Extraordinary claims require extraordinary evidence. This is a logically necessary truth. Notorious Christian apologist William Lane Craig tries to deny this. But only by playing word games. Let’s see how this statement actually pans out, and how Craig is being dishonest in denying it.
Craig, of course, is an infamous liar—as in, he regularly traffics in misrepresentation and distortion, and sometimes even outright falsehoods (documentation here, here, here, here, here, here, here, here, here, here, here, here, here, here, here, and here; and that’s just a sample; for video surveys, try these and these, and now this and this). By now I think he’s a con artist, who plays rhetorical and word games with people on purpose, to sell them on Christ—or really, I think in fact, dupe fellow Christians into not defecting (the actual purpose of most apologetics I have come to believe, as I noted to Randal Rauser, and since have elaborated in Addressing the New Christian Apologetics). Because this dishonest behavior has burned his reputation with atheists. They no longer trust him. So his apologetic mission simply isn’t believable to any other audience than Christians still intent on trusting him.
Be that as it may, Craig has often stated the maxim that “extraordinary claims require extraordinary evidence” is false. And has even attempted to “prove” this with Bayes’ Theorem—in ReasonableFaith.org question no. 604, “Do Extraordinary Events Require Extraordinary Evidence?” He’s been taken to task for his dishonest rhetorical games when making this claim in many other places. And I’ve analyzed his dishonesty about this in video interviews too. But here I will focus on this, his most “official” written statement on the point, which I take to be a more reliable record of his beliefs and reasoning than recordings of his thoughts off the cuff.
I’ve already given the correct analysis of this maxim in Proving History (pp. 114-17; cf. pp. 72, 177-78, and 252-55; which, incidentally, was peer reviewed, including by a professor of mathematics). The following is well supplemented and further explained there, so I highly recommend folks read that first if they want to contend with my point. By contrast, how does Craig’s analysis go?
The Question Posed
On that webpage, Craig is asked by “Mauro” how Craig can call this maxim false, and even claim Bayes’ Theorem proves it’s false, when “every single Bayesian analysis (besides yours) that I’ve read about [it] seems to support it.” And they then present him a correct Bayesian analysis (emphasis mine):
On Bayesian terms, an “extraordinary claim” would be one whose prior probability is very low (Pr (h/b) <<< 0.5). It means that in order to render the claim more probable than not, we need strong evidence in order to counterbalance [that], which is just to say that we need “extraordinary evidence” for such a claim. Extraordinary claims require extraordinary evidence in order to overcome the overwhelming prior probability against such claims being true.
I would refine this to replace “very low” with “extraordinarily low” to maintain consistency (and I have omitted a notation error I’ll discuss shortly). Though “very low” priors do also require “very strong” evidence, usually when we say “extraordinary” we mean even lower priors than that, and thus even stronger evidence is needed than that, hence “extraordinarily low” priors require “extraordinarily strong” evidence. But either way the principle is the same: when the prior probability of a claim is really low, the evidence needs to be really good in order to believe it.
This is always in fact an inviolable mathematical relation: the lowness of a claim’s prior probability of being true is exactly proportional to the highness required of the evidence’s likelihood ratio to warrant at all believing it. Hence Mauro correctly explains that “extraordinary evidence” exists on Bayesian terms when that evidence is “[extraordinarily improbable] if the extraordinary event had not occurred.” And this “is equivalent to say[ing] that extraordinary claims require extraordinary evidence in order to overcome the prior improbability of the claim.” So they ask Craig to explain how he comes to an opposite result using the same math.
Craig’s Opening Argument
William Lane Craig then opens by declaring this questioner has been “misled by sceptical thinkers who are trying to misuse Bayes’ Theorem to support their scepticism about miracles.” So Craig is very definitely declaring what was just presented by the questioner is a “misuse” of Bayes’ Theorem. I cannot believe Craig honestly believes that; I must conclude he’s the one here deliberately misrepresenting facts and logic to evade an important principle posing a danger to his mission. But if you wish to insist on his honesty, you are left with only one remaining explanation: Craig is grossly incompetent in basic math and reasoning. So is Craig here a liar? Or a victim of the Dunning-Kruger effect? I’ll let you decide.
Craig correctly states and describes the Odds Form of Bayes’ Theorem, as calculating the ratio between the Probability of a hypothesis, h, and its denial, ~h, given the evidence, e, and everything else we know about the world, b, thus:
Craig’s first argument is (I think) to call out a notation error Mauro made:
You’ll notice that Bayes’ Theorem doesn’t require you to assign a probability to (h | e) as a means of determining Pr(h | e&b). Therefore it is plainly false that “in order to render the claim more probable than not, we need strong evidence in order to counterbalance the claim’s low prior probability (Pr (h/e) >>>> 0.5), which is just to say that we need ‘extraordinary evidence’ for such a claim.”
The only thing that is “false” here is the notation (in bold). The statement without that mathematical notation is true. So Craig is making a very confusing statement here. It looks like he is saying the maxim is false because there is no need to “assign” a value to Pr (h | e). But that cannot be what he means—as that would be mathematical gibberish, and a blatant non sequitur.
