The Revd Thomas Bayes, 1701-1761
The current discussion among Jesus-deniers and mythicists over whether probability in the form of Bayes’s Rule can be used in historical research is more than a little amusing.
The current fad is largely the work of atheist blogger and debater Richard Carrier who despite having a PhD in ancient history likes to tout himself as a kind of natural science cum mathematics cum whachagot expert.
Carrier’s ingenuity is on full display in a recent book published by Prometheus (Buffalo, NY) in which he makes the claim that Bayes Theorem–a formula sometimes used by statisticians when dealing with conditional probabilities– can be used to establish probability for events in the past. That would make it useful for answering questions about whether x happened or did not happen, and for Carrier’s fans, the biggest x they would like to see answered (he claims ) is Did Jesus exist or not?
The formula looks something like this:
Let A1, A2, … , An be a set of mutually exclusive events that together form the sample space S. Let B be any event from the same sample space, such that P(B) > 0. Then,
| P( Ak | B ) = | P( Ak ∩ B )
P( A1 ∩ B ) + P( A2 ∩ B ) + . . . + P( An ∩ B ) |
Invoking the fact that P( Ak ∩ B ) = P( Ak )P( B | Ak ), Baye’s theorem can also be expressed as
| P( Ak | B ) = | P( Ak ) P( B | Ak )
P( A1 ) P( B | A1 ) + P( A2 ) P( B | A2 ) + . . . + P( An ) P( B | An ) |
Clear? Of course not. At least not for everybody. But that isn’t the issue because the less clear it is the more claims can be made for its utility. Its called the Wow! Effect and is designed to cow you into comatose submission before its (actually pretty simple) formulation, using the standard symbols used in formal logic and mathematics.
What is known by people who use Bayes’s theorem to advantage is that there are only certain conditions when it is appropriate to use it. Even those conditions can sound a bit onerous: In general, its use is warranted when a problem warrants its use, e.g. when
–
- The sample is partitioned into a set of mutually exclusive events { A1, A2, . . . , An }.
- Within the sample space, there exists an event B, for which P(B) > 0.
- The analytical goal is to compute a conditional probability of the form: P ( Ak | B ).
- You know at least one of the two sets of probabilities described below.
- P( Ak ∩ B ) for each Ak
- P( Ak ) and P( B | Ak ) for each Ak
The key to the right use of Bayes is that it can be useful in calculating conditional probabilities: that is, the probability that event A occurs given that event B has occurred. Normally such probabilities are used to forecast whether an event is likely to occur, thus:
Marie is getting married tomorrow, at an outdoor ceremony in the desert. In recent years, it has rained only 5 days each year. Unfortunately, the weatherman has predicted rain for tomorrow. When it actually rains, the weatherman correctly forecasts rain 90% of the time. When it doesn’t rain, he incorrectly forecasts rain 10% of the time. What is the probability that it will rain on the day of Marie’s wedding?StaTTrek’s solution to Marie’s conundrum looks like this:
“The sample space is defined by two mutually-exclusive events – it rains or it does not rain. Additionally, a third event occurs when the weatherman predicts rain. Notation for these events appears below.
- Event A1. It rains on Marie’s wedding.
- Event A2. It does not rain on Marie’s wedding.
- Event B. The weatherman predicts rain.
In terms of probabilities, we know the following:
- P( A1 ) = 5/365 =0.0136985 [It rains 5 days out of the year.]
- P( A2 ) = 360/365 = 0.9863014 [It does not rain 360 days out of the year.]
- P( B | A1 ) = 0.9 [When it rains, the weatherman predicts rain 90% of the time.]
- P( B | A2 ) = 0.1 [When it does not rain, the weatherman predicts rain 10% of the time.]
We want to know P( A1 | B ), the probability it will rain on the day of Marie’s wedding, given a forecast for rain by the weatherman. The answer can be determined from Bayes’ theorem, as shown below.
P( A1 | B ) = P( A1 ) P( B | A1 )
P( A1 ) P( B | A1 ) + P( A2 ) P( B | A2 )
P( A1 | B ) = (0.014)(0.9) / [ (0.014)(0.9) + (0.986)(0.1) ] P( A1 | B ) = 0.111 Note the somewhat unintuitive result. Even when the weatherman predicts rain, it only rains only about 11% of the time. Despite the weatherman’s gloomy prediction, there is a good chance that Marie will not get rained on at her wedding.
When dealing with conditional probabilities at the loading-end of the formula, we are able to formulate the sample space easily because the “real world conditions” demanded by the formula can be identified, and also have data–predictions– regarding Event B, which is a third event, A1 and A2 being (the required) mutually exclusive events.
So far, you are thinking, this is the kind of thing you would use for weather, rocket launches, roulette tables and divorces since we tend to think of conditional probability as an event that has not happened but can be predicted to happen, or not happen, based on existing, verifiable occurrences. How can it be useful in determining whether events “actually” transpired in the past, that is, when the sample field itself consists of what has already occurred (or not occurred) and when B is the probability of it having happened? Or how it can be useful in dealing with events claimed to be sui generis since the real world conditions would lack both precedence and context?
To compensate for this, Carrier makes adjustments to the machinery: historical events are like any other events, only their exclusivity (A or not A) exists in the past rather than at the present time or in the future, like Marie’s wedding. Carrier thinks he is justified in this by making historical uncertainty (i.e., whether an event of the past actually happened) the same species of uncertainty as a condition that applies to the future. To put it crudely: Not knowing whether something will happen can be treated in the same way as not knowing whether something has happened by jiggering the formula. Managed properly, he is confident that Bayes will sort everything out in short order:
If you treat every probability you assign in the Bayesian equation as if it were a syllogism in an argument and defend each premise as sound (as you would for any other syllogism) Bayes’s theorem will solve all the problems that have left [Gerd] Theissen and others confounded when trying to assess questions of historicity. There is really no other method on the table since all the historicity criteria so far have been shown to be flawed to the point of being in effect (or in fact) entirely useless. (Carrier, “Bayes Theorem for Beginners,” in Sources of the Jesus Tradition, 107).
What? This is a revolution in thinking? Never mind the obvious problem: If all the historicity criteria available have been shown to be “in fact” entirely useless and these are exactly the criteria we need to establish (“treat”) the premises to feed into Bayes, then this condition would make Bayes compeletly useless as well–unless opposite, useful criteria could be shown to exist. Bayes does not generate criteria and method; it depends on them, just as the solution to Marie’s dilemma depends on real world events, not on prophecy. Obversely, if Bayes is intended to record probability, the soundness of the premises is entirely vulnerable to improbable assumptions that can only poison the outcome–however “unarguable” it is by virtue of having been run through the Carrier version of the Bayes Machine. Moreover, he either means something else when he talks about historicity criteria or is saying they exist in some other place. In any event, the criteria must differ from premises they act upon and the conclusion Bayes delivers.
“Fundamentally flawed,” as I noted in a previous post, is the application of Bayes to data where no “real world data and conditions” can be said to apply. It was this rather steep lapse in logic that led a former student of mine, who is now studying pure mathematics at Cambridge to remark,
Is this insistence [Carrier’s] of trying to invoke Bayes’ theorem in such contexts a manifestation of some sort of Math or Physics envy? Or is it due to the fact that forcing mathematics into one’s writings apparently confers on them some form of ‘scientific’ legitimacy?
The fact of the matter, as far as I know, and as I thought anyone would realize is that Bayes’ theorem is a theorem which follows from certain axioms. Its application to any real world situation depends upon how precisely the parameters and values of our theoretical reconstruction of a real world approximate reality. At this stage, however, I find it difficult to see how the heavily feared ‘subjectivity’ can be avoided. Simply put, plug in different values into the theorem and you’ll get a different answer. How does one decide which value to plug in?
Secondly, is it compulsory to try to impose some sort of mathematically based methodological uniformity on all fields of rational inquiry? Do there exist good reasons to suppose the the methods commonly used in different areas that have grown over time are somehow fatally flawed if they are not currently open to some form of mathematization?
If this kind of paradigm does somehow manage to gain ascendency, I assume history books will end up being much more full of equations and mathematical assumptions etc. While that will certainly make it harder to read for most (even for someone like me, who is more trained in Mathematics than the average person) I doubt that it would have any real consequence beyond that.”
In fairness to Carrier, however, the use of Bayes is probably not being dictated by logic, or a respect for the purity of mathematics, nor perhaps even because he thinks it can work.
It is simply being drawn (unacknowledged) from the debater’s handbook used by Oxford philosopher Richard Swinburne, who (especially through 2007) was active globally debating the question of God’s existence, under the title “Is there a God?” using Bayes’s Theorem as his mainstay. Not only this, but Swinburne is the editor of the most distinguished collection of essays on Bayes’s Theorem (Oxford, 2002). In case you are interested in outcomes, Swinburne formulates the likelihood of God in relation to one argument for his existence (the cosmological) this way: P (e I h & k) ≥ .50 The “background knowledge” Swinburne needs to move this from speculation to a real world condition is “the existence [e] over time of a complex physical universe.” In order to form a proposition for debate properly, Swinburne depends on the question “Is There a God,” which gives a clear modality: A and A1.
Unlike Carrier, I believe, I have had the dubious pleasure of having debated Swinburne face to face at Florida State University in 2006. A relatively complete transcript of my opening remarks was posted online in 2010. In case it is not clear, I took the contra side, arguing against the proposition.
