Yet I cannot help but compare Carrier’s approach to the work of Richard Swinburne, who likewise uses Bayes’ theorem to demonstrate the high probability of Jesus’ resurrection, and wonder if it is not fatally telling that Bayes’ theorem can be used to both prove the reality of Jesus’ physical resurrection and prove that he had no existence as a historical person.49
49 Richard Swinburne, The Resurrection of God Incarnate (Oxford: Oxford University Press, 2003).
The above quotation is from page 16 of Daniel Gullotta’s 37 page review of Richard Carrier’s On the Historicity of Jesus [OHJ].
To make such a comparison one would expect the author to be familiar with how the Bayes’ rule is used by both Carrier and Swinburne. Unfortunately Gullotta nowhere indicates that he consulted the prequel to OHJ, Proving History, in which Carrier explained Bayes on a “for dummies” level and which was referenced repeatedly in OHJ. Gullotta moreover indicated that he found all of the Bayesian references in OHJ way over his head — even though the numbers used were nothing more than statements of probability of evidence leaning one way or the other, such as when we say there is a 50-50 chance of rain or we are 90% sure we know who’s been pinching our coffee at work. Robert M. Price has expressed similar mathemaphobia so Gullotta is not alone.
Anyway, we have a right to expect that the reviewer is familiar with the way Bayes is used in at least one of the works he is comparing, and since he skipped the Bayesian discussion in OHJ he is presumably aware of how Swinburne used Bayes to effectively prove the resurrection of Jesus.
Bayes’ theorem is about bringing to bear all background knowledge and evidence for a particular hypothesis, assessing it against alternative hypotheses, and updating one’s assessments in the light of new information as it comes along.
If that sounds no different from the common sense way we ought to approach any problem, that’s because it is no different from common sense methods. That’s why Bayes “cracked the enigma code, hunted down Russian submarines and emerged triumphant [even in historical studies!] from two centuries of controversy“.
Anyway, scholars who ought to know better have indicated that they can safely dismiss Bayes because Richard Swinburne used it to prove the resurrection of Jesus. Never mind that that’s like saying we should never use syllogisms in argument because some joker used one to prove everything with two legs was a man.
So let’s see exactly how Swinburne used a tool that some of the smartest people in the world use for all sorts of good things in order to prove Jesus is alive today and about to come and judge us all.
Bayes works with facts. Hard data. Real evidence. Stuff.
For Swinburne, anything in the Bible is a definite fact that requires us to believe it if there is nothing else in the Bible to contradict it. That’s the “hard data” that Swinburne feeds into his Bayesian equation!
Notice some of Swinburne’s gems found in The Resurrection of God Incarnate (with my own bolding as usual):
Most of St Paul’s epistles are totally reliable historical sources. The synoptic gospels are basically historical works, though they do sometimes seek to make theological points (especially in the Infancy narratives) by adding details to the historical account. St John’s Gospel is also basically reliable, at any rate on the later events of the story of Jesus . . . . (p 69)
I argued earlier that, in the absence of counter-evidence, apparent testimony should be taken as real testimony and so apparent historical claims as real historical claims. (p. 70)
It seems fairly clear that the main body of the Acts of the Apostles is intended to be taken as literal history. It reads like any other contemporary work of history, and the later parts (which contain no reports of anything miraculous) are so detailed and matter-of-fact as to have a diary-like quality to them. (p. 71)
Hence there is no justification for thinking that Mark is trying to do anything else than record history when he writes about these events . . . (p. 73)
I conclude that the three synoptic Gospels purport to be history (history of cosmic significance, but I repeat, history all the same). (p. 74)
Just as apparent testimony must be read as real testimony, so real testimony must be believed, in the absence of counter-evidence. (p. 76)
I have argued in Part II that the data we have about the life and teaching of Jesus are such as it is not too improbable that we would find if Jesus was God Incarnate, and had become incarnate for all the reasons considered in Chapter 2. The probability is far greater that Jesus was God Incarnate than is the probability on available data concerning any of the other prophets of human history that any of them was God Incarnate. (p. 140)
In discussing this problem, I am going to assume for the present that Mark is correct in telling us that there was a visit by women to the tomb on the Sunday morning. This testimony, like all testimony, is to be believed, in the absence of counter-evidence. (p. 151)
11 Rival Theories of What Happened
Abstract: If Jesus was not raised bodily, some rival theory of what happened to his body must be true. The only possible theories are that Jesus was not dead when taken down from the cross, the body remained in the tomb but the disciples misidentified the tomb, enemies stole the body, grave robbers stole the body, friends of Jesus (probably the ‘women at the tomb’ on the Sunday morning) stole the body. The latter is the least improbable of these alternatives to the traditional account. But it involves great deceit, which would probably have been recognized by the Christian leaders, and it involves those friends giving the body an improper burial. And it would still not account for the large number of appearances, some of them to many disciples together. The traditional account is certainly the simplest. (p. 174)
The only possible theories do not breathe a hint that the entire story might be theological fiction. Finally, here is one more peek at the “hard evidence” that Swinburne enters into his calculations:
In order to articulate the structure of the argument of the present book, it will now be necessary to give different meanings to the above letters. Let k now be not a mere tautology, but the evidence of natural theology (including the sinning and suffering of humans). Let e be the detailed historical evidence, consisting of a conjunction of three pieces of evidence (e 1& e 2& e 3 ). e 1 is the evidence of the life of Jesus set out in Part II. e 2 is the detailed historical evidence relating to the Resurrection set out in Part III. e 3 is the evidence (summarized in Chapter 3) that neither the prior nor the posterior requirements for being God Incarnate were satisfied in any prophet in human history in any way comparably with the way in which they were satisfied in Jesus. (p. 210)
For a serious scholar to seriously draw a comparison between the claim that Bayes’ theorem can prove the resurrection on the one hand and Carrier’s use of Bayes’ on the other is surely nothing less than a failure in intellectual honesty.
