Extraordinary Claims and Extraordinary Evidence
Another common slogan, also popularized by Sagan, is that Extraordinary claims require extraordinary evidence. Much depends, of course, on what counts as extraordinary, both in a claim and in evidence. It cannot be simply that a claim is unprecedented. At a certain level of detail, almost any claim is unprecedented; but this does not necessarily mean that it requires evidence out of the ordinary to establish it. Consider this claim: “Aunt Matilda won a game of Scrabble Thursday night with a score of 438 while sipping a cup of mint tea.” Each successive modifying phrase renders the claim less likely to have occurred before; yet there is nothing particularly unbelievable about the claim, and the evidence of a single credible eyewitness might well persuade us that it is true.
The case is more difficult with respect to types of events that are deemed to be improbable or rare in principle, such as miracles. It is generally agreed in such discussions that such events cannot be common and that it requires more evidence to render them credible than is required in ordinary cases. (Sherlock 1769) David Hume famously advanced the maxim that No testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish (Beauchamp 2000, p. 87), which may have been the original inspiration for the slogan about extraordinary evidence. The proper interpretation of Hume’s maxim has been a source of some debate among Hume scholars, but one plausible formulation in probabilistic terms is that
P(M|T) > P(~M|T) only if P(M) > P(T|~M),
where M is the proposition that a miracle has occurred and T is the proposition describing testimonial evidence that it has occurred. This conditional statement is not a consequence of Bayes’s Theorem, but the terms of the latter inequality are good approximations for the terms of the exact inequality
P(M) P(T|M) > P(~M) P(T|~M)
when both P(~M) and P(T|M) are close to 1. There is, then, a plausible Bayesian rationale for Hume’s maxim so long as we understand it to be an approximation.
It does not follow that the maxim will do the work that Hume (arguably) and many of his followers (unquestionably) have hoped it would. Hume appears to have thought that his maxim would place certain antecedently very improbable events beyond the reach of evidence. But as John Earman has argued (Earman 2000), an event that is antecedently extremely improbable, and in this sense extraordinary, may be rendered probable under the right evidential circumstances, since it is possible in principle that
P(T|M)/P(T|~M) > P(~M)/P(M),
a condition sufficient to satisfy the rigorous condition underlying Hume’s maxim and the slogan about extraordinary events. The maxim is therefore less useful as a dialectical weapon than is often supposed. It may help to focus disagreements over extraordinary events, but it cannot resolve them.
43 comments:
I agree with this.
I think, ECREE is a good rule of thumb you can teach to people as an introduction to skeptical inquiry on paranormal claims, but eventually you'd want a more robust epistemology for evaluating claims. It has it limits, as do all rule of thumbs, but its not necessarily bad.
P(T|M) are close to 1
Really?
Are the McGrews claiming there was a probablity of close to 1 that a gospel would appear in about 65AD?
And there was a probability close to 1 that the 15th chapter (not the 14th or 16th) of Corinthians would contain an account of 500 unnamed people at an unknown time and place witnessing something not described?
Surely the probability of any given piece of testimony , granted a miracle has happened, would be very low.
Even before we factor in that Jesus allegedly told people to be quiet after some of the miracles. Didn't he realise that the probability of testifying was close to 1?
Of course, as all religions so far examined have been based on frauds and lies, the probabilitu of a New Testament miracle has to be considered as less likely than those in the Book of Mormon and the Koran
To take another example, the New Testament records Jesus flying into the sky and disappearing into a cloud on his way to Heaven.
We have overwhelming testimony that a) people do not fly and b) ascending into the sky was a primitive superstition believed by people who lived long long before Copernicus and Galileo.
William Lane Craig boasts that no more than a quarter of Bible scholars doubt the empty tomb.
I can’t check his figures, but imagine trying to convict somebody of stealing a loaf of bread when a quarter of the witnesses called claim they doubt there was a loaf of bread in the first place.
If the evidence is not good enough to convict somebody of stealing a loaf of bread, how can similar evidence be put forward as proof that somebody rose from the dead?
Steven writes: "ascending into the sky was a primitive superstition believed by people who lived long long before Copernicus and Galileo."
Oh, really? Then how is it that I, an amateur astronomer (obsessed with it, actually), who probably knows more scientific facts about the universe than you've ever dreamed of, who has actually read Copernicus and Galileo (their own words, not someone else's re-telling), believe in the Ascension? How is it that both Copernicus and Galileo were ardent Catholics and believers in the ascension until the day of their death?
Have you read either of these Great Men, Steven? Until you've done so, don't be so rash as to cite them in one of your lame, literalist arguments. They wouldn't appreciate it.
And while you're at it, try reading C.S. Lewis's account of the Ascension in his book Miracles. He does an admirable job explaining why the imagery used in those accounts is precisely right, and how any other method of describing the event would be a gross distortion of the Truth being conveyed here.