I knew enough of Swinburne’s work (and enough of his legendary style from graduate students he had mentored at Oxford) to be on guard for his use of Bayes. Unlike Carrier, Swinburne is both a theologian and a specialist in formal logic, whose undergraduate degree was in philosophy, politics and economics. He travels the two worlds with ease and finesse and his most prominent books—The Coherence of Theism, The Existence of God, and Faith and Reason--are heavy reads.
But he is quite uncomfortable with historical argumentation. Historical argumentation is both non-intuitive and probabilistic (in the sense of following the “law of likelihood”); but tends to favor the view that Bayes’s excessive use of “prior possibilities” are subjective and lack probative force. So, when I suggested he could not leap into his Bayesian proofs for God’s existence until he told me what God he was talking about, he seemed confused. When I scolded him that the God he kept referring to sounded suspiciously biblical and fully attributed, he defended himself with, “I mean what most people mean when they say God.” When I retorted that he must therefore mean what most atheists mean when they say there is not God, he replied that arguing the atheist point of view was my job, not his. When I said that any God worth arguing about would have to be known through historical documents, the autheticity and epistemological value of which for a debate like this would have to be tested by competent historical research, he became impatient to get back to his formula, which works slowly and cancerously from givens to premises–to the prize: the unarguable conclusion. It seems Swinburne thought the fundamentalist yahoos (not my interpretation) would be so dazzled by the idea of an “unarguable argument” for God’s existence that he would win handily.
Except for those pesky, untended, historical premises. Not to let a proficient of Bayes get past his premises is the sure way to cause him apoplexy, since Bayes is a premise-eating machine. Like any syllogistic process, it cannot burp out its unarguable conclusions otherwise. The result was that in an an overwhelmingly Evangelical-friendly audience of about 500 Floridians, the debate was scored 2 to 1 in my favour: Swinburne lost chiefly because of The Revd. Thomas Bayes.
And this is the trouble Richard Carrier will also need to confront, sooner or later. He will not solve the primary objections to the use of Bayes’s Law by telling people they don’t get it (many do), or that there are no other methods on the table (where did they go to?), or that all existing historicity criteria, to use a more familiar word in the lexicon he uses on his blog, are “fucked.”
It is rationally (still a higher term than logically) impossible to use the existence of the world in which thinking about God takes place as the real-world condition that makes it possible to use cosmology as the real-world condition proving his existence. As Kant complained of Anselm’s ontology, existence is not essence. It is not argument either. The defeater in this case is history: God has one, in the sense that all ideas about God are historically generated and directly susceptible to historical description and analysis.
And he could learn a thing or two from Swinburne’s sad fate, which is adequately summarized in this blog review of the philosopher’s most extensive use of the Theorem in his 2003 book, The Resurrection of God Incarnate.
Using Bayesian probability and lashings of highfalutin’ mathematical jargon, Swinburne argues that “it [is] very probable indeed that God became incarnate in Jesus Christ who rose from the dead” (p. 214). His mathematical apologetics for the resurrection boils down to the following argument:
- The probability of God’s existence is one in two (since God either exists or doesn’t exist).
- The probability that God became incarnate is also one in two (since it either happened or it didn’t).
- The evidence for God’s existence is an argument for the resurrection.
- The chance of Christ’s resurrection not being reported by the gospels has a probability of one in 10.
- Considering all these factors together, there is a one in 1,000 chance that the resurrection is not true.
It’s almost impossible to parody this argument (since in order to parody it, you would have to imagine something sillier – a daunting task!). But let me try:
The probably that the moon is made of cheese is one in two (since it is either made of cheese or it isn’t);
the probability that this cheese is Camembert is also one in two (since it’s either camembert or it isn’t); and so on.
At any rate, while Carrier loads his debating machine with still more improbable premises, I am going on the hunt for those missing historicity criteria. They must be here someplace. I do wish children would put things back where they found them.
The New Oxonian 
I think this argument is almost exactly what I would want to say about Bayes’ theorem in history, social science, etc. But only almost exactly. It seems just right to me to say that Bayes’ theorem cannot provide methods in the historical sense (although it can in a statistical sense). That is, Bayes’ theorem does not tell you which set of hypotheses should be tested, what the conditional probability of the evidence given the hypotheses should be, or what the observed evidence in fact is (let alone background knowledge games). All of that has to come from things like substantive expertise, social-science and historical reasoning, and plain old interpretation of textual and other evidence. If you want to use Bayes’ theorem it will be a kind of back-end bookkeeping after the traditional work of history has already been done. In my view that kind of bookkeeping can nonetheless be a good idea — but it by definition produces no new knowledge.
The one line of reasoning in this post to which I’d object involves the arguments regarding the set of domains to which Bayesian reasoning can be applied. Bayesians routinely defend a subjective conception of probability as epistemological confidence, an idea that obviously applies much more broadly than just to problems of prediction or objectively chancy processes. A useful overview is here: http://www.princeton.edu/~bayesway/Book*.pdf
While people have a variety of reactions to the idea of subjective probability, that is a complex and at least hopefully separate debate from arguments over mythicism. If we grant that subjective probability is a plausibly coherent worldview, then we have to agree that probability can be relevant to history. But we should return to insist that probability theory adds no knowledge to the argument — it by definition is a truth-preserving mode of analysis, and therefore can only re-express what we already knew in other ways. In history, this means that any probability analysis is only as good as the standard historical analysis that is fed into the front end.
Brilliant!!! And now I am off to Turkey to get some fun in the sun -:)
One of the problems with using Bayes’ theorem is that in the context of historical arguments is that you would need to have some background in mathematics to know when and when not to apply it. The reason Bayes’ theorem works for roulette wheels and other simply physical phenomena is that the results being predicted are unentangled from considerations other than the condition. That is, one spin of the roulette wheel under condition X is just like every other spin of the roulette wheel under those conditions. This cannot be said for historical circumstances which are notoriously messy. One cannot, for example, use probabilities to determine whether particular Roman emperors might have been poisoned without considering circumstances unique to their particular situation and controversies arising at the time. Such conditions make a calculation impossible since there is no precedent as the circumstances of each emperor was unique. What Carrier is doing is an example of someone with just enough knowledge to not realize he is in way over his head. At least Swinburne was an expert on the subject and perhaps knew just how far to reach. Carrier just makes a fool of himself.
Excellent post. I hope for more from you in that direction.
Richard Carrier defines delusion by three criteria: certainty, incorrigibilty and impossibility or falsity of content. He argues that “the Christian religion is so manifestly contrary to the facts, belief in it can only be held with the most delusional gerrymandering imaginable.” Yet Revd Bayes was Christian, therefore according to Carrier, deluded. Has Carrier been seduced by the delusional gerrymandering of a Christian?
I’m pretty sure Gerd Theissen and others are entertained by the naive certainty of Carrier’s self confident claim that “all” the “historicity criteria” so far have been shown to be “flawed to the point of being in effect (or in fact) entirely useless.” How extraordinary. He might be surprised to discover his assumption is not actually ‘unarguable.’
Swinburne, how ironic. On the debate, I’d wish I could have heard all of it. And the essay above, Antonio said it first – brilliant.
Why should good theologians and believers, be afraid of, of hesitant about, Math and Science? There is really no good reason why in fact, the good Reverand Bayes’ and/or other theories of probability, shouldn’t be applied to religious history, as well as to future predictions. The principle is the same: in both cases, whether we are going forwards, or back into the past, we are dealing with unknowns; and trying to calulate the probability of this or that assertion, relative to know facts.
And? It is not so hard to get known facts out of History, after all. Especially consider: particularly, presumably, the Laws of Physics for example, held in ancient times, as well as today. And therefore? We might use the Laws of Physics, and other scientific facts, as a certain constant or baseline. That would be presumed to hold in the (relatively recent) past, as well as in our own time.
It is a shame that IN your Florida State (?) debate with Swinburne, the Oxford professor, he chose an uweildly first example: the attempt to prove God. Which indeed, quickly leads to problems of 1) premises; defining God. And 2) problems of entanglement; finding “facts” that can be firmly said to be “independent” of that premise. (Though many might say that scientific facts, the laws of conventional physics in everyday life, would be independent?).
But Swrinburne, as our author here acknowledges, holds a far, far more prestigeous postion at Oxford, than lowly Florida State. And we should listen to him: no doubt his application might be saved, with a few tweaks, a few refinements. For example? First of all, consider applying Bayes to a more modest application: say, attempting to calculate teh probability of specific miracles by Jesus. Like say,the likelihood of walking on water. Examining that, relative to the (also Historical facts, like), the Laws of Physics, the known capacities of human beings, physical evidence, and so forth.
In fact, furthermore, the number of variables in looking at the past, is not necessarily so much greater than applying probability today, in roulette wheels, or in scientific experiments. Even in Historical studies, the number of variables can in effect, be controlled, by careful selection, narrowing, of the target: what we choose to try to prove as likely, or unlikely. While the scientific and historical base can be established simply by chosing scientific facts, laws, as our historical baseline of even historically likely/certain facts.
