Do Extraordinary Claims Require Extraordinary Evidence?
June 6, 2007 Posted by Amy Hall
In yesterday’s debate, Hitchens brought up an oft-cited argument against Christianity, saying that we would need an extraordinary amount of evidence before we could believe that an event as exceedingly improbable as the resurrection actually occurred.
I did a quick search on the internet and brought up a short debate (only 38 pages) between William Lane Craig and Bart D. Ehrman titled Is There Historical Evidence for the Resurrection of Jesus? that addresses this very issue.
Craig first presents four uncontested facts and clarifies the issue:
For now, I want to sketch briefly how a historical case for Jesus’ resurrection might look. In constructing a case for Jesus’ resurrection, it’s important to distinguish between the evidence and the best explanation of that evidence. This distinction is important because in this case the evidence is relatively uncontroversial. As we’ll see, it’s agreed to by most scholars. On the other hand, the explanation of that evidence is controversial. That the resurrection is the best explanation is a matter of controversy. Now although Dr. Ehrman says that there cannot be any historical evidence for the resurrection, we’ll see that what he really means is that the resurrection cannot be the best explanation of that evidence, not that there is no evidence. (pp. 3-4, emphasis mine)
Ehrman dismisses the facts presented by Craig as irrelevant since he has already ruled out the possibility of interpreting them as describing a miracle:
[M]iracles are so highly improbable that they’re the least possible occurrence in any given instance…. I wish we could establish miracles, but we can’t. It’s no one’s fault. It’s simply that the cannons of historical research do not allow for the possibility of establishing as probable the least probable of all occurrences. For that reason, Bill’s four pieces of evidence are completely irrelevant. There cannot be historical probability for an event that defies probability, even if the event did happen. (p. 12)
Therefore, in this debate, Ehrman’s position that there is no historical evidence for the resurrection is based on a philosophical objection, not on a lack of available facts.
Since the objection prevents Ehrman (and many people) from ever considering the actual evidence, Craig then confronts the charge that a miracle, by definition, will always defy probability despite any and all evidence. He argues that we must take into account not only the intrinsic probability of the resurrection in light of our general knowledge about the natural world, but also in light of the specific evidence for the resurrection (I would argue that this should also include our evidence for the existence of God as well as any other background factors that make the resurrection more probable). One also has to place the explanatory power of the counter-hypothesis that there was no resurrection into the equation. He then proceeds to give a mathematical formula that will statistically account for all these factors, explaining where Ehrman’s mistake lies:
Specifically, Dr. Ehrman just ignores the crucial factors of the probability of the naturalistic alternatives to the resurrection…. If these are sufficiently low, they outbalance any intrinsic improbability of the resurrection hypothesis.” (p. 16)
I won’t recreate the formula here since it would probably cause many of us to run screaming from our computers. But if you’re mathematically or statistically minded, take a look. I heard Richard Swinburne speak about this formula once, and he came up with a probability of .97 for the resurrection (Craig notes this in the Q&A section at the end of the debate).
Related posts:
- God is Never the Answer
- Interview With Glenn Lucke – Part Two: Is Evidence Valuable When Telling Others About Christ?
- Can One Prove the Existence of a Miracle?
- Pre-Biblical Account of the Resurrection
- The Tomb Storytellers
- Book Review: Truth and Fiction in the Da Vinci Code by Bart Ehrman
Posted in Amy's Posts, Apologetics, Main Page
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June 6th, 2007 at 6:14 pm
In that debate, Dr. Ehrman says, “I am sorry. I have trouble believing that we’re having a serious conversation about the statistical probability of the resurrection or the statistical probability of the existence of God. I think in any university setting in the country, if we were in front of a group of academics we would be howled off the stage—”
I’m always amazed by arguments such as this, against finding statistical probabilities for the Resurrection of Jesus, or for certain Intelligent Design theories. Crack open any astronomy textbook and look up the Drake Equation. You’ll find serious discussions by academics about the probability of finding intelligent life in the universe, based on far shakier and more speculative science. Then turn to the section on SETI (the Search for Intelligent Life in the Universe), and read about how your tax dollars are being spent to listen for signals from outer space. I assure you, there’s far greater evidence for the Resurrection than for intelligent civilizations capable of communicating with us. So why are SETI and the Drake Equation considered acceptable science?
June 6th, 2007 at 6:26 pm
Great point!
August 26th, 2007 at 4:02 pm
Caveat emptor: this result is not conclusive, I admit, but it is interesting and relevant.
Craig states during the debate: “Now probability theorists have developed a very complex formula for calculating probabilities like this, and I'm going to walk you through it one step at a time…”
He then uses the phrases “intrinsic probability” and “explanatory power” as definitions for the terms in his equation. The implication here is that these are the terms used by the probability theorists when develping this very complex formula.