And to everyone else (other than Steven) reading this, have you noticed how the New Atheists love to employ snarky, adolescent language when discussing matters of Faith (e.g., flying off into the sky, invisible sky daddy, etc.), thinking they have somehow “scored a point” by doing so? But all it does it make them look like immature schoolboys taunting each other at recess.
I can only think of two possible explanations for this counter-productive behavior during debate/discussion:
1) They actually think that such language works, and can possibly help them “win” the argument. (Hint to Steven: It doesn’t . It just makes you look like an ass.)
2) The real target for such infantilism is themselves. they know, deep within their heart of hearts, that they are wrong, wrong, wrong, but use these phrases as a last-ditch defense against admitting their error, falling on their knees, repenting, and actually acknowledging the Lord of the Universe (and of their own lives).
Fess up, Steven. You’re afraid.
While Mr. Prokop undoubtedly feels better by indulging himself in a spot of Christian love - ie childish abuse - he may like to recollect that his Old Book does have stories of his Jesus flying into the sky.
It is not recorded whether or not Jesus was on the back of Pegasus.
Or am I thinking of Muhammad?
One thing religious leaders often do is fly into the sky.
It makes it hard to tell one religion from another.
I am not a new or an old atheist, but the account in Acts clearly depicts the disciples staring up at the sky as Jesus departed this world. That's funny stuff.
Of course sophisticated believers assure me that these accounts were never meant to be taken literally--only stupid fundamentalists do that.
"his Old Book does have stories of his Jesus flying into the sky."
And I believe them (along with at least 1/3 of the world's population). We celebrate the event each year at the Feast of the Ascension.
And, Steven, I was very much engaging in "a spot of Christian Love". Thank you for noticing. If you think that calling you out on your own acts of infantile pseudo-sarcasm is abuse, then so much the better. The first step toward repentance is to see yourself as others do.
That's how God won me over - by showing me what an absolute wretch I truly was.
Walter, I was being serious to Steven. Read the Ascension account in Lewis's Miracles. You'll see why the descriptions of the event in Luke and Acts are completely appropriate, and any other way of narrating it would be misleading.
Bob Prokop believes his Jesus flew into the sky.
Thanks for playing. Better luck next time.
Could we have the next religion that wants to play 'Where is outer space?'
'Read the Ascension account in Lewis's Miracles.'
Bob insists people must not read the Bible without a covering cocoon of spin to protect themselves from what is written on the page.
Or else they will catch atheism if they are exposed to unshielded Bibles.
Oh, Steven, Steven. Where to begin, where to begin?
You pride yourself on believing you know more than the Medievalists, yet even they understood the concept that Heaven is not located in "outer space", but is outside the created universe. As Dante wrote in the Paradiso, "Heaven is outside of space, and has no pole." How clear can one get? And yet you seem utterly unable to grasp this simplest of ideas. How do you presume to speak on complex matters when you haven't yet mastered the very basics?
And as for the reality of the Ascension, yes, Christ did indeed literally and physically rise from the surface of the Earth, and this motion was literally followed by the Apostles until a cloud hid Him from their view.
Why do you find this at all strange? We are physical beings, and we apprehend reality by means of our senses. God condescends to use physical means to teach us of spiritual realities. Thus:
In Baptism, the water used is real water. You could drink it, if you so chose. But it is more than that. It is also a sign, a physical, tangible sign, of Christ's redeeming act (while still remaining water).
In the Holy Eucharist, the bread and wine remain bread and wine, but they are also more (far, far more) than simply bread and wine. they are a sign of Christ's literal and physical presence among us. (We'll leave the Doctrine of Transubstantiation for another thread.)
In the Anointing of the Sick, the oil is just oil, but it is also a sign of Christ's healing power in our lives.
So yes, yes, yes. The Ascension was a literal rising into the sky, seen by witnesses, as a sign of Christ's assumption of Kingly Power. It is God's way of manifesting spiritual realities to our senses. What better way to do so?
Your embarrassingly infantile postings remind me of the atheist Soviets, gloating after the first cosmonaut went into space. They boasted that since Yuri Gagarin did not see God while in orbit, religion had been proven false. (And yes, I am old enough to remember such things!) Do you really wish to descend to such a crude level of discourse? Is that the sort of foolishness you choose to defend?
Carr,
learn to read english.
McGrew is using Bayes theorem, which says that
P(M|T)=P(T|M)*P(M)/P(T)
and
P(~M|T)=P(T|~M)*P(~M)/P(T)
This means that P(M|T)>P(~M|T) if and only if
P(M)*P(T|M) > P(~M)*P(T|~M)
so
Now, the usual reading of Hume is that
If P(M|T) > P(~M|T), then P(M) > P(T|~M)
And McGrew points out that this is not generally the case. But Hume would be right if you would approximate P(T|M)/P(~M)~1, for example when P(T||M) and P(~M) are both close to one.