No doubt there will still be many variables and unknowns in the application of Math and science to ancient history. Still, the application of Math and probability should begin to bring a much, much higher degree of accuracy, to our study of this era. Now that we have passed through (and answered?) Dr. Hoffmanns’ preliminary objections to the first, admittedly crude attempts to apply the Theory.
You should read Joe’s post. We have no way establishing probabilities for events in the distant past. As one commenter asked, what would be the odds that an emperor 2000 years ago died by assassination rather than natural cause? We have no way establishing this. What profit do you really think would be gained by using Bayes to the miracle of walking on water? Does it really require an equation to tell us that this has never been observed to happen and is not possible according to known laws of physics? Joe and Steph are right; Carrier’s idea is nothing more than a garbage in garbage out machine.
It does not indeed, require an equation to tell us that it is unlikely that Jesus literally walked on water. But 1) the information supporting this is not “garbage”: it is Science.
And then? 2) Having that and other relative certainties, as reference points, we can next begin to triangulate other, less certain asserted realities around them, assessing their relative probability, and likely nature.
So that? 3) We CAN begin to see which items in current histories are likely to have been true … and which are not.
So that? We can begin to find out what most likely, actually happened.
By the way? 4) Nuclear Physics did pretty well with mere probability; and, with due reservations and modifications, Probability will also do wonders, even in (currently) less exact applications, in History.
Certainly, 5) it will be no more inaccurate than many other methods currently accepted in history; especially the various “criteria” used in Historical Jesus Studies.
Though for that matter? 6) Historical Jesus studies in part, already use some of these criteria; when they ignore, write of, the miracles of Jesus, they are using Science, as one of their relatively certain reference points.
7) Can Probability even tell us whether it was likely that a given emperor was assassinated, or died of natural causes? Of course it can; if we know that he died say, in Pompeii when the eruption occured for example, that would indicate a high probability of natural causes. Especially if we find next, even more corroborating evidence.
Do we get absolute certainty out of Probability? Not always. But we get some real insight into the past, at last.
brentongarcia,
In the example you gave of nuclear physics doing well with probability, you unwittingly revealed exactly why it does not apply when discussing ancient history. Physics is determined by laws where the experiment is repeatable and testable and it would not matter if you performed the experiment in 2012 CE or 2012 BCE – the results of physics should be the same.
This is not the case when determining probabilities for complex social interactions in different eras. One of the most common mistakes is to project our own expected reaction to a given situation on those from entirely different cultures in different eras. There is simply no possible way of setting the probabilities for the sorts of events that would be interesting.
@Albert. Precisely. It is very nice to be able to use that word; I do not think I have had a chance to do so once in this discussion. I will send you the 866-number for your prize as soon as I buy it.
Richard Carrier defines delusion by three criteria: certainty, incorrigibilty and impossibility or falsity of content. He argues that “the Christian religion is so manifestly contrary to the facts, belief in it can only be held with the most delusional gerrymandering imaginable.” Yet Revd Bayes was Christian, therefore according to Carrier, deluded. Has Carrier been seduced by the delusional gerrymandering of a Christian?
I’m pretty sure Gerd Theissen and others are entertained by the naive certainty of Carrier’s self confident claim that “all” the “historicity criteria” so far have been shown to be “flawed to the point of being in effect (or in fact) entirely useless.” How extraordinary. He might be surprised to discover his assumption is not actually ‘unarguable.’
Swinburne, how ironic. On the debate, I’d wish I could have heard all of it. And it the essay above, loved it.
Dr. Hoffmann, I too hope for more from you on this topic. Though I think you misread Carrier if you think he is motivated in any way about scoring debating points.
I think he makes his motivations clear in his recently published book (i.e. problems with historical methodologies in general and with respect to HJS in particular). And it is to those motivations that I would be most interesting in hearing your opinions. Whether you agree with his analysis or not. And why or why not.
Clearly, you disagree that Bayes Theorem can play a part in solving the problems Carrier is interested in addressing. But if you agree with him that there are methodological problems in HJS then what do you see as the solution?
And if you disagree that there are problems then can you comment on the scholarly references he points to? Is he just cherry picking?
Thanks.
@Mark. Yes, I’m actually in the middle of a book on non-historicity, and have had to enlarge it to take account of views of non-historicity that use probabilistic rather than analogous argumentation, and Bayes is a form of probabilism. Actually, as I hope I suggested, Bayes can be great fun as a debating tool or device, but it isn’t probative at all. At its guts in the historical arena it can’t be better than the evidence and verdicts on the premises are highly intuitive. In short, it does not seem to satisfy the sort of real world conditions that would justify its use.
Mark: No critical biblical scholars deny that there are problems in methodology and application of criteria, particularly in view of some of the more evangelical approaches for example. This is why critical scholars continually discuss methodology and incorporate interdisciplinary approaches. With debate and new evidence and argument, methodology evolves. We do not pronounce ‘all’ traditional method and criteria redundant because they are not. An analogy to demonstrate – my piano is out of tune but it does not need to be thrown out – it needs to be retuned. Or a better analogy, my computer needs software upgrading. That’s not right either because it’s only another analogy and by definition analogies are always false. But you might get my drift.
If historical probabilism can’t be better than historical facts (which I don’t accept), then that would at least, put it on par with Historical Jesus criteria, say, and their “facts.”
But for that matter, how reliable are the Historical Jesus “criteria,” and the things they claim to derive? Carrier – a real, not strictly religious historian – criticized them.
And I here submit that HJ criteria, are so inexact for their own part, that if they are applied as they commonly are misapplied to Jesus, but now to a cartoon character like Daffy Duck – historical Jesus “objective criteria” would also “prove” Daffy Duck’s “real historical existence”:
1) The Criterion of MULTIPLE ATTESTATION: hundreds of Daffy Duck cartoons attest to the existence of Daffy Duck: therefore, Daffy is historical. (While competing accounts, that say Daffy is a myth or “cartoon,” can be discounted as heresied, or deviant accounts. As follows).
2) The Criterion of EMBARRASMENT This suggests that accounts of our miraculous, talking duck, MUST represent a real historical tradition; since no one would invent anything so daffy, or silly. The Daffy accounts, could only have been retained, in spite of their embarrasingly funny and improbable nature …. because they represented a solid historical tradition, that could not be simply dropped.
3) Criterion of DIFFERENCE. If there are other, different media accounts, that refute Daffy’s miraculous self? (I.e., accounts by “Loony Tunes” writers and producers, that they “created” Daffy? ). Again – extending the criterion of Embarrasment – this merelysuggests that the Historical Daffy accounts were retained, even in the face of oposition; so that therefore, they must be historical and true.
Therefore? Carrier is right: the various allegedly objective “criteria” used to “prove” the existence of Historical Jesus … are actually simply, literally, laughable.
So that indeed? A better historiographical methodology – one incorporating Bayes for example (in spite of Bayes’ nominal religiosity), would no doubt be an improvement over what we have today, in Historical Jesus Studies for example.
@Garcia: I post this with some reluctance because it is full of mistakes, beginning with the assertion that “If historical probabilism can’t be better than historical facts (which I don’t accept), then that would at least, put it on par with Historical Jesus criteria, say, and their “facts.” What do you not accept? Probability is not a condition of facts; it is the likelihood of an event occurring. You then go through Carrier’s standard debate spiel regarding some methods of criticism often applied to biblical texts. These methods were not designed to address the question of the historicity of Jesus; they were designed to establish what might be primary and what might be later or secondary to the tradition. You have presented, moreover, a satire of them, based on Carrier’s misrepresentations. And you conclude on the basis of this satire that “Carrier is right.” Right about what? That the criteria are imperfect; sure. That Bayes can operate in their place? How? BayesT has no way of creating the organic relationship or “real world conditions” under which the historical record developed, and it cannot operate on thin air. It has to be fed premises that are based on interpretations; if interpretations deriving from the historical method that does have an organic relationship to the life situation described in the record are set aside, where do we go for fuel? Bayes is useful for certain conditions, usually predictive of events that have not yet occurred–a drop in stock values, e.g.–but for which a sample field can be constructed. Its use in historical studies has no track record, and not for no reason: no one is afraid of it; it is just that it cannot do the job that it is claimed by Carrier it can do. Finally: What do you mean by Bayes’ “nominal religiosity”–I suspect it means that you thought he was a computer scientist and not an 18thc century preacher? And best till last: you say, “How reliable are the Historical Jesus “criteria,” and the things they claim to derive? Carrier – a real, not strictly religious historian – criticized them.” There are surely criteria for dates, origins, textual occurrence, and even putative authorship (Paul or imposter Paul) which are used by critical biblical scholars at places like Oxford and Harvard and Claremont to name only a few. Questions of forgery or textual date, for example, might be fun to play with using Bayes, like putting donuts in a sausage machine, but it would be no improvement on the standard ways of assessing evidence from the past. To be blunt, I see no groundswell of enthusiasm for Carrier’s proposals at any of the places I just mentioned, and many people who are employed at these places might dispute the notion that he, not they., are “real scholars.” I think you might well quit while you are only a little behind. You need to understand these ironclad premises you like to form; they are actually a very good example of why feeding BT the wrong food will always give you the wrong answer.
Thank you for withholding some criticisms; my doctorate is not in the field of Religious Studies, for example, and no doubt I occasionally make some obvious mistakes here. But I do feel that, as a specialist in Interdisciplinary Studies, I can still make an occasionally valid contribution. Even as? The Rev. Bayes, though he was “in religion,” was nevertheless also able to make a contribution, in Mathematics. (Enough to make some wonder at his devotion to religion?).