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49 thoughts on “How Bayes’ Theorem Proves the Resurrection (Gullotta on Carrier once more)”
As u no, Carrier himself castigates Swinburne’s infelicitus use’v Bayes:
“…Swinburne of course also argued “from the resurrection” that the probability God exists is much higher than 50%, in yet another book, The Resurrection of God Incarnate. Which is also filled with standard bogus Christian premises. He just translates his bogus premises into numerical notation. That doesn’t make them any less bogus. I already refute all Bayesian arguments that “Jesus was probably resurrected by God” with a correct Bayesian model in The Christian Delusion (pp. 291-315). I see no need to repeat any of that here. But if you check that out you’ll notice, Swinburne just repeats the usual false claims about the evidence, and builds his probabilities on those false claims. But false claims in, only gets you a false claim out.”
Another scholarly (presumed) confutation of Mythicism comes from prof Bermejo-Rubio in this article.
You will not find anyone will accept mythicism if their career depends on them not accepting it. And I don’t just mean scholars. Anyone who has a business, any sort of business, which has cultivated a Christian clientele, if they were to suddenly stop masturbating them, Christians would boycott the business for sure. I have seen two kinds of people, people whose livelihoods collapsed after doing so and people who maintain an illusion that they are Christian while not admitting agnosticism publicly. People have criticized me for calling these people cowards, but I don’t do so lightly. No one forced you to base your business on a Christian clientele. What I’m talking about isn’t running a business based on Christian principles but actually using Christian imagery on your marketing, hiring openly Christian staff. If you take any of that away, Christians notice, with their wallets.
Do you have access to that article — the link and download are only to the schedule of the conference.
The professor “cannot help” but make a spurious and sophistical comparison. The intellectual dishonesty is rampant. The “historical Jesus” scholars in the departments of religion all appear to START with the proposition that the historical Jesus does not involve miracles of any kind, be they resurrections, healings, walking on water, etc. To my knowledge, none of them claim (as Swinburne does) that the synoptic Gospels are primarily historical works. These scholars usually END with the proposition that Jesus was some kind of humble itinerant Jewish peasant-preacher, NOT that the dove came down and the voice came out of the clouds, NOT that the thousand were actually fed with loaves and fishes, and on and on. In other words, one would not expect any of THEM to apply the theorem to the Resurrection, which they all admit at the outset is a fictional overlay. It gets more and more ridiculous.
Gullotta is not yet a professor but perhaps with this review article he has established his credibility within the guild as the one who “demolished” Carrier. No-one now needs to bother reading Carrier, nor even all of the 37 pages of the review. Gullotta did not even have to have read the relevant sections of the books he was comparing. Just repeating the rumour in a scholarly context was enough. He is being thoroughly moulded into correct thoughts and outputs to qualify him as a good biblical scholar of impeccable credentials and standing. But of course he would not even be doing the PhD program at Yale had he not demonstrated sufficient compliance with correct thoughts in the first place.
Is this being review being touted by the usual suspects; the ones so dismissive of lack of credentials in others, even if they are in PhD programmes in the relevant fields?
Interesting that in the review Gullotta has a fair bit to say about “academic detachment” being necessary in approaching this question and he faults the mythicists on this score. Yet Gullotta also lists McGrath and Hurtado as among the scholars he consulted in preparation for his review. Oh the irony the irony.