So what you are objection to is not McGrew, you are objecting to Hume.
Matthew has come up with a startling refutation of Hume.
Matthew claims that Hume's objection to miracles is only right, if and only if the probability of any particular piece of testimony is close to 1, given that a miracle has happened.
But even if a miracle has happened, the chance of any particular piece of testimony occurring will not be close to 1.
Therefore, Hume is wrong.
I congratulate Matthew on this simple refutation of Hume - one which has eluded philosophers for 2 centuries.
Bob Prokop appears to have gone nuts, and is now spouting Christian jargon as though it meant something.
Perhaps it would be easiest if he told us where the Hell Jesus was going when he flew into the sky.
ECREE for what? What is the evidence supposed to do? Change the mind of the fanatic skeptic who thinks maybe the Matrix movie is true? There is only one type of evidence - ordinary.
The extraordinary has nothing to do with the quality of the evidence demanded, it has to do with the degree of change required in the person considering the evidence. I respect that the change of a world view or the change of a human heart is extraordinary.
"[Bob] is now spouting Christian jargon as though it meant something."
Uhh... just what did you expect a Christian to do? Spout Zoroastrian jargon?
Seriously, Steven. You've got to stop doing this. People will start thinking I invented you, just so I could have a ridiculous strawman to put away in debate.
No, fellow posters, I did not make Steven Carr up. If I really wanted to invent an opponent, I would at least make him seem plausible!
I see Bob still cannot say where Jesus was going when he flew into the sky.
I will give him a clue.
The story was made up by people who thought that it was fitting that people flew into the sky, because they lived in a world where such a cosmology was believable.
Later stories of Muhammad flying into the sky also fit the pattern.
Muhammad needed a horse of course, while Jesus managed it on his own power.
>I see Bob still cannot say where Jesus was going when he flew into the sky.
Why does he have too? What does that have to do with anything?
Steve yours is a teenagers Atheism.
I see that people have decided to brazen out the fact that their New Testament was written by people who thought it was suitable for their hero to fly, just as JK Rowling thought a wizard like Harry Potter should be able to fly.
Sorry, but why not have Jesus just, say, spitting on people to cure blindness?
Oh I forgot. He did in Mark 8:23.
You have to laugh at the primitive nature of people who believed magic spit could cure blindness and wonder why such beliefs are taken seriously.
Before even reading the OP, allow me to offer a simpler rebuttal to Sagan --
Sagan: "Extraordinary claims require extraordinary evidence"
Sagan: "Consider this claim: as I walk along, time -as measured by my wristwatch or my ageing process -slows down. Also, I shrink in the direction of motion. Also, I get more massive. Who has ever witnessed such a thing? It's easy to dismiss it out of hand. Here's another: matter and antimatter are all the time, throughout the universe, being created from nothing. Here's a third: once in a very great while, your car will spontaneously ooze through the brick wall of your garage and be found the next morning on the street. They're all absurd! But the first is a statement of special relativity, and the other two are consequences of quantum mechanics (vacuum fluctuations and barrier tunnelling,* they're called). Like it or not, that's the way the world is. If you insist it's ridiculous, you'll be forever closed to some of the major findings on the rules that govern the Universe.
*The average waiting time per stochastic ooze is much longer than the age of the Universe since the Big Bang. But, however improbable, in principle it might happen tomorrow."
Response/rebuttal: lying hypocrite.
It's not just one event---it's ...all the claims of miracles from the time when the supposed miracle occurred--whether read via basic "frequentist" probability (as Hume was) or Bayes, and given the "uniformity of experience" (Hume's posit more or less). Then count up the putative resurrections--every day there wasn't a resurrection (or ghost, or UFO, etc), vs the day there was supposedly one (and considering mistaken testimony..or a hoax, etc). Makes it rather unlikely (tho even Hume would say...not impossible).
What McGrew does is a misuse of stats. In the usual use of Bayes, it would be like comparing reports of success of a potential vaccine vs. reports of failures. So if you had reports of approx .01 success (ie, quite more than the prob. of a Resurrection, given...2000 years or so) and .99 failure yd say it failed. But that's not what the McGrews are saying--they want to suggest the testimony itself shows ...likelihood. But that can't even be weighed IMHO . How do you know its even reliable data in the first place? So...BS ,mostly. You believe or not-- not based on odds.
Response/rebuttal: lying hypocrite.
That's you Idion the Mormonic, like yr new pal "Prokop" (actually Mr Carr, and VR=--note no blog, bizarre profile with pig latin, no posts. A troll, indeed a rather nasty one (tho he's actually a lib-rall, Al Gore fan, vegan, and...get this, Donny Osmond wannabe. So Idion--your new pal--a gay green, aka Byro). More info. to follow
J: You are going off the deep end. Stop now.