Today to be sure, in spite of an already-fairly-long early history, probability is in its infancy as applied to history. And yet iit has long been used in Sociology. And in our computer era? No doubt it will be making continuous advances; just as Statistics became immensely important, in Sociology.
To bring Probability up to date, and expand it? here I used the term “Probabilities,” to stand for, at times, not just the likelihood of a thing, but the “probable event” itself. The statiscially-indicated entity.
And? of course, since statistical Probability is already applied in Sociology, to almost the full range of human events? It can easily be extended beyond study of religious texts. And therefore, beyond Carrier himself? It can be applied to the historical question of the likilihood of Jesus’ real existence, and its exact nature.
How can it do this? If all we have are subjective historical accounts, How can it recreate “real world” conditions to help its predictions of the likilihood of this or that historical event?
I’ve just attempted to answer that in another part of this blog: in part, it can rely on Science, and the laws of nature, roughly understood, as being constant, and inhereing in, forming events, in the time of Jesus, as well as in our own time.
Presumably, the laws of Physics existed in the time of Jesus too. and form a sort of constant baseline reference. Earthquakes, eclipses, dietary habits found in ancient bones, and tons of scientific data too, can then be cross-referenced aagainst subjective historical accounts, to triangulate the probable reality of what happened in ancient times.
“Presumably, the laws of Physics existed in the time of Jesus too. and form a sort of constant baseline reference. Earthquakes, eclipses, dietary habits found in ancient bones, and tons of scientific data too, can then be cross-referenced aagainst subjective historical accounts, to triangulate the probable reality of what happened in ancient times”
Great, then using the laws of physics, earth quakes, eclipses and dietary habits ask “Dr” Carrier to find out whether Alexander the Great had a tomb and where we can find it. Hell, I would settle for Jimmy Hoffa.
Brettongacria so pathetically misrepresents the methodology of history that I must almost cringe when I read such utter squabble.
The historical criteria do *not* apply to modern day TV animations. That is so inconceivably obvious that it anyone who makes a failure as great as Garcia regarding such a simple fact should simply be excused from discussing history. The historical criterion apply to documents, historical documents. In reality, Daffy Duck does is not attested in any historical documents, and thus blatantly fails on the historical criterion to have any historicity. Daffy Duck is only attested to in… TV animations. Worse then that, the very genre of these animations is fiction.
Likewise, because there is no attestation in any historical documents to Daffy Duck, Daffy necessarily fails all other criterions for historicity.
It’s almost mind blowing that Richard Carrier could have caused someone to become so utterly stupid, that they decide that all the great historians to ever live in the past, today, all the millions of publications that have been made in this field, are all obsolete because they failed to take into account Garcia’s analogy of a duck that appeared in an animation! LOL! Just as Richard Carrier astoundingly fails to understand the methodology of Bayes Theorem before he uses it, so too does Garcia utterly fail to understand the methodology of history when he uses it.
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More irrelevant over confident incompetence. Ridiculous.
More simple judgments from Steph, with no rational arguments offered.
Excellent summary of Hoffmann’s blog post! Short and to the point.
Confused? Anyway, I see you have written your part two. Will straighten you out on your assertions after the weekend when I have time. It’s going to have to roast in moderation purgatory until then. But a quick preview: No one is arguing that BT cannot be used in cases where the word “probability” occurs because semantically probability relates to the likelihood of occurrence. I suggest that when you deconstruct the word likelihood however and transpose likelihood to complex historical data from ancient periods you will have identified a good reason why using Bayes is not warranted—-useful.
BG and Malcolm. Do you really believe that mock ‘review’ on Vridar deserves more than six words? No. You merely ‘bite’ with malicious ad hominen comments and pontificate with verbose pseudo ‘lectures’ or silly caricatures.
I’m afraid Mr. Godfrey did not understand the basic tenor of the conversation in the video he cited. Again, you find the speaker noting Bayes’ success in finding things where the decision process involved purely physical criteria: missing wreckage of an airplane, proving cancer causes smoking, etc. Given some basic though incomplete criteria, Bayes is very successful determining the probabilities for such phenomenon with limiited information because of the constancy of the physical processes involved. The physical/chemical/biological processes are the same regardless of the time and place. He simply does not get the difference between such phenomena and complex socio-political interactions that introduce unique circumstances to the decision process. As someone with a background in mathematics, this is what happens when someone with a limited background in both mathematics and history does when they attempt to use both.
I will first make my own situation and position clear on this: I am niether a mathematician, nor an historian. I am aware of the fact that no mythicist case has ever made it through peer review. I also feel that mainstream scholarship has not done an dequate job of refuting mythicism for the popular audience. I wish someone like Ehrman who writes not only for scholars, but also for the popular audience had not chosen to dismiss it in the same way. Because even if schol;ars can understand what the problem with it is, they have not managed to convey it properly to those who are not from their ranks. A much better exercise in debunking is needed and that is sorely missing. Someone like me, who is an amateur finds much of what Doherty says (for example) significant and hard to ignore. But I am willing to see how a proper scholar would undermine his case. This is not something mainstream scholarship has shown much intention of doing.
Similarly, I have been a fan Carrier’s work for some time. His responses to apolgists on the secular web are amongst the best available, and I have benefitted much from what he has written. In fact I will certainly buy this book in order to support him and his work.
That said, I have been ambivalent about this work of Carrier’s for some time. Bayesianism has been heavily debated in philosiophy for decades now. For an outsider like Carrier to come in and think that he could settle the issues on this seems quite strange. I actually thought that all that Christian apologists would have to do to dismiss such a case would be to appeal to standard counter-arguments from the philosophical literature and be done with it. I didn’t actually expect this to become such a bone of contention amongst atheists.
As for Vridar’s comment, however, it seems like he is missing the points made. Moreover, what does he mean by saying:
“his former student who’s studying “pure mathematics” (bright, shiny, and clean, no doubt) at Cambridge”
Does he not know that “Pure Mathemtics”, “Applied Mathematics” etc. are actual subdivisions of the subject of Mathematics as it is normally taught? In fact here are the links to the two departments at the very university Dr. Hoffmn mentions:
http://www.dpmms.cam.ac.uk/
http://www.damtp.cam.ac.uk/
And then he says:
“You don’t have to do very much research to discover that Bayes’ Theorem does not fear subjectivity; it welcomes it. Subjective probability is built into the process. And you say you’re not sure about what value to plug in for prior probability? Then guess! No, really, it’s OK. What’s that? You don’t even have a good guess? Then plug in 50% and proceed.
It’s Bayes’ casual embrace of uncertainty and subjectivity — its treatment of subjective prior probability (degree of belief) — that drives the frequentists crazy. However, the results speak for themselves.”
I wonder if he even understands what the fellow he is ridiculing was actually arguing (or alternatively, I may not be understanding it), but it seems to me that he has conceded the point. Because on the basis of what is he going to make his guess? Will Bayes solve that? If you don’t have a good guess then pluHence BT’s imposed discipline is extraordinarily useful, since we can now haggle over the inputs (that’s why they’re called variables) rather than argue over intuitive conclusions about plausibility g 50%? William Lane Craig thinks that the probability that God would raise Jesus from the dead is “inscrutable”. Should we plug 50 %? I may think the probability that documents survived from the destruction of Jersalem that became the basis of Tacitus’ knowledge of Christianity is 5%. You may think it is 0.0005%. I may think that the probability that something actually stood at the place where the Testimonium Flavianum now stands (after having read all arguments from both sides) is 3.87446%. You may think it is 0.845532%. J.P. Meier may think it is 50%. Crossan may think it is 42%. Josh McDowell may think it is 90%. Is Bayes going to tell us which to use? And if so, then it will only do so by assuming other probailities to begin with. How are we going to get these? That is how ‘Plugging in different values gives us different answers’. But to Vridar, this is natural because it is a “common feature of equations.” So what? The fact that there is such uncertainty nd ambiguity involved here is exactly the point beuing argued. The fact that it is a common feature of equations makes one wonder if equations of this nature actually are the tools that should be used to decide things here. And that is the point in dispute.
Yes @Hajk: I was laughing politely when Vridar/Godfey made the bumble about “pure mathematics” in scare quotes; it reveals that he is a complete loser in anything related to mathematics, and when he goes on to complain that Bayes doesn’t “fear subjectivity it welcomes it” may as well toss in the towel as far as its probative force goes. Odd, someone conceding your points and then claiming victory. Even well-wishers of Carrier’s in various blog reviews have remonstrated that he should not have used the Jesus question as a test case, especially when the whole question of its application in historical studies is as yet unproved. Maybe we should plug in “Bayes is/is not useful in historical study” and see what happens with the probability. Godfrey also doesn’t know the difference between statistical/mathematical and epistemological probability, but it is clear that some people making claims of the later variety are hoping to present tham as “certainties” in the former category. I also give you the trophy for the most rational BT comment of the day: “William Lane Craig thinks that the probability that God would raise Jesus from the dead is “inscrutable”. Should we plug 50 %? I may think the probability that documents survived from the destruction of Jersalem that became the basis of Tacitus’ knowledge of Christianity is 5%. You may think it is 0.0005%. I may think that the probability that something actually stood at the place where the Testimonium Flavianum now stands (after having read all arguments from both sides) is 3.87446%. You may think it is 0.845532%. J.P. Meier may think it is 50%. Crossan may think it is 42%. Josh McDowell may think it is 90%. Is Bayes going to tell us which to use? And if so, then it will only do so by assuming other probailities to begin with. How are we going to get these? That is how ‘Plugging in different values gives us different answers’. But to Vridar, this is natural because it is a “common feature of equations.” So what?” As Morton Smith once said, I would rather put my trust in the myths of the Bible than in anything the mythics come up with: this is another example of hyperhypotheticalism with strong lashings of Macbeth 5.5 ( “it is a tale
Told by an idiot, full of sound and fury,Signifying nothing.”)
