrection in our lifetime. Probably we all agree that there has not been a resurrection for at least a little less than 2000 years. I think it's been quite a bit longer.

SH: That was not the point of my illustration. My illustration took for granted the occurrence of the murder.

The question, rather, was whether the multiplication of hypothetical and contradictory explanations count against the guilt of the estranged wife (now widow).

If that’s the position you’re going to take, then we could never convict anyone of murder since one can dream up an indefinite number of alternative scenarios, and if you assign a cumulative probability to these alternatives, then they will incrementally outweigh the probability that the accused was guilty of the crime, even if the evidence of guilt were absolutely overwhelming.

This consequence is clearly irrational.

JC: Because of this the value for the initial probability you would use in Bayes' Theorem for a resurrection would be substantially lower than that for murder. Orders of magnitude lower.

SH: Even if we accepted BT as our operating framework, it’s simplistic to assign prior probability on the basis of relative frequency alone.

JC: But murders involve intelligent agents. And murders are still rare. The initial probability for the report of a murder (this is the value that represents only your background assumptions about murder, not the positive evidence for a given murder) would be pretty low as well. Since we are certain that many millions of murders have occurred in recorded history and equally certain of zero resurrections, the initial probability for the resurrection of Jesus must be lower by at least 6 or 7 orders of magnitude. Now, let's plug that in to Bayes' Theorem and see how it affects things. Here's Bayes' Thoerem as layed out by my brother in his post on ESP.

SH: This is a very confused and question-begging claim.

1.It’s precisely because a murder, like the Resurrection, involves personal agency, that there’s a lot more to the calculation than the sheer mathematical variables.

Suppose the killer goes to the high school prom. Suppose there are 1000 students at the prom.

Does this mean that the victim has only a one in a thousand chance of being murdered?

That might be true if the murder were purely random.

But suppose the killer plans to kill Bobby because Bobby stole the killer’s girlfriend?

Does Bobby still enjoy a one in a thousand chance of being murdered? Hardly!

Bobby is the intended target.

2.To say that “we are equally certain of zero resurrections” assumes what it needs to prove.

JC: Since P(resurrection) is 6 or 7 orders of magnitude lower than P(murder) you can see that this means the numerator is likewise 6 or 7 orders of magnitude smaller for an evaluation of the resurrection than an evaluation of a murder. Correspondingly, if you have a certain value for the denominator and it affects your result in the case of murder, you can have a value 6 or 7 orders of magnitude smaller in a resurrection analysis and it would affect the result in the same way. Hence 1 in a million matters in the case of a resurrection, but not necessarily so for the case of a murder.

SH: Which, as I just explained, is irrelevant to the case at hand.

JC: So your more outlandish theories become relevant when discussing a resurrection but these might be irrelevant in the case of a murder. Sorry, but when you make an extraordinary, outlandish claim, then extraordinary outlandish theories become good enough as a refutation.

SH: Other issues aside, observe the equivocation of terms.

Curry has defined “extraordinary” as rare. So let’s plug that definition into his criteria:

When you make a claim about a rare event, then rare alternative explanations become as good enough as a refutation.

Now, I ask the reader: does this make much sense?

I don’t believe in X because X would be a rare event, and rare events are overwhelmingly improbable.

And it’s sufficient to refute an improbable event by postulating a lot of other improbable alternatives whose combined improbability is even more improbable, by several orders of magnitude, than the improbability of the original claim.

JC: No, that's not what I'm saying. I am saying that a supernatural explanation must start with a presumption against it. It has a taller hurdle to get over. This doesn't mean that the naturalistic explanation "reigns supreme." It just means the naturalistic explanation has less of a burden.

SH: So what comes out of BT depends on what goes into BT. It is not BT itself that assigns the prior probability value to naturalism or supernaturalism. That’s a separate argument.

So it’s not BT which creates the presumption.

JC: In my view that is reasonable. When people report events that have occurred we automatically assume those events have a natural explanation. Whether we're talking about ordinary events (I bought gas yesterday, I had a ham sandwich yesterday) or claims of extraordinary events (Benny Hinn healed Evander Holyfield and raised the dead to life in Ghana).

SH: Note yet another fatal equivocation, as between a “natural” explanation and “naturalistic” explanation.

A supernatural worldview doesn’t deny that ordinary events are generally the result of natural causes.

That, however, is completely different from assuming that ordinary events imply or presuppose a naturalistic outlook.

Indeed, one argument for supernaturalism is that nature is not a se. Yes, you may be able to account for a local effect by reference to a second causes, but how do you account for global condition of causality itself? Why is there a world with natural forces?

JC: I'm not ruling out the supernaturalistic explanation from the start. I'm saying that I start by assuming it is extremely unlikely. That's the nature of supernatural claims. If they weren't extraordinary and rare they wouldn't have any force as far as persuading us to follow a religion.

SH: This assumes that God is inevident apart from the evidence of a supernatural event.

But natural theology would argue to the contrary. We can infer the existence of God from ordinary events just as well as we can from extraordinary events.