It’s hard to tell if this is a deliberate attempt to deceive, or just really phenomenally bad writing. But the only thing Craig could actually correctly mean here is: it is true that “in order to render the claim more probable than not, we need strong evidence in order to counterbalance the claim’s low prior probability, which is just to say that we need ‘extraordinary evidence’ for such a claim,” but it is incorrect to annotate that as Pr (h/e) >>>> 0.5; the correct notation is Pr (e/h) >>>> Pr (e/not-h). Mauro miswrote Pr (e/h) as Pr (h/e), and incorrectly wrote >>>> 0.5 instead of >>>> Pr (e/not-h). But instead of merely correcting the notation error and acknowledging the maxim is true, Craig appears to turn this into an argument against the maxim. That looks duplicitous.
Because Mauro did go on to correctly say that “strong evidence” can only be defined as evidence that is extraordinarily improbable if the extraordinary event had not occurred, which means (in correct notation) that Pr(e | not-h&b) must be extraordinarily low. That’s just not “the probability (h | e).” So that should have been the only point Craig made here. Otherwise, Craig’s first argument does not present any evidence the maxim he is claiming is false, is false. It’s merely a trivial statement about notation.
Defining “Extraordinary”
The only thing Craig says that could relevantly be an objection to the maxim “extraordinary claims requires extraordinary evidence” is in his following paragraph. Which begins by declaring:
What is needed to counterbalance any low prior probability of (h | b) is that e be much more probable on h than on not-h. You correctly note this factor in your penultimate paragraph.
This literally restates the maxim Craig declares false. So Craig is now affirming the maxim and thus contradicting himself. So what is going on here? Craig is playing a verbal game. Because he then immediately claims:
But then you erroneously infer, “But this. . . is equivalent to say[ing] that extraordinary claims require extraordinary evidence in order to overcome the prior improbability of the claim.” That is plainly wrong, unless one begs the question by simply defining “extraordinary” to mean “more probable on h than on not-h”
But that is not an inference from what Craig just affirmed. It is a literal restatement of what Craig just affirmed. So Mauro cannot have “erroneously inferred” his statement from Craig’s. Nor can Mauro’s statement just quoted be wrong. Much less “plainly” so. It’s actually right.
Craig seems to have only one actual argument then: that it “begs the question” to “define” the word “extraordinary” to mean “more probable on h than on not-h.” But that’s not begging the question. That’s defining the word. Mauro’s entire point is that this is what “extraordinary evidence” means: that “extraordinary claim” must mean a claim with an extraordinarily low prior; the only way to overcome that is with extraordinarily improbable evidence; therefore that is what we mean by “extraordinary evidence.” That is a correct inference. And it simply restates what Craig himself just affirmed is true.
Craig is thus not responding to Mauro’s point. He is instead lying: he is claiming that people who affirm this maxim don’t mean by “extraordinary evidence” evidence that’s extraordinarily improbable unless the claim is true. But Mauro just said that was what he means. And in actual fact it is what everyone means who uses this maxim. Craig cannot simply assert Mauro meant the opposite of what he said; nor can he claim this isn’t what everyone else is saying. As Mauro himself notes: “every single Bayesian analysis (besides yours) that I’ve read about [it] seems to support it.” Because all those analyses mean by “extraordinary evidence” exactly what Mauro means by it. Craig gives no evidence or reason to doubt this.
Nevertheless, Craig continues this bluff by claiming that, instead, “what the sceptic means by ‘extraordinary’ is something like ‘enormous or unusual’.” But that is just restating the same thing in different words. What does “unusual” mean? Improbable. They are literally synonymous. What does “enormous” mean? A lot. Why is “a lot” of evidence “extraordinary” evidence? Because having so much evidence is improbable, unless the claim is true. There is literally nothing else “sceptics” can mean by these words. And when we substitute for those words the only thing sceptics can mean by them, we get what Craig just admitted was true: “what is needed to counterbalance any low prior probability of (h | b) is that e be much more probable on h than on not-h.”
So Craig is not actually making any argument against the maxim here. He is instead lying, about what sceptics mean, claiming they mean instead something they cannot possibly mean, and then arguing that “that” meaning produces a false maxim. And we can be sure this is a lie, because there is literally nothing else sceptics could mean by “enormous or unusual” than “very improbable” (“unless h is true”). So there is no way Craig could honestly think they mean something else by it. Particularly as this is literally what Mauro just told him he means by it!
Craig’s “Argument”
So now that Craig has deliberately created a sham meaning for the maxim, something Craig dishonestly declares contrary to the meaning just told him by the person using the maxim, Craig goes on to beat down the straw man he dishonestly created:
In that sense the evidence need not be extraordinary. Otherwise we’d be forced to deny many non-miraculous events which we know to have occurred despite their high improbability. For example, I recently heard on the news that a particular person in South Carolina had won a powerball jackpot of over a billion dollars. I’m told that the odds of winning were something like one chance out of 320 million. So do I need extraordinary evidence to believe the report on the evening news that that particular person had won? Of course not! The evidence that it takes to counterbalance the low prior probability of that person’s winning needn’t be enormous or unusual at all but just more probable given the truth of the hypothesis than its falsehood.