However (and refer to my cavear emptor), a google search on
“intrinsic probability” “explanatory power”
yields results ONLY directly related to this argument (and some results which use the phrases in a different context altogether). There are no links to papers on probability theory. No links to web sites on probability theory. No links to anything outside theological arguments. This seems more than a bit misleading and devious to me. Couching an argument in terms of rigor but inventing your own jargon.
Like I said, not conclusive but VERY interesting.
August 27th, 2007 at 1:53 pm
Ken, I think you've misunderstood somewhat. “Intrinsic probability” is not a technical term. “Intrinsic” merely means the probability it has within itself (before the other factors are considered). The symbol Pr (R/B), then, refers to the probability of the resurrection (R), given what we know about the world (B). The words “intrinsic probability” describe that, but it's not a technical term everyone would use. Instead, he's translating for his readers (philosophers), using the philosophical words (e.g., “intrinsic”) to describe to philosophers what the mathematical terms (R/B) are stating.
In the same way, he translates the mathematical formula, Pr (R/B&E), into philosophical terms. The formula is intended to show the probability of the resurrection to explain the available evidence. In philosophical terms, this formula shows the explanatory power of the theory.
The philsophical phrases are not changing the way the formulas work, he's merely communicating the work the formulas are doing to an audience who speaks “philosophy” rather than “mathematics.”
August 28th, 2007 at 12:52 pm
Fair enough.
August 28th, 2007 at 5:48 pm
Not sure how versed you are in probability theory. I've done a tiny bit but don't fully understand the math.
I found a reference which states that Swinburne uses Bayes' Theorem for his result. I then read a little bit about Bayes' Theorem and it is applicable to random variables. It “relates the conditional and marginal probabilities of stochasitc events A and B” (from wikipedia).
So, my questions is: Is it even valid to apply Bayes' Theorem to this problem? Are the resurrection and our background knowledge of the world random variables?
August 30th, 2007 at 1:41 pm
I'm not that familiar with probability theory, but going to Wikipedia, here is my understanding of the statement you quoted. The variable is random until its probability distribution is assigned. So “random variable” is a technical term for the variables that are being considered in the theory in order to determine their likelihood of occurring together (i.e., how random they are).
Some more clarifying definitions from Wikipedia:
In other words, it measures the likelihood of the resurrection given the available evidence. It does this in part by measuring the probability of the present variables occurring together randomly. If such a thing is unlikely, then the resurrection looks more likely.
September 2nd, 2007 at 10:40 am
I do know that a “random variable” can take on random values. Sometimes these random values are in a certain range — like the toss of two dice. You can get numbers 2 through 12. But you get each of the values randomly.
Every random variable has a probability distribution which is a function telling how often each random value comes up. So, in the case of the two dice, the probability distribution is peaked at 7 and decreases towards 2 and 12. This is because it is much more likely to get a 7 than a 2 or 12 because there is more than one way to get a 7.
So, the probability distribution has nothing to do with reducing the randomness of a variable. It simply tells you how likely each possible random value is.
The key — from what I understand — is that a random variable has the necessity of repeatability. A random variable is one that can be measured again and again and again so that the probability distribution is generated. The toss of the dice, the flip of a coin are both random variables because you can do it again and again. Yes, you can talk about the likelihood of THIS roll producing a 5 and this seems like an isolated event but the analysis is based on this same event being repeatable.
So, perhaps I'm just not “getting it” but I don't see the resurrection of Jesus as a random variable at all. It happened once to one man. It's not repeatable. There's no probability distribution function because there's only one data point. I guess we could phrase it something like “the probability of a person being raised from the dead” and then the case of Jesus is one instance of this. But I'm not sure that this even works.
Anyway, I'm still not satisfied that the analysis method is valid for this case but I don't know enough (and don't have the time to learn probability theory right now) to figure it out. I'm going to ask someone who is much more versed in probability theory and then I'll get back to you.
September 5th, 2007 at 5:35 pm
So, perhaps I'm just not “getting it” but I don't see the resurrection of Jesus as a random variable at all.
I could be misunderstanding, but I don't think the resurrection is one of the variables–that's what they're trying to measure the probability of, in light of the variables. The variables would be things like the empty tomb, the beginning of the church, etc. What is the likelihood that all of these present variables would occur at the same time if there were no resurrection? Or does the resurrection actually have the most explanatory power (as opposed to other theories)?
I don't think probability theory is only used for repeatable, mathematical things. For example, actuaries determine things like the probability that a person will get a serious illness for health insurance companies. They look at the variables present (they smoke, they drink, etc.) and determine risk of illness. They have ways of assigning values to the variables, but I have no idea what those ways are, not being a statistician.