After this he goes on to say:
“The proper application of BT forces us to estimate the prior probabilities. It encourages us to quantify elements that we might not have even considered in the past. It takes into account our degree of belief about a subject. And it makes us apply mathematical rigor to topics we used to think could be understood only through intuition. Hence BT’s imposed discipline is extraordinarily useful, since we can now haggle over the inputs (that’s why they’re called variables) rather than argue over intuitive conclusions about plausibility — because truthfully, when a scholar writes something like “Nobody would ever make that up,” it’s nothing but an untested assertion.”
And what about the numbers that we choose to make up that Vridar suggests we “haggle over”? Will they be anything beyond untested assertions? How does one go about testing what the probability that Justus of Tiberias would have mentioned Jesus, given that Jesus had existed is? This isn’t some lab situation where such testability normally works.
That said, Vridar may have a point in saying that BT may in some cases force us to think about things that we may have otherwise missed. For example, it is possible that a scholar considers many things plausible, but considers something else implausible. However, someone may use Bayes theorem to argue that if she considers A and B and C plausible (so maybe above 50% probibility), then she ought to consider D plausible as well. In this manner it can perhaps be helpful, i.e. as a means to force people to be consistent in terms of their subjctive evaluations. Of course once people get the hang of it they’ll simply start readjusting their initial probability estimates. As such, its primary purpose would be to force people to admit some of their biases by quantifying them. The question remains as to whether such quantification can even apply to such things (again, I am not a mathematician, but I assume this will assume the existence of a function that yeilds a one-one correspondence between the [0, 1] interval on the real line and the set of biases that a person can hold, a mathematician can correct me on this however). That of course has to be the assumption that must be granted before we start working with this. But if that assumption is granted, then it can be a bookkeeping tool as someone here has also mentioned.
In that way, one can use it in addition to the traditional methods of doing history (which will also help one in trying to reach different subjective probability conclusions on these issues).
Once again, I will state that in general I am admirer of Richard Carrier’s work, and still think that there may be much useful historical argumentation in what he has written, even if divorced from the Bayesian context. In fact as I have not really read his book as yet, I am still willing to wait and see if he actually has dealt with these problems well. But I do believe Vridar’s response here was nowhere near strong enough to legitimize the way he is deriding the ones who don’t agree with him. He should also recognize (just like Ehrman and co. should with the mythicist position) that there are more legitimate questions here than he acknowledges, and flippant mockery or dismissals will not do much to remove them. Nor, as I have indicated, am I currently trying to enter the interminable philosophical debate over Bayesianism (for those interested in this, they may start here:
http://plato.stanford.edu/entries/epistemology-bayesian/)
Apologies for any bad spelling or misunderstandings etc. because English is not my first language.
Albert, I don’t know what video you think I have cited but everything I have myself written on Bayes’ theorem is archived at http://vridar.wordpress.com/category/historiography/bayes-theorem-historiography/ along with two posts by Tim Widowfield. If you find anything amiss in what I have written — with any of my own views and understanding of Bayes and its potential relevance — do feel free to address my words.
Nonetheless, I do find a comment of yours to be based on a lack of understanding of the application of BT in historical questions. You write:
I don’t know why you presume that I do not “get the difference” between the predictable processes governing physical/chemical/biological phenomena and “complex socio-political interactions”. Would you like to demonstrate or clarify your point with a specific example that you fear I might misapply to a Bayesian process?
Do you have difficulty with the way BT is applied in archaeology?
As Tim Widowfield has recently pointed out, some critics of BT here are really failing to understand the basics addressed and regularly confuse conclusions with prior probabilities. http://vridar.wordpress.com/2012/06/05/hoffmann-serf-reviews-my-bayes-theorem-post-proving-this/
@Godfey again: As to Widowfield: Who has used the term prior probabilities? Not me. Don’t confuse an assertion—-e.g., Bayes theorem cannot be made to work in a field driven by hermeneutics and complex historical data from the distant past — with not understanding how Bayes’s theorem operates. It is precisely that we do understand that we are saying it is inapplicable and useless. Disagreement does not betoken misunderstanding-it just points to disagreement. So that I don’t repeat myself–you ask elsewhere about BT in archaeology. Archaeology is that field of study that we used to joke was stuck between a rock and a hard plant. Archaeology makes use of all kinds of statistical bases for dating purposes. The use of Bayes can be defended when hard evidence is available. Even in archaeology there are better methods, however—BT being far too subjective. The gospels are only hard evidence if we are talking about manuscript or papyrus history–what 19th century scholarship called the lower criticism. Try this: If we had a unique MS written in Hebrew (make it Latin to keep Spin happy) dating irrefragably from the year 35 that described the trial and execution of a criminal named Yeshu ben Stada, what would you do with it? I know that a Christian fundamentalst would say it “proves” Jesus. I know a skeptic would say “What’s 35 got to do with it: Yeshu is a common name.” We have scholarship because the divide between these positions, even if you can reduce it to equations, will NOT be settled by an equation. The reason for that is that the hermeneutical task—the high criticism–is not amenable to shortcuts, especially ones that are designed to “solve” problems that the theorem was never intended to solve.
@Neil Godfrey
First, I apologize for the lateness of this response. Your comment was lost in the shuffle and I did not realize until this time you had responded to me.
I have no problem with the way things were applied in archaeology or in finding the missing airplane, etc., but this illustrates the iterative nature of applying Bayes. That is, it works best when there is an endgame: they find the missing archeological location, they find the airplane, etc. The reason is that even when you make a wrong assumption, the mathematics guides you to a good first place to look, then an iterative process of elimination and reapplication guides you further until you close in on the paydirt. Thus it is a process to guide where to look for something when you have some idea when you have achieved the correct answer. It does not, however, make your prior iterations correct – they are merely the best place to look at each iteration. At some point you will find the thing and Bayes is a great way for conducting a search. In a sense, one might compare it to googling nature itself to find what you are looking for but you need to know when some particular iteration has hit paydirt to move to the next step.
So how exactly does one “find” when Jesus existed? Or, better yet, how does one find a “nonexistent Jesus”? Or how does one find the inner thoughts of someone: For example, how do we know when we have reached Constantine’s real thoughts when he issued the Edict of Milan? We can make judgments based upon his later actions and his earlier beliefs but there is no point where Bayes will lead us to the process of elminating a possibility in such situations.
Subscribing.
Gosh.
Okay, so how is it that one can go back in time and re-produce what happened around 2000 years ago? Does someone have a time machine that i don’t know about?
@Scott: The simple answer if you can’t. “Re-produce” is not the task anyway.
And I agree, I was asking the mythicists how they might be able to do scientically what belongs to the field of hermeneutics. Apparently I need to think through rather than just type and post (:
Funny. Again, I point out that creationists use this argument to critique the theory of evolution.
Dear Mr Grog: Please remind me again what argument you are referring to as it seems to make sense to you and no one else: the only analogy I can think of in relation to creationism is the one between young-earth theorists’ argument from the silence and gaps of the fossil record and the mythers’ position that Paul’s silence proves there is no historical Jesus. Do you also think the devil made up stories about Jesus to taunt us, the way some creationists think fossils were planted by God in the rocks to test our faith? Or do you hold a more limited conspiratorial view of how it began? But perhaps you meant something else.
My memory is somewhat hazy, but IIRC Swinburne used the numbers in the ressurecfion argument merrly for illustrative purposes (please correct me if I’m wrong if you have a quote that shows it) so it seems like the cheese-parody misses the point.
@ Ham No: He used it argumentatively; quotes? Read his books. A bit of the debate between Mackie and Swinburne is here but you will actually have to crawl off the web to read the article or buy it. http://www.jstor.org/discover/10.2307/40021213?uid=3739832&uid=2129&uid=2&uid=70&uid=4&uid=3739256&sid=47699055556647
Statistics – including Probability – has already contributed a great deal to Sociology, Anthropology, Psychology, Physics, Biology, and History. While all of these fields have in turn, contributed a great deal to religious studies.
Statistics has already inputted hugely into religious study, especially by way of Anthropology, Archeology. And would contribute far, far more … if specific applications like Bayes were not so adamantly resisted, here.
@Garcia: What is your point? Biblical archaeologists and historians and sociologists of religion use statistics all the time; frequency distribution depends on it is establishing texts dating; so does orthography. You seem to be working under the misapprehension that someone has challenged the use of statistics and scientific method.