Craig has pulled a rhetorical trick here (and someone has already pointed this out on his own website). He is claiming winning a lottery is an extraordinary claim, and yet we believe it on non-extraordinary evidence, “therefore the maxim is false.” And yet both those assertions are false. And thus so is his conclusion.
Winning lotteries is an extremely common, superbly-well documented phenomenon. It is therefore ordinary. It is not extraordinary. That is why there is a vast difference between saying a South Carolinan won a lottery, and saying a South Carolinan rose supernaturally from the dead. That people win lotteries has been supremely verified as a common occurrence. That people rise supernaturally from the dead has not. That’s what makes it an extraordinary claim. Not a “merely improbable” one.
Translated mathematically:
- The prior probability of someone winning a lottery is low (say, millions to one against), but not extraordinarily low—as there are millions of people playing lotteries every day, so the prior probability of there being a lottery winner in any given month is not low, but as near to 100% as makes all odds. And we’ve reliably documented thousands of cases (and few ever turn out false). So many, in fact, as to make it one of the most ordinary claims around today.
- But the prior probability of someone rising supernaturally from the dead is vastly lower than that—so low, in fact, that unlike lottery winners, we’ve reliably documented not even a single instance of it in thousands of years. Nor of any powers capable of it. Of course, setting aside the “one instance in thousands of years” that Craig wants to claim is well documented—but we mathematically must set it aside, as that cannot be included in the prior probability, which is conditional only on background knowledge (b), not the evidence of that case (e).
And when a claim is that improbable—having a prior so low it gives us an effective frequency of ~0 across all of human history (see How Not to Be a Doofus)—the evidence we would need to believe it happened has to be, as Craig himself admits, just as improbable (unless the claim is true). Hence, we need extraordinary evidence to believe extraordinary claims. Lottery wins are ordinary claims, so ordinary evidence suffices for them. But miracle claims are extraordinary claims. And that’s why they need extraordinary evidence. Which means, just as Mauro said, evidence that is extraordinarily improbable unless the claim is true.
How Extraordinary Evidence Actually Works
There are many different ways to get evidence that strong. You can, indeed, get there by having “a lot” of it—since the more evidence there is, the less likely it can all have arisen from other causes (like lies, errors, delusions, myths and legends, and the like), so eventually the amount of evidence can reach the scale of the extraordinary: which is when the probability that all that evidence would exist and the claim still be false is extraordinarily low. You can also get there by having a little evidence that’s extraordinarily “good.” Which means, evidence that even by itself is extraordinarily improbable unless the claim is true. Either is “extraordinary evidence.” And either or both would be sufficient to prove likely an “extraordinary claim.” Like rising from the dead.
Just continue the analogy of lottery winners. What if we lived in a world where magically rising from the dead were as common as winning lotteries? In that world, the amount of evidence proving resurrection a thing would indeed be extraordinary, and thus more than sufficient to establish that resurrection in that world is an ordinary claim. And still be as rare as lottery wins—just as with lottery wins. But nevertheless still as ordinary as lottery wins, and thus resurrections could be believed on just the same scale and quality of evidence as lottery wins are.
Much the same follows even if resurrections specifically were not so common or even yet known, but supernatural powers capable of effecting resurrections were. For instance, if we lived in Harry Potter’s world, like him, we would have acquired by now more than extraordinary evidence (in scale and quality) that magical powers exist. And so for us, that resurrection might be possible would no longer be an extraordinary claim. It might be extremely rare, perhaps unattested; but it would still be within the same realm of probability as teleporters are in our world now, and thus would require no more evidence to believe than we’d need to believe teleporters had been invented.
Craig has not only falsely claimed “sceptics” don’t mean by extraordinary “extraordinarily improbable,” and dishonestly misrepresented ordinary events (like winning lotteries) as just as extraordinary as miracles—thus dishonestly not refuting Mauro’s maxim while pretending to have done so—he also dishonestly misrepresents the evidence we have for lottery wins as not itself extraordinary! But alas, it is. If we had the same scale and quality of evidence for miracles as we have for lottery wins, miracles would be easily proved real.
And indeed, evidence for lottery winners is extraordinary. Think of the vast scale of evidence we have confirming that “winning a lottery” is a common phenomenon today, and the extraordinary improbability that all that evidence could be faked or mistaken. If we had that kind of evidence for the resurrection of Jesus—or indeed of any South Carolinan today—we would indeed be warranted in believing it. There is no sense in which the vast system of records and multiple verifications and checks against falsely reporting them, that warrant our trusting reports of lottery wins today, would not be extraordinary enough to verify at least a wondrous resurrection (even if we’d need yet more to confirm its cause).