Which is more probable: gross violation of the laws of physics or fantastic fiction of some kind? I might make allowance for Joe Bloggs in the pew, he is perhaps merely ignorant. This is a post-grad. Who has spent a hundred grand or more inculcating himself in nonsense on stilts.
Interesting form of *peer* review where the reviewer begins by admitting he doesn’t understand the paper at hand.
I wonder* if the editors would have let him publish if he took pride in knowing no Greek.
*No I don’t.
While I don’t know Greek, I’ve had Christians who also don’t know Greek tell me that I don’t understand something because of how it’s to be read in Greek.
The problem is that it entirely inappropriate to use Bayes’ Theorem (BT) to try to answer such questions. BT says that the probability of A given B is equal to the probability of B given A, times the probability of A, divided by the probability of B.
This works just fine if you can calculate or already know the probabilities on the right hand side of the equation; if, for instance, you want to know the probability of filling an inside straight given the cards already showing. However, if you don’t know or can’t calculate those probabilities, then you have to guess what they are, and your answer will be no better than your guesses.
If A is “Jesus existed” and B is all the evidence we have, then to use BT you have to input the probability that we would have the evidence we have if Jesus existed, the probability Jesus existed, and the probability of the evidence we have. Obviously, we don’t know and can’t calculate any of those probabilities. Anyone who tries to use BT to answer this question will have to just make stuff up to plug into the equation, and the result will be just as fictional as the input. And if you don’t like the resulting fiction, you can just tweak the fictional input to get the fictional output you want.
You’ve just disproved about a half of bayesian inference. Thousands of scientists worldwide are packing their bags as we speak.
Just who are these alleged scientists? Frankly, I would hesitate to call anyone who abuses Bayes’ Theorem a scientist.
I wonder if this is a case of being able to trust some people’s (scientists’) guesses more than other people’s (religionists’) “facts”.
In science, nobody’s guesses are trusted. That’s why they do experiments.
Bayes’ is a reiterative process. As we continue to search for the answer we continually encounter new evidence and revise our confidence in our hypothesis accordingly .
We can’t do experiments in history, but we can do historical investigation and evaluate each new piece of evidence or background information.
But the inputs to Bayes’ Theorem are not the bits of evidence, but probabilities. While the discovery of, say, a new gospel manuscript may change the probability that some particular story is true, there is still no way to say what that probability is.
In historical reasoning we can do predictions: What would we expect to find in the data if X were true? We test those predictions against the results.
The inputs are not probabilities but data.
The discovery of a manuscript would prove nothing of itself nor change probabilities simply because of its discovery. The new manuscript would be subject to the same predictions tests as the existing gospels or letters.
It is data that is input. Probabilities are assessments about the data and need ongoing testing.
I’m not sure what experiment you could come up with to test the probability of resurrection.
Yeah Mike, I mean scientists literally, that means theologians and crackpots like Swinburne don’t count.
Bayes theorem is in fact perfectly appropriate to try and answer such questions.
Let’s not blame the method for ignorance of those trying to abuse it.
Not at all. I was able to use Bayes perfectly fine for just such a question (relating to James the brother of the Lord) at http://vridar.org/2012/04/22/putting-james-the-brother-of-the-lord-to-a-bayesian-test/ and historians (not just Carrier) do use Bayes (see Aviezer Tucker). I take it you have read neither Proving History nor On the Historicity of Jesus. If not, let me know, and I can show you exactly how what you describe is not the problem you think it is.
Your post on James illustrates what I am talking about. At one point you say, “I would say the typicality of our hypothesis should be ‘very probable’, let’s say 0.95.” Where did the 0.95 come from? You didn’t measure it; you didn’t calculate it. It is just a guess, as you yourself seem to realize in your next two sentences, “Or am I being overly generous here? Will I think the same tomorrow?” If you had a solid basis for the 0.95, you wouldn’t say that. Can you imagine a physicist saying, “The speed of light is three times ten to the eighth power meters per second, but tomorrow I might use a different figure.”?
Even later you say, “If I juggle the figures a bit to try to be more accommodating to what evaluations I would expect historicists to make, I can bump up the figure to 66% probability the hypothesis is true.”, which illustrated another problem I mentioned.
No, I haven’t read Carrier’s work; I have little reason to think that it would be worth the time.
Just because some historians use Bayes’ Theorem does not mean that they are using it correctly.
Note that I am not criticizing the theorem itself. it is a perfectly good theorem. When used correctly. There are even situations in which estimates of the input probabilities, or even just illustrative values, might be all that is needed for the purposes of the calulation (I am thinking of the usual example showing counter-intuitive results of medical tests).