Garcia says, uncontroversially, but drawing a very large category: “Statistics – including Probability – has already contributed a great deal to Sociology, Anthropology, Psychology, Physics, Biology, and History. While all of these fields have in turn, contributed a great deal to religious studies.” We were talking about BT in connection to the question of Jesus. You do see the difference between the use of normal means of measurement and a theorem that is being touted as a cure for the imputed “chaos” of historical research?
“If probability theory only applied “to future events” then there wouldn’t be a name for a misunderstanding of probability theory in court trials, which necessarily deal with past events. I’m not aware of any definition of probability theory that says it only applies to future events. It applies to incomplete information (I suggest everyone read that link. In normal language if we use terms like “x hypothesis is more likely than y hypothesis” this is necessarily mathematical language and can only make sense if expressed numerically).
But Hoffmann’s post seems to be arguing that Bayesianism is only about ontological or objective probability and not epistemic or subjective probability. This is part of the ongoing debate between Frequentism and Bayesianism, which for now is unresolved. Frequentists generally think that probabilities are inherent properties of objects or experiments (ontological). So if we have 95% confidence in some experimental outcome, and if you run that experiment 100 times, 95 of the experiemnts run should give the same result. 95% is an inherent property of the experiment. Or, a fair coin inherently has a 50% chance of landing heads because that is the definition of a fair coin. You can continue to flip a coin in a succession of experiments and it will regress towards the mean of 50%. This might explain the accusation of attempting mathematical precision; mathematical precision only applies to ontological probability.
But we can also talk about epistemic probability, or how much confidence an individual has in some hypothesis or idea. This is one reason why Frequentists accuse Bayesians of being too subjective. So for example, in the study I posted we had this scenario:
Linda is thirty-one years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations.
[How probable is it that]:
Linda is a teacher in elementary school.
Linda works in a bookstore and takes yoga classes.
Linda is active in the feminist movement.
Linda is a psychiatric social worker.
Linda is a member of the League of Women Voters.
Linda is a bank teller.
Linda is an insurance salesperson.
Linda is a bank teller and is active in the feminist movement.
If we were only talking about ontological probability, then telling students to rank these options by how likely they are would make no sense. In reality, Linda ontologically is either a bank teller or she isn’t (this is how Swinburne failed in the example). She isn’t 80% bank teller. But we can still have some sort of epistemic warrant for believing that she is/isn’t; we can give a number for how likely it is — based on our own personal experiences — that she is a bank teller. We should be able to translate “I think it is highly probable that Linda is a bank teller” to “I have 80% confidence that Linda is a bank teller” (based on the first link I posted).
Of course, this experiment is an example of why Occam’s Razor makes sense. OR follows from probability theory; Linda being a bank teller and a feminist is less likely than her just being a feminist. Even though that doesn’t make intuitive sense, it is the “simpler” hypothesis.
Overall, if you take only a Frequentist view of probability, then attempting to use probability theory in historical analysis might not make sense. Yet there seem to be some Frequentist applications to historical questions. But if, for example, one of Hoffmann’s students missed class he would probably conclude that it was more likely that the student was sick or goofing off instead of having been kidnapped by aliens. If he agrees with that reasoning, he has just used Bayes Theorem!”
Comment by J. Quinton — 2012/06/01 @ 6:42 am Vridar
@Quinton: Interesting if confused: Can you point to a verdict in court case based on Bayes Theorem or one in which a jury was invited to weigh evidence taking it into account? If on the other hand your comment is about probability, which is not convertible to–limited to or coextensive with–with–BayesT, then there is no argument here: historians have been using it for 200 years, many are quite good at it, and most of the concrete results we have to show in Biblical studies use probability in some form, but the form will always be dictated by the nature of the evidence. Swinburne, as I have said, has used BT effectively to show that there is at least a 52% chance that God exists. He has used that datum in turn to show that there is a better than even chance that God made the world and that Jesus rose from the dead. I regard all of these conclusions as “literally” false but, given the procedure he uses, unarguable. The error exists at a factual level, not in probability. How would you go about uncovering the root of the problem–the disjunct between “probability” and “fact” (I am not conceding btw that Swinburne’s premises are any sounder than Carrier’s in the use of Bayes)? As I suggested in my piece: Historically, because the postulate of God cannot exist independently of language about God. Is God a “past event,” a “presnt reality,” an “ens realissimum” or an epistemic necessity? How would what you think God is affect your formulation? You appeal to parsimony in the form of Occam: So does Swinburne. I can arrange evidence to show that God is a more efficient explanation for the cosmos than a physical event using Bayes. Even if you are a non-possibilist on Flew’s terms, you would have to accept the outcome because all that Bayes requires is a sound arrangement of the terms–Just (as Carrier claims) in a syllogism. Bayes can be made to work in a variety of situations for which is is not suited nor intended. Swinburne liked it because it got beyond another calculation, Pascal’s. This however is not about a court trial in which events that have normally happened before and happen all the time have happened again recently and for which, because of these data, a knowledge field,and real world conditions can be established petty easily and the evidence assessed. It is about a verdict on the existence of an individual from 2000 years ago. Surely even you can see the differences involved.
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There’s a lot to critique in this blog post, but I’m going to start with the following quote because I judge it to be the worst:
“So far, you are thinking, this is the kind of thing you would use for weather, rocket launches, roulette tables and divorces since we tend to think of conditional probability as an event that has not happened but can be predicted to happen, or not happen, based on existing, verifiable occurrences.”
You might to think of conditional probability that way, if you knew nothing about probability theory, had never taken a course in probability or read a probability textbook, never used words such as “likely” or “probably,” even intuitively, and didn’t take a moment to really think about it, but you’d be badly mistaken.
Conditional probability is the probability that something is true, given that something else is true. For example, if you know that a woman has 2 kids, what is the probability that she has 2 boys? 25%. So the conditional probability that she has 2 boys given that she has 2 children is 25%. That’s a typical example of conditional probability, which doesn’t concern any future event, and you would probably find it (or something just like it) in Chapter 1 of most introductory probability texts.
Bayes’s Theorem (or Formula or Rule) is just a simple equation that follows from the axioms of mathematical probability theory and the definition of condition probability. It can be applied to any situation that involves probability.
Here’s a textbook example of the application of Bayes’s Theorem:
A certain virus occurs in 1% of the population. There’s a test for this virus that has a 1% false positive rate, but is 100% accurate when the virus is actually present. Somebody’s test result is positive for the virus; what is the chance that he really is infected? Using Bayes’s formula, one get’s the result, 1/1.99 or about 50%. This is a standard analysis that has employed for decades. And note that again no future events are involved here.
Next, I’ll turn to your description of Bayes’s formula, and the restrictions on its use, in particular. You list several criteria for the applicability of the equation, but they are really much less onerous than you make them out to be. In particular, since we can always restrict attention to our hypothesis and it’s negation, the first restriction can always be satisfied. The second, that P(B)>0, is also satisfied in any real-world situation where we are not dealing with continuous variables (and even then it can be overcome), since the prior probability of any already observed evidence being true is always > 0, unless your evidence consists of something that you would have judged to be completely impossible if you hadn’t seen it. The third “restriction” is actually just a statement of what you’re seeking; this is not a problem since we know that we want the conditional probability of the hypothesis given all the evidence. Only the fourth is any kind of limitation, but this just says that we need to know the prior probabilities and conditional probabilities of the evidence on the hypothesis and its negation. Using Bayes’s rule is all about estimating them – that’s where all the effort and controversy lies – so this is not so much a restriction as just an acknowledgment of what our inputs into the equation are.
I’ll continue my critique in another post.
@Malcolm: This isn’t a critique; it’s just an unnecessary lecture which, in fact, repeats the more obvious points about conditional probability from my post. The first recourse of defense (I see Vridar using it in his typically facile way, e.g.) is always to say that someone doesn’t “get” the theorem rather than to say precisely how or why the theorem is useful in a particular context. Nevermind that I specifically said that this would be the first line of defense: when you have a case, argue the case; when you don’t have a case, say your opponent is missing the point. The problem is, I am having trouble finding any groundswell of enthusiasm outside the mythicist cult for the use of BT, and I don’t see anyone outside the cult being convinced by its display of rhetoric.
I have no idea whether you are simply another myth disciple. I am pretty sure you don’t make a case either. However your post is slightly interesting. Bayes theorem is subjectivity dressed up like a robot to make intuitions look more impressive. It can be used by apologists in just the same way it can be used by people who have serious reason to use it. It follows from axioms (I already said that in my piece) that require real world possibilities. But it’s also used all the time to deal with “constructed” possibilities–such as Swinburne does by using the “world that exists” equivocally to establish a “real world” from which he can get to ontology, and then to God. Fortunately, this doesn’t nullify Bayes; it simply illustrates that a part of constructing real world possibilities includes the intuition and subjectivity of the user. Indeed, I am not sure why you bother to go through this rudimentary stuff (and evidently you think all that time I spent reading philosophy didn’t introduce me to logic: drat) since it does not address the core issues of when it is and when it isn’t heuristic (if you like that word) to employ BT; nothing demands it, and as you say, any situation involving probability permits its use. I said that too. By its nature then–as everyone knows–it does not protect against subjectivity, misinformation, or deceit. History is loaded with all three. If for example the question to be decided is “What is the likelihood that Jesus was a myth,” there are two inherent questions: (a) Did Jesus exist or not exist? (b) Does his nonexistence entail that his story is a fraud or an entertaining fiction (using a discredited definition of the word myth).