And that’s not just true for “lottery winners” as a general phenomenon, but even for individual wins. Though for that the evidence we have might not qualify as extraordinary, but neither are claims of winning extraordinary, given all that vast evidence of the phenomenon in general. The evidence we have for individual lottery winners is still more improbable (unless those claims are true) than winning is; which is why we believe reported wins. So although individual lottery wins are not extraordinary claims, they are improbable, in the sense that few people do win; but the evidence available to us for each winner is more than improbable enough to satisfy the requirements of belief. Thus satisfying the maxim.
After all, what is the known base rate of media reports of lottery winners being false? It’s extremely low; much lower than the probability of any individual winning a lottery (indeed, can you even think of an example?). And how do we know the base rate of media-reported lottery wins being false is so low? A vast array of background knowledge about the social system we now reside in, where reported wins are commonplace, and it would be effectively impossible for the media to falsely report wins and not have been caught at it. (And the imagined conspiratorial systems required to make that even likely, are themselves extraordinarily improbable without any evidence of their operating, as all Cartesian Demons are.)
For how this all plays out when looking at the deeply problematic evidence sets we have for ancient times, see my talk on Miracles & Historical Method. And for further explication in respect to Craig’s dishonesty here, see my article Crank Bayesianism: William Lane Craig Edition.
Conclusion
Craig concludes:
There is no dispute here about Bayes’ Theorem. What is really at issue is the meaning of the term “extraordinary.” Sceptics seem to equivocate on its meaning in order to mislead people into thinking that an enormous or unusual amount of evidence is required in order to establish an event which has a high prior improbability.
It is not “sceptics” who are “equivocating” on the meaning of the term “extraordinary.” That is literally what Craig just did—despite knowing full well what Mauro actually meant by “extraordinary” (because Mauro literally just told him) and what Mauro understands all other “sceptics” to mean by it (because Mauro literally just told him).
Craig presents no evidence that any advocate of the maxim “extraordinary claims require extraordinary evidence” defines “extraordinary” in any way contrary to how Mauro just defined it right in front of Craig. And yet on Mauro’s own definition, Craig actually concedes that maxim is correct. But wanting instead to declare it false, Craig fabricates a nonsensical definition for “extraordinary,” dishonestly attributes it to Mauro and all other “sceptics,” and then makes a completely fallacious argument even from that fabricated premise. And there is no way this can be an honest mistake.
That’s William Lane Craig’s entire life schtick in a nutshell.
The bottom line is this:
Craig admits “what is needed to counterbalance any low prior probability of (h | b) is that e be much more probable on h than on not-h” and therefore Craig admits the maxim “extraordinary claims require extraordinary evidence”—as actually defined by advocates of that maxim—is true. Not false. And his attempt to nevertheless claim it is false is entirely built out of dishonestly false definitions, and blatant errors in determining the probability of ordinary events and evidence.
Winning lotteries is not extraordinary. It is in fact so incredibly common and widely documented as to be totally ordinary. Moreover, we actually do have extraordinary amounts of very strong evidence that news reports of winners are almost always true. For miracles, neither is ever the case. They have never been verified as commonplace factual events the way lottery wins have; and we have no evidence for any miracle even remotely as vast or strong as the evidence we have for the reliability of reported lottery wins.
And that is why the maxim “extraordinary claims require extraordinary evidence” is demonstrably true, and not false as Craig dishonestly attempts to claim; and why it effectively refutes all miracle claims to date. All of which are genuinely extraordinary; yet for none of which is any evidence so.
All you ever get is smoke and mirrors- as if the ordinary reader is too dumb to see the holes and false claims in their arguments, as if the reader’s inability to make the same leaps of “logic” is somehow because he or she is stupid.
I never get that with your arguments. You lay it out step by step and let me make my own judgement. And believe me If I had problems following what you said or felt you made patently false assumptions I would stop reading you. I read you only because I find your arguments cogent. And that’s the way it should be.
This is painful… For anyone with a modicum of mathematical knowledge, he’s clearly out of his depth and being poetic at best and deceitful at worst.
The lottery is an interesting example because although it’s common for there to be a winner, the probability of any given person winning is extraordinary low. The way to demonstrate this is to subtly modify the background:
Imagine someone sat down to watch the lottery draw with you and told you they were going to win. Thus primed, if they did win, you might conclude they tricked you. It’s hard to set up a trick, but still easier than winning the lottery. You would need extraordinary evidence to persuade you otherwise.
I actually discuss that scenario, with respect to poker hands, in Proving History (see the cited pages in the above articles).
But your version could have a different analysis, since you need to account for how many people say that, i.e. how many people will tell someone they are sure they will win. If, for instance, most lottery players say that, then their saying that and then accidentally also winning is not so unlikely after all. But if what is said is actually unusual, then your analysis follows. For instance, if someone started engaging in massive investments before having the cash, fully confident of a coming win. And then they won. That is more typically going to happen when a fix is in, and thus a fix is more likely, even accounting for the rare fool who’s false belief is that extreme.