No, you are confusing two quite separate things here. Your statement about the physicists knowledge of the speed of light is not a probability estimate but a known figure. It’s a known. No estimates required.
If I say that it is 95% probable that the evidence of black clouds and temperature drop means it is going to rain soon, then I am not just wildly guessing without any justification. I have lots of experience and knowledge about typical signs that precede a storm. But it is still a probability estimate and not a fact because sometimes there can be changes in winds or pressure systems that turn the storm away — and then I find that the 5% gap kicks in and I was wrong. But most times I would be right.
To take another common illustration. I can say that I am 99% sure my wife is faithful to me. But if someone shows me evidence that suggests the contrary, then I may revise my estimate down to say 90%. That’s still a pretty high estimate and confidence. But if I keep on getting new information that supports the alternative hypothesis then I revise my confidence in my own hypothesis down accordingly.
That’s how it works. I don’t see any problem with that.
First off, I apologize for taking so long to answer. Time just got away from me.
The speed of light was not a good physical constant to use here, since its value is set by definition. That is, the length of the meter depends on the speed of light, not the other way around. So let’s use Planck’s constant, instead. The currently accepted value (in the beginning of 2018, and since 2014) is 6.626 070 040(81) x 10^-34 J s (https://physics.nist.gov/cgi-bin/cuu/Value?h). That “(81)” is the uncertainty. All measurements have uncertainties. The actual value has a 68% chance of being within the given uncertainty. Further, the values of the physical constants are constantly being revised. The recommended values are set by the Committee on Data for Science and Technology (CODATA), and are revised every few years. So yes, their values are estimates, albeit very good estimates.
At any rate, the difference between your weather examples and Biblical (or other historical) applications of Bayes’ Theorem is that in the scientific cases the input probabilities to the theorem can be measured, although perhaps with large errors. As you say, further measurements or observations can result in modification of those probabilities.
But in the historical cases, that just isn’t possible. The input probabilities are no better than guesses. There are no further measurements or observations that could affect them. How, for instance, could anyone know the probability that the gospels would say what they do say given that Jesus existed? What further measurements or observations could be made to affect the estimate of that probability?
Let me be clear about what I object to. I object to using Bayes’ Theorem to get a numerical answer that is presented as truth when the inputs to the equation are just guesses.
I also object to not even trying to assign uncertainties to those guesses, and to not propagating those uncertainties through to the result of the equation. I wouldn’t be surprised that if that were done properly, the result would be an answer like “the probability of Jesus existing is 0.3 ± 0.5”.
That “±” on the last line is supposed to be a plus-or-minus sign. I guess character entities don’t work here.
No one is suggesting that historical reasoning is as precise as controlled physical measurements but it doesn’t have to be.
Yes, sometimes we do start out with nothing very much better than a wild guess — I’m thinking of the way Bayesian reasoning is used by, say, search for aircraft beneath the sea. But searching gradually reduces the parameters of the initial guess as more data emerges, as we have seen in historical instances in the Indian and Atlantic Oceans.
As for your particular question, there is indeed a probability figure that could be given for the gospels saying what they do given that Jesus existed. We use background knowledge. We compare what biographies say of comparable people we know existed; we compare the gospels with other forms of literature and identify its sources that way — and compare with literature that writes about comparable known persons.
If we say we give very slight or very strong or roughly even chance of something happening or having happened then we are using quantifying language and that can be represented by numbers. We can do that all the time. We don’t refuse to do so because we can’t get the figures as precise as we need for a certain physical measurement to operate some equipment or whatever.
Probability estimates are not a once-off do or die exercise. If we have absolutely no idea then, yes, we do take a wild guess, and proceed to look for further feedback and information as we do our search and refine our initial estimates in accordance with the new information. It’s a reiterative process.
> This works just fine if you can calculate or already know the probabilities on the right hand side of the equation; if, for instance, you want to know the probability of filling an inside straight given the cards already showing. However, if you don’t know or can’t calculate those probabilities, then you have to guess what they are, and your answer will be no better than your guesses.
This misunderstands the point of Bayesian inference. Bayes’ Theorem was known for a long time; the revolution was in showing that the probabilities involved can be identified with “levels of confidence” or “how much we should believe a certain proposition”, and so that the process of drawing conclusions from evidence follows Bayes’ Theorem. In other words, it’s a mathematical formalisation of correct reasoning. Yes, it’s garbage-in garbage-out – it should be, if it’s true. The value it brings is in describing the process in between the two. The point isn’t to get true outputs regardless of the inputs, it’s to understand how the outputs relate to the inputs. And that understanding is generalizable even when we don’t have precise numbers.