Going? When has he ever been anywhere else?
This 'J' appears to be the same "troll" who periodically leaves his vile droppings at my blog (as he recently did using the 'J' sockpuppet); but I always wash such vileness away as soon as I see the email notification. I'm sorry he has has chosen to take advantage of your more lax attitude, VR.
No, Doc VR--that's not how Bayes is used. For one you have a very limited number of witnesses (where..assuming Testimony of M is assumed True).. What about the testimony of those who assumed M was False? Like, everyone else in the world at the time? Or just ..within Judea? Weird. But if you work with frequentism (ie, reports of miracles vs non miracles over....2000 years) then it's nearly statistically impossible that the "miracles" of the New T. happened.
The rest of the comment was for your benefit (not the thug Idion, or his cronies).
Frequentism can't solve the problem of the single case. I argued that in my Infidels paper, and I have never seen that refuted.
Don't have to be a Bayesian to use Bayes' theorem, J.
If you want to go down the road of prob interpretations, propensity interpretation is better than frequentist and Bayesian. Probabilities are objective facts about how the system would behave in the long run. Can calculate with N=1 or N=0 for that matter.
Also gets around silly subjectivism. There is a fact of the matter about likelihood of coin coming up tails, and that fact doesn't depend on my beliefs about the coin, but the properties of the coin.
Learn about it here.
the troll wiki'd Bayes for a few hours, and you are completely wrong--Bayesian inference IS a subjectivist tactic. Frequentism IS the empirical method, however basic (ie, about actual...events--ie, counting the flips of a coin, or alleged miracles, over years, vs...normal experience--
not beliefs, or mere testimony (whether in ghosts, chupacabras, or ancient biblical miracles).
But lets ask VR--what do you think the probability of the Resurrection is, using Bayes T.? (or pseudo-Bayesian--ie, no researcher would use mere testimony as data, especially nearly 2000 years old).
Learn about it here.
Again, you're wrong, as usual, mormon troll with 5000 names.
Speaking of alleged miracles, lets figure out the ..prob. of one Joseph Smith encountering an Angel with golden plates in America with ancient languages on them. About...00000
Victor,
Where can we find your Infidels paper?
What is it even responding to. Eww gross don't touch it.
P(M|T) > P(~M|T) only if P(M) > P(T|~M),
That's not quite Hume's maxim. He also said, given the "uniformity of experience"--perhaps a legalistic point--even subjective ala Bayes--but relevant. Ie, humans havent seen ghosts. Now, perhaps..one person has. Whether we believe his testimony or not, he might have better reasons for believing the dead can come back to life than ordinary mortals do (not that a judge--Judge Hume-- would likely listen to him).
So given the UoE, only the first part of McGrew's little formula would matter--weighing of testimony== With ancient reports more or less impossible (whether Jeesus or..Boodha, etc)--it's more reasonable to assume mistaken testimony than assume the supernatural event occurred. And...Hume's points contra-miracles had secular implications (in theory at least)--ie, scripture would not be used as a dogmatic basis for the law .
But in regard to real time claims of the supernatural--spoonbending, via..spoonbending falsified (in a public setting..another point theists overlook). Claims of spoonbending are subject to frequentist interpretations of P (ie, Kreskin in a room for hours with camera, witnesses, Amazing Randi's crew). It would only matter..if you could show that it's more reasonable (ie, likely) that the miracle/supernatural claim occurred than it didn't occur ( witnessing a bent spoon). And in brief...that doesn't occur--ie, spoonbending has been falsified/shown as a hoax countless times when put to the test.
That said, the metaphorical interpretation of "miracles" remains (ie, the Resurrection's not about..ghosts, but like..the arrival of Spring,etc)--and IMO, that's what the writers of New T most likely intended. Besides, if G*d could do large scale miracles..why not when panzers or the Red Army are rolling--angels at Dachau, etc? Another point fundamentalists forget.
Awaiting yr response Dr VR.
Are Ilion and J the same guy?
Is Anonymouse a fool?
That was a rhetorical question: to ask it is to answer it.
Those who can't understand philosophical writing can always try to derail it, or ban it--whether fundamentalists (Idion), or druggie troll-perps (Anny, Prokop, etc).
J is not Ilion/Troy. This is clear: J hasn't gratuitously called anyone intellectually dishonest, quoted the same sentence multiple times for dramatic effect, or claimed to have refuted all of atheism in one blog post.
I know it shouldn't, and yet it does still continuously amaze me that some persons, rather than modifying their behavior (*) which gives me the opening, would rather whinge (*) about me pointing out (**) their intellectual dishonesty (*). Why, it's almost as though they can't quite figure out that I don't care (**) about their whinging (*).
(*) which is something they can control
(**) which is something over which they have no control
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