That reasoning is illustrated in Proving History as well, in the analysis of McCullagh’s example of the suspected murder of King William by King Henry (see the index under “William and Henry”). Henry engaged in certain preparations for soon ascending the throne, immediately before William died, which is an improbable coincidence unless Henry knew of the impending death, which is an improbable coincidence unless Henry was in on a plot to kill William.
All that said, though, lottery wins are not, properly speaking, “extraordinarily low” probabilities. They are extremely low, but they are not low in the sense the probabilities of miracles are. An event that’s 300 million to 1 against will occur to a probability near 100% in a population of 6 billion. Even limiting the “population” to lottery players of the same lottery, a win that’s 300 million to 1 against occurs to a probability near 100% in any given year, owing to repeated plays (which amounts to far more than 300 million tickets sold). The only thing that one would count remarkable is that a specific person won, but since this probability is the same for all players, those improbabilities cancel out (as with drawing amazing poker hands; see also my discussion of the “configuration of the stars” fallacy in Proving History in the second named section of Ch. 6; but most relevant here is the “coefficient of contingency,” which is also in the index, as this is what I mean by shared probabilities “canceling out”).
In short, the thesis “game was rigged” and the thesis “game is random” both have the same P(h|b) for every player (so there is no enormous differential for any individual, so no individual’s winning is remarkable enough to make either thesis more probable in and of itself), and they both have the same P(e), too (the evidence looks identical) for every individual, so no individual’s winning changes the prior either. Unless, of course, you have evidence of a rig (like, for example, someone engaging in massive planning in advance of a draw that’s extremely improbable unless they had good knowledge of a coming a win), then that goes in e, and then P(e|game is random) is much lower than P(e|game is rigged). But in no case are any of the differentials extraordinary. So there is never anything extraordinary in lotteries; not individual wins, nor even if one turned out to be rigged (as rigged games is a thing we not only know does sometimes happen, but is always a thing that can happen, without defying any laws of physics for example, which is why we mount precautions against it).
Yes, I was assuming that “how many people say that” was very low. (For me that number is literally zero, so if someone said that it would be a first of many.) I agree it’s also useful to distinguish between low probability events (lottery, unlikely to happen in my lifetime, willing to bet my life on it, i.e. “extremely” low in your parlance), and even lower probability events (rising from the dead, i.e. “extraordinary” low in your parlance). I do think someone telling you “I will win” could increase P(e|game is rigged), because it’s a sort of “suspicious” behavior. Thanks for the exhaustive analysis!
For me, E.T. Jaynes’s works were transformative, and I was pleased to see you cite “Probability Theory: The Logic of Science” in PH. In many ways, it seems even more suited to “History” than to “Science” (traditionally defined), precisely because assumptions can play such a significant role, approximate results have to be aggregated from multiple studies, and because experiments can’t be replicated in a way that makes frequentist approaches easier to apply.
Craig’s basic misunderstanding is a prime example why your work needs to be amplified.
Excellent piece here! This needs to be circulated and shared with people that still put Craig on a pedestal. It really elucidates the fraudulent nature of his apologetical sophistry. I still think you could release a compendium of several of your blogs relating to Bayesianism in hard copy book form. That would be very useful to us lay folk who find this stuff fascinating. While not a math expert myself, reading (and understanding) Proving History was the single best education in my journey to critical thinking.
I have thought of that. Such a book may come to be.
Over at The a Secular Web I wrote a paper about how Craig and other commit similar probabilistic fallacies:
https://infidels.org/library/modern/aron_lucas/hume.html
That is a superb article. Thank you for referencing it here!
Your article was great. I might have to reference it sometime. I was shocked to read some of WLC’s and Davis’s comments. I’m no math whizz, but even I can see their blatant error, The dice analogy is especially helpful. I think of it like a 6 sided dice that has 1, 1, 2, 3, 4, 5; so 1 is more likely than any other single number, but on any given throw, it’s more likely to be a 2, 3, 4, or 5 than a 1 (in other words, P(#1)<P(~#1)).
I’m interested how apologists would respond, having this clearly pointed out to them. If, for example, WLC were ever to ‘get’ it, he could either lose all confidence in the resurrection (the P of that IMO is ->0), or switch the discussion to assigning probabilities so that, voila! the probability of the resurrection now magically turns out to be >50%, and all other explanations total to less than 50%. The god virus survives by mutation and adaptation, so either he wouldn’t understand the concept, or he would understand it and deconvert, or he would understand it and readjust the probabilities in favour of the resurrection. Suddenly we’d have all apologists finding ways to demonstrate that P(R)>P(~R).
What’s even stranger, is that if you talk to lay Christians and Christian leaders, they talk about the resurrection as if P(R)->1. Meanwhile, apologists are talking as if P(R)=0.4, (and no other single theory is greater than 0.4) and those are supposed to be good odds! Ask any Christian if they believe the resurrection is true with a 40% chance, and they’ll say no way! I think WLC might be confused here by thinking that if the resurrection turns out to be the BEST theory, then it’s enough to be HIGHLY CONFIDENT that it’s the BEST theory. You can be 100% confident that something is the best theory, but if that theory is only 40% likely, it’s still only 40% likely, and therefore not very likely!