September 5th, 2007 at 7:33 pm
For example, actuaries determine things like the probability that a person will get a serious illness for health insurance companies. They look at the variables present (they smoke, they drink, etc.) and determine risk of illness.
Exactly! They look at hundreds of thousands of people who smoke or drink or whatever and figure out who had a serious illness and what it was. Then they assign a probability to you or to me to figure out our premiums. But it's all based on a very very large sample.
Again, from wikipedia (the page on Probability Theory – embedding the url caused a problem):
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. Although an individual coin toss or the roll of a die is a random event, if repeated many times the sequence of random events will exhibit certain statistical patterns, which can be studied and predicted.
And if you follow the link to event, you'll see that an event is with respect to a larger sample space. Think about a UFO crashing on Earth and the alien is dead. Doctors are able to determine (this is hypothetical, after all) that the alien did not die in the crash but rather it died of congestive heart failure (and that is, presumably, why he crashed). Then another alien crashes and he, too is dead but not from the crash. Before doing an autopsy, what is the probability that this second alien died of congestive heart failure? There is, obviously, absolutely no way to determine this because there is no sample space from which to draw the conclusions. Heart disease in this species may be very common or very uncommon. Perhaps it's caused by space travel so it's more likely that the second alien did die from it. But no matter what, there is no way to assign a probability that the second alien died from heart disease.
I see the resurrection as the same situation. It is such a unique event that there is no sample space from which to draw any knowledge.
September 5th, 2007 at 7:35 pm
For example, actuaries determine things like the probability that a person will get a serious illness for health insurance companies. They look at the variables present (they smoke, they drink, etc.) and determine risk of illness.
Exactly! They look at hndreds of thousands of people who smoke or drink or whatever and figure out who had a serious illness and what it was. Then they assign a probability to you or to me to figure out our premiums. But it's all based on a very very large sample.
Again, from wikipedia (the page on Probability Theory – embedding the url caused a problem):
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. Although an individual coin toss or the roll of a die is a random event, if repeated many times the sequence of random events will exhibit certain statistical patterns, which can be studied and predicted.
And if you follow the link to event, you'll see that an event is with respect to a larger sample space. Think about a UFO crashing on Earth and the alien is dead. Doctors are able to determine (this is hypothetical, after all) that the alien did not die in the crash but rather it died of congestive heart failure (and that is, presumably, why he crashed). Then another alien crashes and he, too is dead but not from the crash. Before doing an autopsy, what is the probability that this second alien died of congestive heart failure? There is, obviously, absolutely no way to determine this because there is no sample space from which to draw the conclusions. Heart disease in this species may be very common or very uncommon. Perhaps it's caused by space travel so it's more likely that the second alien did die from it. But no matter what, there is no way to assign a probability that the second alien died from heart disease.
I see the resurrection as the same situation. It is such a unique event that there is no sample space from which to draw any knowledge.
September 5th, 2007 at 7:38 pm
Sorry about the duplicate posts. The first try looked like it failed and I didn't check whether it really did fail or not.
September 13th, 2007 at 2:26 pm
It must surely be recognizable to anyone who examines any claim that no claim is objectively extraordinary. A claim is only extraordinary in context of a given worldview. If a claim contradicts that worldview, it is extraordinary to the degree that it contradicts that worldview. The proof required is extraordinary only to the degree that not accepting that proof requires more effort than does altering one's worldview to take the logical conclusions derived from that evidence into account.
Ex., if I believe in elves (perhaps I am living in the World of Greyhawk) and you tell me that there is an elf outside that wishes to speak to me, this is not an extraordinary claim. It may not be a true claim, but it is one which falls within the context of my worldview.
Ex., if I do not believe in elves (perhaps I am living in the real world) and you tell me that there is an elf outside that wishes to speak to me, this is an extraordinary claim because it is in contradiction to my worldview. Even were it true, I would be liable to dismiss it. I would certainly not accept pointy ears and a smarmy attitude as “proof” that the person on my doorstep was an elf.
Likewise, in the real world, some of the claims made re: Relativity or QM have been, so far as we know, accurate, but have required “extraordinary proof” to be accepted as so for the simple reason that they violated the until-then most popularly held scientific viewpoint.
IOW, “Extraordinary claims require extraordinary proof” is missing the phrase “to be accepted by those to whom the claim seems extraordinary”, which is required for the statement to be sensible.
Hence, “Extraordinary claims” means nothing more than “claims which go against other things that I have accepted as true, and therefore which would require me to alter my belief system should I accept them”, which has little or nothing to do with whether said claims are true. It justifies a “no amount of evidence will change my mind” attitude all too often, though perhaps not in this case.