Let me leave that hanging (while you ponder how you will get from that to axioms that trigger a Bayesian approach) and move to your analogy, which instead of appealing to anything approaching complex historical data from the ancient and pre-ancient period gives me this: “A certain virus occurs in 1% of the population. There’s a test for this virus that has a 1% false positive rate, but is 100% accurate when the virus is actually present. Somebody’s test result is positive for the virus; what is the chance that he really is infected? Using Bayes’s formula, one get’s the result, 1/1.99 or about 50%. This is a standard analysis that has been employed for decades. And note that again no future events are involved here.” Are you equating this to historical questions (“no future events are involved”) because we are using predictive factors in the form of viruses that have already occurred? But that is not what’s happening; the incidence of occurrence which is necessary to make the predictions and establish the sample field is simply a statistical record of existing conditions, not complex historical data from the distant past. Moreover, your case does not involve epistemological probability. And second, what would be the reason for invoking Bayes if there was no implication of a future event: i.e., that “someone will be/get infected.” I don’t think anyone would want to challenge the use of BT in circumstances where its use is warranted as it clearly is here, in disease control. I certainly don’t, and partly because in questions of “pure statistics” and especially in the natural sciences and closely cognate fields, the question of intuition, interpretation and subjectivity do not arise to the same degree.
How do we get from your example/analogy to the question I left hanging, because the question of whether Jesus lived or whether Jesus was a myth is not susceptible of the same kind of analysis. Any probability you assign to an outcome using BT will be loaded with intuition, wrong information, apologetics (at least potentially) and even foregone conclusions. I am not saying that this is the way good historians work; I am saying that not only good historians are looking at the question, and certainly some very clever apologists have become adept at BT.
Maybe you have simply used as you say a textbook example that isn’t your own and thus doesn’t make your point, but it certainly does not constitute an argument for the utility of Bayes is establishing questions based on examples hermeneutical, physical and textual (not to mention chronologically mixed) data from the distant past, and the mixed modes (and results) of critical interpretation — let’s call it subjectivity — that would be applied to this data. Not to be facetious–but the best and as far as I can see the only way to use Bayes in New Testament work would be to use it to estimate the time of the second Coming. I’m sure Swinburne would approve of that. Please understand that no one is arguing that Bayes isn’t fun, and useful in the right instances. It is that for this question it can only be a waste of time and a diversion.
Part 2.
You object to the “subjectivist” interpretation of probability. Fair enough; it is an area still under debate among philosophers. But it’s hardly as if Carrier is breaking new ground in his application of Bayes’s theorem to historical problems, or is employing it in a way that it was not “intended.” So long as one is dealing with probabilities, under any interpretation of the word that satisfies the mathematical laws of probability theory, one can use Bayes’s theorem. He is not jiggering the equation in any way.
Moreover, you yourself seem to concede that historical claims are probabilistic when you say, ‘Historical argumentation is both non-intuitive and probabilistic (in the sense of following the “law of likelihood”).’ Thus, since they involve probabilities, they are amenable to Bayes’s theorem.
Now a digression: Carrier is of course dead wrong when he pompously declares that “all the historicity criteria so far have been shown to be flawed to the point of being in effect (or in fact) entirely useless,” as he himself demonstrates in his latest book how some of these criteria do in fact conform to (and follow from) Bayes’s theorem. Moreover, the idea that all these criteria must be useless because they yield different results when applied by different scholars would also invalidate Bayes’s theorem as a useful method, since different scholars get vastly different results when they utilize it, too. Just because a method is frequently misapplied doesn’t mean it is invalid.
Back to your assertions. You mention in a couple of places that you don’t think Bayes’s theorem can be applied to never-before-observed events. But this objection is not really that forceful, since the situations in which Carrier is applying it do have generic precedents, so reference classes can be identified, and prior probabilities estimated on the basis of frequencies (which is what you seem to prefer). Moreover, even in situations where we really have no background information on which we could form a prior, even if one then inserts 50% (or any other value), the dependence of the final result on this assumption is explicit in the mathematics, so different scholars can compare their results just by plugging in different values for this priors. Then they can agree on the way in which the final result depends on these assumptions, reducing the debate to only a debate about these prior probabilities. This, of course, would be true for any subjective prior probabilities, not just for those for events claimed to be sui generis, and answers the most serious concern raised by your friend at Cambridge as well.
Finally, the debate with Swinburne shows the advantages of Bayes’s theorem, rather than opposite: Employing the theorem forced him to spell out his assumptions, which could then be attacked individually, as could the way they fit together. By offering your own set of prior probabilities, you could then use the same method to produce what you feel is the correct probability. Ultimately the debate would be reduced to arguments for your priors, unless someone had made a logical or mathematical mistake along the way (as he clearly did), which would quickly be exposed.
This discussion is useful; in that it at least establishes, as a first important point, that 1) there is nothing impossible or wrong, in applying probability to past events, per se. As perhaps some of Joe Hoffmann’s remarks might have seemed to imply. Probability can be applied to the future; it can also be applied to the past.
Having resolved that? The NEXT question, would be: 2) even if it is therefore possible to apply probability to past events, are there many good opportunities to do so? It being asserted – by Joe – that our accounts of the past, are not good clean data, from which useful predictions might be made.
I would suggest that often, in fact, there are. First of all because 3) we CAN have a great deal of good information, even about the past; from scientific explorations of it. This is done every day in for example, Archeology. If we hear of many people dying strangely in a given era … and then find a lot of lead in their bones? We can deduce that perhaps they were not so much “cursed by God,” or afflicted magically; but were probably getting their food or water from a high-lead source; perhaps cooking food in lead utensils.
So in fact, and against even Joe’s second objection to the application of Probability, Bayes, to historical problems? There are many things from the past we CAN be reasonably sure of, even in Historical times, first of all. Enough to serve as the basis for useful calculations about probable realities, even in very ancient times. Not by using just fallible historical accounts from the time; but by adding to them, what a modern science can tell us about that same time period.
This is not about whether historians use probability. It is about (1) the use of BT as a statistical tool in assessing complex historical, mainly textual data from ancient times; and (2) whether BT possesses sufficient safeguards in the realm of epistemological probability (not statistical) to warrant its use. My argument is that it is warrantless in such study and thus useless.
For the moment, I don’t have full answers. But perhaps we can canvas some expert contributions here, while covering a few minor objections in the meantime:
Apparently 3) Hoffman’s third – and perhaps his main – objection to the application of Bayes’ theory to History, is to question whether Baye’s theory has been applied to ancient history. We agree now that Statistics in general hae been so applied; so there is no longer an objection there.
How about specifically, Bayes? Here for the moment, I need some time; I seem to vaguely recall that it already has been so applied? In Archeology? Anyone else out there have any examples
Joe Hoffmann’s next objection is that 4) seems to be that any such investigation should have “epistemological safeguards.” (Maybe someone else would like to take on this third objection, while I am taking care of some domestic chores?)
This might be a solution to part of these objections. I (mis?)understand the underlying concern to be, in part, that historical accounts seem so subjective; that there is no firm, good data to base any Bayesian calculation on. But? I want to establish first, that there is in fact, often lots of such data around. Though science. The qualification that we use primarily or only or mainly “TEXTUAL” data, would be a crippling and unnecessary restriction. Why use only or “mainly textual data” – which indeed often IS extremely subjective and unreliable? Why use that … When there is very often, much better, scientific data available, or obtainable? As archeology every day proves. This knowledge moreover, is “EPISTEMOLOGICALLY” rather solid. Since in part, it is based on actual solid objects in part: bone and pottery fragments and so forth.
For example? Archeloogists around the current Talpiot B “Jesus Tomb” excavations, are identifying some villiages areas as probably Gentile, and others as Jewish – by a scientific fact; by the massive number of pork bones in some, but not in others. Once this is established? Then we can use this – probably in fairly a simple Bayesian calculation – to confirm a high probability of a textual assertion: that (admittedly) subjective, textual, biblical accounts of a Jewish community in the area, are still however likely, probably, true.
To be sure? To the extent that we are using any “texts” at all, calculations will be less precisely than carefully controlled modern experiments. And yet? Massively important work has already been obtained by SIMILAR methods.
And so we have established the usefulness of Statistics in general here. And we have addressed some superficial problems with “epistemology.” Next? How has Bayes, specifically, been more precisely applied here? Here to be sure, my own limited math begins to run out.
Any professional mathematicians or statisticians out there, who want to pick up the rest of the account, at this point? I’ll be calling a few….
For example? Archeloogists around the current Talpiot B “Jesus Tomb” excavations, are identifying some villiages areas as probably Gentile, and others as Jewish – by a scientific fact; by the massive number of pork bones in some, but not in others. Once this is established? Then we can use this – probably in fairly a simple Bayesian calculation – to confirm a high probability of a textual assertion: that (admittedly) subjective, textual, biblical accounts of a Jewish community in the area, are still however likely, probably, true. To be sure? To the extent that we are using any “texts” at all, calculations will be less precisely than carefully controlled modern experiments. And yet? Massively important work has already been obtained by SIMILAR methods.