Having grown up in the church, I’ve not only SEEN this happening, I’ve FELT it happening. There’s a bit of a fog around this kind of thinking that blocks people from seeing this clearly. Obviously, if they saw it clearly, they’d leave the church. As RC says, Bayes Theorem is no friend of Christianity, so it’s no surprise to find LEADING Christian apologists confused about how it works. I had to read Proving History twice to get my head around it.
I’m not so sure they are actually confused. They’ve had this explained to them multiple times by actual mathematicians. And instead of try to delusionally argue the mathematicians are wrong, they avoid ever mentioning what mathematicians said and just keep repeating the fallacy they were just schooled on by actual experts. That looks like a scam. Not an error.
But yes, you are right, most people who “hear” these guys speak think they’ve been told P(R) -> 1. The apologists deliberately couch their language in convoluted ways to make that misimpression likely, while getting to “technically” say they meant P(R) < 0.5 “but we are warranted in believing things that are P < 0.5.” Which isn’t actually true. But that it isn’t true they will never mention or admit even when they fully understand it, because that would lose them the flock.
After reading Hume over 50 years ago at the University of Michigan and re-reading his maxim many times subsequently, I remained perplexed by his phraseology. Aron Lucas facilitated a breakthrough in my understanding of Hume’s maxim in the great article on the Secular Web. I clearly understand Hume’s maxim for the first time, by substituting “improbable” for “miraculous” in the maxim. Many thanks!
Craig often aligns himself with John Earman on this point, as if Earman is an ally. Craig notes the similarity between this maxim and Hume’s miracle against belief in miracles. It is true that Earman criticizes Hume’s claim that extraordinary claims require extraordinary evidence, but not because it is false. Rather, Earman criticizes the maxim because it is so obvious that he doesn’t think it deserves to be mentioned. So Earman is no friend of Craig here. In fact, if Hume is to be faulted for staying the obvious, then Craig is to be faulted all the more for failing to see the obvious.
Indeed, Earman actually develops a correct form of the maxim, and is one of the people Mauro is talking about as getting the opposite result from Craig. Can you find an example of Craig actually claiming otherwise about Earman? This may be another lie I can catalogue (Craig often misuses sources this way).
In Reasonable Faith 3rd edition pp.270-274, he discusses Hume’s maxim and regularly cites Earman. In this middle of these pages, Craig uses this opportunity to also critique the ECREE Maxim, ultimately treating them as the same maxim. He never says Earman agrees with him that ECREE is false, but he begins and ends his discussion of Hume’s maxim by referencing Earman. Like Earman, Craig ultimately says that Hume’s maxim ultimately boils down to ECREE, but they respond to ECREE in opposite ways. Craig criticizes Hume’s maxim because he thinks ECREE is false, while Earman criticizes Hume’s maxim because he thinks ECREE is an uninteresting tautology.
That’s actually also what Craig says, too, though. Look at his statements here as an example, e.g. his quotation of McGrew, which I didn’t quote here, and his affirmation of the maxim Earman affirms, which I did quote here: both times Craig essentially says that the maxim is “either false or trivial,” and what Craig calls the “trivial” sense is actually ECREE, and the sense Mauro actually means; so Craig deliberately misinterprets what Mauro means to mean something “else,” claiming skeptics in general mean something other than ECREE when they say ECREE, and criticizes that something else that he just made up and that no one affirms.
So I would say Craig is skirting untruth with respect to Earman by your description, not outright lying. He is writing in a misleading and dishonest way, but he isn’t outright saying Earman said “the maxim is false.” He only uses Earman disingenuously as somehow criticizing Hume, without specifying what Earman does or doesn’t affirm about testimonial evidence, and juxtaposes this with Craig’s assertions that the “sceptic’s maxim,” duly and disingenuously reinterpreted, is false, in the hopes no one notices he isn’t connecting them, but hoping the mere juxtaposition of “Earman disagrees with Hume” and “Craig says the reinterpreted maxim is false” tricks the reader into thinking they have just been told Earman agrees with Craig.
That’s a lot more complicated to explain than just saying “Craig says ECREE is false.” He doesn’t really; he gives the impression he is, so he may be counting on his readers thinking he is; but what he really is doing is agreeing with ECREE (in Earman’s sense) and then asserting the maxim ECREE used by sceptics is a different maxim than that, call it ECREE2, and then “refuting” ECREE2, but without really explaining that’s what he just did, thus misleading his readers into thinking he just proved ECREE1 false.
And Craig does thus with well crafted language, e.g. when he affirms ECREE he cleverly avoids using the word “extraordinary”; he also smartly avoids explaining that the principle he affirms iterates by degree, such that extraordinary improbability on one side requires extraordinary probability on the other side. Even though that is exactly what Mauro just explained to him and told him to respond to. There is a reason Craig avoids ever acknowledging or responding to the actual question.