Or put another way – yes, your answer will be no better than your guesses. You use Bayes’ Theorem to make sure it won’t be *worse*. Which is not trivial.
Your argument is basically like saying that Aristotelian logic is useless, because we can make logically correct arguments that aren’t sound. And because it involves absolutely true and false propositions, and we can never be absolutely certain of things in real-life cases. (and in fact Aristotelian logic is a special case of Bayesian inference in cases where the probabilities involved are 1 and 0).
“The point isn’t to get true outputs regardless of the inputs, …”
Yet that is how it is used, at least as I understand things. Doesn’t Carrier use the theorem to conclude that the probability of Jesus existing is low, so he is a myth?
“… it’s to understand how the outputs relate to the inputs.”
And you would do that by looking at the partial derivatives of the result with respect to each of the inputs. How often have you seen that done? Does Carrier do it?
“Anyone who tries to use BT to answer this question will have to just make stuff up to plug into the equation, and the result will be just as fictional as the input.”
You mean, like for example, creating your own version of the Rank-Raglan list and arbitrarily declaring that, because your subject meets half of the criteria, the prior probability of his existence = 33%?
The proper object of explanation is the observable data. Swinburne treats “the empty tomb” as a ‘fact’ though the “empty tomb” is not observable data – all that is observable is that we have a *story* about an empty tomb, which of course exposes the crack in Swinburne’s argument, as there are many plausible ways a story about an empty tomb could arise without it actually happening.
I read Carrier’s book and found it rather persuasive. But I found the Bayesian analysis to be a distraction, rather than a convincing demonstration. If it was helpful to Carrier in reaching his conclusions, then it was useful. But the details could have been put in an appendix.
And that’s what Richard Swinburne did — reserving the details for an appendix. That’s one way Carrier might have usefully copied Swinburne.
The use of Bayes Theorem by historians was the central point of the prior book, Proving History: Bayes’s Theorem and the Quest for the Historical Jesus. Other than that, there isn’t any quantitative methodology of arguing any thesis of history. Christian argumentation is all about bringing along as many distracting points as possible and making a big tapestry out of them. It doesn’t help that this is the norm in history in general.
Did Swinburn use a mathematical version of Bayes, or just some more informal one?
‘Most of St Paul’s epistles are totally reliable historical sources. The synoptic gospels are basically historical works, though they do sometimes seek to make theological points (especially in the Infancy narratives) by adding details to the historical account. St John’s Gospel is also basically reliable, at any rate on the later events of the story of Jesus . . . . ”
Did he do the same sort of analysis Carrier did? Estimate the probability the gospels are historical? Consider how they would look if historical, compared to how they would look if they weren’t historical?
Swinburne writes from within a parallel universe. In his world God sits on his throne above us all and Jesus was also god and God’s plan to save humanity by sacrificing his son are all matters of “fact” for Swinburne. That’s how he starts his book. Note that one of the “facts” he feeds into his Bayesian analysis is that Jesus’ death and resurrection fulfilled the plan of God to save humanity. Yes, he uses Bayesian equations but he is like an actor in an imaginary story when he does so.
From that description, I am not sure it really qualifies as using Bayes theorem
The point of Bayes theorem is to quantify our biases. If he’s done that by putting in high probabilities for supernatural occurrences and shows us his work, we can’t say the method is invalid, we can say that his results are invalid because his inputs are invalid.
In this argument we are using likelihood rather than probability. Likelihood is based upon subjective assessment whereas probability is based upon statistics. So any specified likelihood value is derived from some assessment performed by the person presenting the argument. For likelihood we expect a range of values for the assessment, given each person has his/her own life experiance and knowledge. Whereas for probability the number is the same regardless of who does the assessment.
These arguments usually begin with assignment of Initial Probability of 0.5. But this requires and assumes that the Background Knowledge includes knowledge of God. In the case where there is no knowledge of God in Background Knowledge, the Initial Probability that God exists is 0.
These arguments usually begin with assignment of Initial Probability of 0.5.
• Carrier (9 October 2012). “Understanding Bayesian History”. Richard Carrier Blogs.
where there is no knowledge of God in Background Knowledge, the Initial Probability that God exists is 0.
• Carrier (6 July 2017). “What Is Bayes’ Theorem & How Do You Use It?”. Richard Carrier Blogs.
“Subjective assessment” in Bayesian analysis is in effect a subjective (but justified) approach to “statistical probability” — see the opening minutes of this lecture:
(used in Tim’s post: https://vridar.org/2016/11/22/whats-the-difference-between-frequentism-and-bayesianism-part-1/)