JC: I'm saying I agree with Professor Davis. I'm saying that a resurrection is a highly unusual and extraordinary event. Though not necessarily false, it must shoulder a significant epistemological burden. I've shown it with illustration, with math, and yet you just keep denying it. There isn't much else to say.

SH: Illustrations like what? Comparing the resurrection to alien abductions?

But that doesn’t show how the resurrection must assume the burden of proof. As I said before, it’s an argument from analogy minus the argument.

The math is irrelevant because the math only kicks in after the assignment of a prior probability value.

JC: Again, mutually exclusive hypothesis do count against a particular hypothesis. Look at the denominator in Bayes' Theorem that I provided above in my resonse to Jason. It consists of mutually exclusive hypothesis. I'm not making this up here. This is not my thoery. It's not something I invented. It's a standard way to evaluate various claims. If you don't like it that's not my fault.

Yes, you and others have repeated the same mistake that I've corrected many times. Look at the equations I provided Jason. The denominator contains any number of mutually exclusive hypothesis. This is not something I'm making up to prove Christianity false. This is not my theory. This is Bayes' Theorem. If you think the equations are wrong and you're a really smart mathematician and can offer corrections to the equation then make an argument.

SH: Several problems here:

1.Suppose we have ten mutually exclusive alternative theories to the resurrection. On the most charitable reading possible, at least nine of these theories must be false.

Since they contradict each other, they can’t all be true. At best, only one could be true, while all could be false.

So the question is how a set of admittedly false alternative explanations count against the truth of the resurrection.

2.As Steven Davis points out, we have to take personal agency into account. If a car dealer has a 1000 cars, then, mathematically speaking, you could say that there’s only one chance in a thousand that any particular car will sell.

But suppose that I, as a prospective buyer, am uninterested in most of the makes and models on the lot. So they were never in play in the first place. That’s not a live option.

Suppose, instead, that I go to the dealership knowing exactly what I want, and there is only one car on the lot that answers to my exact specifications.

Are the odds one out of a thousand that I’ll buy that car? Or is there a 100% certainty that I’ll buy that car?

3.What Curry is doing is sleight of hand. It’s all a question of where you distribute the evidence. How much to you plug into the background information, to create the initial presumption, and how much do you save for later to overcome the initial presumption.

It isn’t the Bayesean apparatus that determines the outcome, but certain preliminary judgment calls.

Does theism figure in the background knowledge? Does Messianic prophecy figure in the background knowledge?

4.Suppose I’m an unbeliever. If so, then I naturally regard a miracle as unlikely.

However, that may merely be a default position, due to my inexperience. There may be no positive evidence for my presumption. Just a lack of evidence for the supernatural or paranormal in my personal observation.

Do I need extraordinary evidence to overcome my presumption? No. All I need is some evidence. I have no contrary evidence which must be overcome.

Suppose I experience something miraculous or paranormal. That may be all it takes.

And this happens in real life. Consider, for example, the conversion of Jerome Hines, the American opera singer, who had been an atheist— tutored in math, chemistry, and physics.

This is My Story, This is My Song (1969) ISBN 0-8007-0313-8

5.As I pointed out before, there are a number of internal difficulties with BT. Curry chose to duck that issue by claiming that “Really, I'm not trying to prove anything about Bayes' Theorem. I raised it, but my purpose is not to get into a debate about the validity of it.”

But at this stage of the argument he is clearly using BT to justify his position, in which case he needs to justify BT in relation to the problems I cited.

He also needs to interact with the quote from Coady, which his also chose to dodge. This is quite germane to the assignment of prior probability values.

6.One reason that some of us are unimpressed with Curry’s appeal to BT is that we don’t regard Curry as an authority on BT—especially when there are experts in the field (e.g. Stephen Davis, John Earman, Timothy McGrew, Richard Swinburne) who clearly have a very different take on BT than he does.

4 comments:

  1. Once they quit the booze and drugs they get addicted to God

    As usual the boozeers and druggies that quit and then get addicted to God have to try and shove it down our throats, even though the rest of us don't have addiction problems. There seems to be a certain kind of person that takes everthing to an extreme whether it's an "alternative" lifestyle or a bible thumping clueless zealot.

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  2. Anon,

    Christianity is a sinner's religion. If you don't think you're a sinner, then it's not for you. The reality is though, that you're addicted to sin and apparently blind to it. Your statements betray your ignorance...

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  3. S&BL,

    Didn't you notice s/he was speaking of his/herself when s/he said: "There seems to be a certain kind of person that takes everthing to an extreme whether it's an 'alternative' lifestyle or a bible thumping clueless zealot [or an anonymous poster who pretends self-righteousness]"? :-)

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  4. Steve Hays said:

    "Jason will have to speak for himself, but I believe that when Jason gets into these debates, he brackets the argument from religious experience, since that is inaccessible to an outsider, and confines himself to common ground arguments."

    Yes, that's correct.

    He also wrote:

    "To my knowledge, Jason is noncommittal on BT."

    Yes.

    Steve writes:

    "Does theism figure in the background knowledge? Does Messianic prophecy figure in the background knowledge?"

    I made that point to Jon repeatedly in my discussion with him in another forum last year.

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