Ultimately, what Craig is “literally” arguing is that ECREE2 is not ECREE1, that ECREE1 is true but trivial and trivial maxims can’t be used against miracles (the latter is false of course, but now Craig gets to avoid ever addressing why we should have thought it true; he gets to just assert it as if the word “trivial” is sufficient to evoke the conclusion), and that ECREE2 is false. Even though no one ever uses ECREE2. It’s something Craig literally just made up.
He then argues ECREE2 is false by saying “sceptics” mean by “extraordinary evidence” having “a lot” of evidence or having “unusual” evidence, but he never explains how either is any different from having extraordinarily improbable evidence, or how you can have extraordinarily improbable evidence any other way than it being “a lot” or “unusual.” Indeed, he smartly avoids ever explaining that, because that would expose his scam. He wants readers to think he just said something meaningful when he actually didn’t. And worse, even after pulling that trick, his inference from his fake ECREE2 definition isn’t even logically sound, as he falsely claims lotteries are as improbable as miracles and are believed on trivial rather than (as they actually are) really good evidence. So his false premises there construct a false analogy, which is yet another scam.
No intelligent human being could do this and not be aware of it. Unless it was someone who really rambled like an incoherent crank. And Craig is not an incoherent crank.
I agree that he’s wrong and his logic is terrible, but please, for the love of the gods, stop saying he’s lying! I know it feels so much like he (and other Christian apologists) must be an outright shill, but he’s not. As a former believer myself, I can say he genuinely believes that everything he’s saying is true, and it’s frustrating to read how a complex psychological ‘disorder’ (aka the ‘god virus’) can be flabbergastedly written off as just telling fibs. It’s much more complicated, and you’ll never understand them, while continuing to grow more frustrated, if you don’t make the attempt to understand how a human brain can pump out such sewer-worthy logic and yet totally believe it. It’s baffling, but it’s also fascinating. I was there.
He does this far too often, particularly misrepresenting and quote mining what other scholars have said, but also crafting sentences in misleading ways, repeating false claims he has been repeatedly told by actual experts are false (without mentioning that fact), switching positions from debate to debate when it’s convenient, and many other like things (as I even show here; but also check the long string of links I started with as even more examples).
Craig cannot be doing this “by accident.” I have met plenty of delusional Christians who really believe their bad reasoning or false claims. They do not do what Craig does, at least not so widely, consistently, and pervasively. This is how we know he is running a con. He is not one of them. He argues disingenuously. Not delusionally. And that makes him a liar.
I used to think as you do. But after all the evidence I’ve accumulated to now, I no longer do. It’s not possible to continue running with the charitable hypothesis. It’s been falsified too many times. And indeed you should ask yourself how many examples do you need, before you concur? Is no amount of evidence enough? Or will we just always evade the conclusion, no matter how much evidence we accumulate of it?
Don’t underestimate the power of the delusion. In Craig’s universe, God sent his son to die, and come back to life. The truth must point to that, somehow. Logic (and awareness of logic) is something we’ve comprehended recently; but beliefs, I think, are things that have defined reality for us since before we were swinging in trees. I haven’t personally investigated many of Craig’s claims, so you could be right that he really is a conscious liar…. but personally I doubt it (at least, I suspect cognitive dissonance is working its charms on him well enough to prevent him from realising he’s a con). It’s not the amount of evidence that would convince me, but the quality of evidence. Do we have emails of him confiding in someone that he’s fooling everyone? Taped conversations? Mind viruses are the worst….
Craig’s worse offense in this area was in his Parsons debate. He said:
“It doesn’t take extraordinary evidence to establish that someone is alive…Nor does it take extraordinary evidence to establish that someone is dead…but to establish the resurrection of Jesus all you need is good testimony that someone was alive and then he was dead and then he was alive again.”
Craig is simply guilty of treating all claims as if they have equal priors. It’s true that it doesn’t take much to prove someone is alive. Let’s say P(testimony|alive)/P(testimony|dead)=.99/.01, so there’s a Bayes factor of 99. Let’s say we get the same Bayes factor when someone testifies that someone is dead. The priors for the claim that someone is alive or dead are high, so a Bayes factor of 99 is more than enough for ordinary claims like these. Any prior above 1% can be overcome by this evidence.
Craig seems to be saying that a resurrection is simply the conjunction of the claims “someone was dead” (D) and “then they were alive” (A), and since each of the conjuncts D and A can be established by a Bayes factor of 99, then so can the conjunction D&A. But this is obviously false. Even if the Bayes factor is sufficient for each individual conjunct, their conjunction is necessarily less probable, and therefore requires a larger Bayes factor to make it probable. To make matters worse, D & A are not probabilistically independent. A, conditional, on D, is EXTREMELY improbable, so the conjunction D&A is extremely improbable, so a Bayes factor of 99 won’t cut it, even if that Bayes factor is sufficient for the conjuncts taken individually.
That’s a really good point. I hadn’t known he had tried that stunt. Thanks for quoting it here. And you are quite right.
As someone from South Carolina, I’m pretty sure the correct term is “South Carolinian,” not “Carolinan.” At least that’s the only way I’ve ever heard it. Of course, given South Carolina’s educational system and generally poor pronunciation, maybe going by local consensus isn’t the best idea.
Both are correct. If you google around you’ll find many uses of both in professional periodicals, history books, etc.
As an ex-Christian, I am sharing your arguments regularly with the old crowd. They won’t even engage with your arguments. Now there are many reasons for this, but everyone of them highlights the narrow-mindedness of the ‘narrow path’ to Christ. It’s quite worrying.
That’s standard. All delusional people avoid anything that poses a serious critical threat to their beliefs. It’s called “avoidance behavior.” They will only interact with poor or weak critiques, and ignore or lie about good or strong ones.
The good news is that though most delusional people behave that way, there is always a sizable percentage that is too ashamed to, and they eventually escape the delusion. I have already met hundreds of people for whom this is true even from having read just my work; and I’m just one significant critic among thousands, and the deconverts I actually meet are just a small percentage of those there will have been.
In essence, strong critics always divide the target audience between avoiders-and-deniers and worriers-and-checkers. The worriers, those who are bothered by the strength of a critique and can’t let it go and thus try to fact-check or debunk it rather than ignore or dismiss it, are the ones who eventually argue themselves out of the delusion.
One of the greatest advantages of mathematically formalizing an argument is that it enables us to arrive at precise conclusions, as long as we agree with the premises. So, if we are attempting to mathematize the maxim “extraordinary claims require extraordinary evidence” we might as well go all the way. I believe that the main issue here is the definition of “extraordinary”.
Let us then say that an event x is extraordinary if its probability is less than some value L, assumed to be sufficiently low. In order to ease notation I will avoid writing dependence on background information and assume that it is understood. So, we write the statement that x is extraordinary as P(x) < L. Let h denote a hypothesis, i.e. a claim, and e the evidence for it. Saying that h is extraordinary then means that P(h) < L. If, given the evidence, the hypothesis is more likely than not this means that P(h|e) > 1/2. We want to see if this implies that P(e) < L, that is, that the evidence is extraordinary. Bayes theorem tells us that
P(h|e) = P(h) P(e|h) / P(e).
Since, by assumption, P(h|e) > 1/2, we have that
P(e|h) = P(h) P(e|h) / P(e) > 1/2.
Multiplying both sides of the inequality by 2P(e) we obtain that
2 P(h) P(e|h) > P(e).
Moreover, since we are assuming P(h) < L, we use the last inequality to establish
P(e) < 2 P(h) P(e|h) < 2 L P(e|h).
So we see that we can guarantee that e is extraordinary ONLY if P(e|h) < 1/2, that is, if the hypothesis is not a good explanation for the evidence. Therefore, if we agree with the proposed definition of extraordinary the maxim is false as stated, since it is missing the assumption that P(e|h) < 1/2. Assuming that, however, would be strange, since we want h to be a good explanation for e.
Although we cannot conclude that the evidence must be extraordinary, there still something we can say about its probability being low. Regardless of the value of P(e|h) we know it is at most 1, since it is a probability, so we can conclude that
P(e) < 2 L P(e|h) < 2 L,
which means that the evidence is at most twice as likely as an extraordinary event. Since L was assumed to be very low, 2L must continue to be low. However, by definition, an event with probability 2L is strictly more likely that extraordinary. If we were to say that any event with probability less than 2L but larger than L continues to be extraordinary, we can always repeat the above arguments for an alternative h’ with P(h’) < 2L and conclude that whatever evidence e’ we have for it must have probability P(e’) < 4L, which, again, does not guarantee that it is extraordinary. If we continue pushing the threshold of extraordinarity in this way we will get to a point where any event will be considered extraordinary, which is absurd. So either the reasoning I present here is incorrect (and thus someone should be able to point out where I have made a mistake), you disagree with this definition of extraordinary, or the maxim is false as stated. If you continue to hold that the maxim is correct, the question would then be what do YOU mean by “extraordinary”?
That’s an incorrect analysis.
An extraordinary claim has a prior odds of 1/L, therefore extraordinary evidence must have en evidential odds of L/1 or greater (at exactly L/1 you get the claim’s probability all the way up to 50%; and any amount more it goes higher). They are thus the same threshold. They are defined the same way. Thus extraordinary claims (1/L claims) require extraordinary evidence (L/1 evidence).
QED
WLC’s last resort: appeal to the testimony of the spirit. For a parallel, on the video First Peoples, Season 1, Episode 4, at 23’11”, an aboriginal Australian lady says with great sincerity and conviction, “When I call out to them [Mimi spirits], I can feel their presence, and they’re nearby me. And it make me cry, ’cause I not with them. I’m here alive. But when I’m gone, I’ll be here [at the spirit cave] with them.” (Grammatical errors in original.)