Well, though it doesn’t prove the resurrection, no bones of Jesus are likely to be found. The archaeological research you cite uses statistical probability of physical evidence; as I said, textual evidence in NT studies is the norm, sometimes supported but not usually by archaeological remains, e.g, the Pilate stone but nothing dispositive about Jesus. Epistemological certainty, as in philosophical and “abstract” questions (and ancient historical questions are in limbo in that respect) employ statistics with big Caveats written all over them. I find your appeal to statisticians rather sweet: when you round them up, will they be taking courses in paleography? Or are they like my fundamentalist accountant who uses statistics all the time but would put the probability for Jesus on the basis of the gospels alone at 99%. Let me pose you a question: If it is true that 50% of the gospel is “fiction” what criteria would you use to prove, if you wanted to, that the remainder isn’t, in the absence of external evidence. Would you employ a perfectly plausible calculation that if the made-up portion rises to that number there is a strong likelihood that the remainder is made up too? Or would you be satisfied, using not BT but simple diallelus and CSC that our certainty stands at 50%. {BTW, Bayes is not being used to corroborate these finds; it is a simple deduction from the evidence and prior assumptions about dietary rules & plausible assumptions.)
Well, Bayes could be used in this situation.
Basically, in part, Bayes is a method of adding up all the probabilities of various related events, or aspects of a single event. To see what the probability of any given single, related event is.
So for example? Suppose we want to know – a key question for me, in theology – whether Jesus was considered a good Jew. And not a Hellenized Jew, or “Samaritan,” say. How might we try to calculate that, related to the above?
Suppose we assume for the moment (for simplicity; from preliminary observation of observant Jews today; from previously-established historical evidence, or preliminary data), that 1) there is a 90% possibility that many of those who lived in the village in the time of Jesus, ate pork. While 2) there is only one chance in ten – a 10% possiblity – that a good Jew would live in close proximity, in a tiny village, with … folks who ate lots of “pig meat”.
Suppose we also assume for simplicity, that Jesus as a youth, lived largely in Nazareth. So? We go to Nazareth, dig around with a few Archeologists and dig bums. And? We find tons of pork bones, all OVER the tiny town of Nazaret. Including the stratum that corresponds to Jesus’ lifetime: finding petrified pork chops, ribs, sausage casings, etc.. All over town.
So? We factor in the probabilities of TWO events – 1) 90% probability of pork eaters in Nazareth; then 2) the 10% possiblity that a good Jew would live in proximity with such a thing. And? Then, from these two facts (based in part on Archeological science) calculate the cumulative, final probability that Jesus would be considered a good Jew, by his peers. Which probability, in this case, being ..quite low.
Here we are getting much closer to Bayes, I think?
Granted of course, you might well choose to use this very example, as an example of how many assumptions and presumptions in Bayesian analysis, could go wrong. And indeed, to perfect this example, dozens and dozens of tweaks would have to be made. So that finally, only a full page of calculations will be adequate. And to be sure? we would need statisticians that know archeology and religious history. It would be an interdisciplinary effort.
But also note this: the more such things we do, as we accumulate hundreds, then THOUSANDS of likely “fact”s? As we have more and more data points, points of reference? Gradually, the whole elephant begins to emerge … with greater and greater certainty.
Though to be sure, at first our accuracy is rather low – quite low compared to experiments in controlled conditions? Eventually however the strength of Bayes in part, is that it begins to add up, cross-reference, more and more and more probabilities. While the final result, is quite a bit more certain, more accurate, than just a few calculations based on just a very few investigations.
@Garcia: Yikes: you have just driven the final nail in the Revd Thomas Bayes’s coffin.
One thing I keep noticing from the Mythicists, the folks who seem to believe all other methods are”F…..” is: “look folks, Bayes is all we’ve got therefore we ought to be using it in exclusion of other methods that have known limitations”.
The practice of hermeneutics is often difficult and pain-staking; that has been stated on this site and I heard plenty of it some 25 years ago sitting through classes in history and comp lit. If there is such a thing a progress in hermeneutics (and I think there is), it is achieved for the most part by getting one’s hands dirty, i.e you have to work through your sources, have your lexicons, submit you work for peer review, etc.
It’s for the reasons above that I think trying to apply Bayes to the field of biblical hermeneutics is anything more than a form of pseudo intellectual nihilism that will do far more harm than good.
@Scotteus: True, worse, you can’t even get to the hermeneutics until you get your hands dirty with questions of dating, authorship, papyrology, and paleography. –Won’t go into linguistics (but to do the work you have to). There was a time when some of the mythters had critical biblical backgrounds–Drews, for example, D. F Strauss and Bruno Bauer (who hated each other). The last two were different denominations of Hegelian and devoted to the belief in “movement” and progressive ideology in history, so the Jesus story became totally subordinate to them as data while the reality of Christianity became the focus. The establishment of their day regarded them as second rate ideologues who were diluting method with their Big Ideas, and rightly considered Drews a hack and second rater to boot. Unfortunately, modern mythtics are simply unaware of the social context of this generation that had some training. They think of their works as the suppressed enlightenment of an era (?? it was all published, all critically reviewed, all discussed). They get a lot of their talking points from them but have almost entirely missed the rebuttals and lack the training to sort out the details. So they continue to talk about “Paul’s silence” as some sort of mysterious conspiracy cloaking the fact that Jesus was a cipher. The honest thing to do would be to give it up: It doesn’t work. Bayes is just the latest chapter in the general confusion. The most charitable thing one can say about it is that it’s a form of shortcutting unwarranted by the nature of the task and thus literally useless. The least charitable I won’t say.
Not at all. Bayes’ theorem is not to be used to the exclusion of all the other methods; but in fact, it should be used as the synthesis of all of them.
It is only because previous scholarly findings were so careful, and have accumulated at last some degree of probability … that we are now in a position to start adding up and cross-referencing all these probabilities. In a more organized, logical way. To come up with at least a rough outline of the larger picture, at last.
Some mythers might be indeed, trying to simply substitute one new methodology for all those that went before. But that is not how I would apply Bayes here. Far from it. Good mythicism is built on, and depends on, tons of good scholarship that went before it.
Bayes theorem should now be employed to (as a Hegelian might like to say), “Synthesize” the countless different positions and findings; even those formerly thought antithetical. By cross-referencing the various probable findings.
Garcia: BT “is the synthesis of all of them” — but it isn’t. It follows from certain axioms. It is a theorem–like this, which you will remember from high school–Let ABC be a triangle with side lengths a, b, and c [In the following the ‘2’s should be superscript or squares, which I can’t generate in this program, sorry]. This is the equation form of the Pythagorean theorem. If a2 + b2 = c2, then a triangle is right. If a2 + b2 > c2, then a triangle is acute. If a2 + b2 < c2, then a triangle is obtuse. Theorems are based on conditions–like conclusions follow from premises: their use is restricted by warrants. The more broadly you apply something like BT, the less useful it is and by the time you enter the realm of textual interpretation and related subjects I suggest it is useless. Prove me wrong.
I am enjoying this very much, though it puts me in mind of the mind-buggaring logic problems I used to look at in the Sunday press, eg:-
Q. If I have one banana and you have five oranges, what colour is the bed-spread?
A. Purple, because the dog has got fleas..
I think there is a lot of swinging and barely missing going on here. Carrier does *not* fail because Bayes rule is inapplicable to the distant past. Swinburne does *not* fail because he has taken on too ambitious a task.
If Carrier estimates the probability of the existence of a historical Jesus at under 90%, then (I expect strongly) he is making an error in his application of Bayesian reasoning. I haven’t read the book, so I don’t know that. If he is criticizing specific historical claims about Jesus, his reasoning may be sound as far as it goes. I understand that Carrier is a mythicist, so it is clear that he has not successfully applied Bayesian reasoning to the question of simple historicity, but I don’t know if he has even attempted it. His curiosity may not have led him that far.
Similarly with Swinburne: if he estimates the existence of a Judaeo-Christian God (or any anthropomorphic God) over a fraction of a percent, then he is making errors in his application of Bayesian reasoning. If he really addressed the God question with a sincere desire to know the answer, and successfully applied Bayesian reasoning and the available evidence to the problem, then he would likely announce that any type of personal God is extremely improbable, and that the alien god of science is extremely probable.
*Bayes really only tells us how our probability estimates should change (optimally, under formal mathematics) when we consider evidence and can accurately estimate how probable it is that we would see that evidence given that our theory is true and how probable it is that we would see it given that our theory is false.* That’s all it does.
Mathematics is timeless. It either works or it does not. If it fails for the first century, then it fails for the 21st century. If it works for the 21st century, then it works for the 1st.
Bayesian probability is the mathematical engine behind any science, historical or otherwise. It may not be appealed to directly, but science can always be re-formulated in Bayesian terms unless it contains some real error in reasoning.
smijer: Thanks, yes, in general. But you make a significant mistake: “Mathematics is timeless. It either works or it does not. If it fails for the first century, then it fails for the 21st century. If it works for the 21st century, then it works for the 1st.” Timeless and Platonic. It is not a question of whether mathematics qua mathematics being true then is also true now. We are not dealing with that level of certainty and proof; we are dealing with variables hidden within variables, not a single x. Apply Bayes to Socrates/Plato on justice and you have a nearer analogy.
There are difficulties with historical studies – difficulties that make it hard to nail down probabilities. Hidden variables, even. But that goes to the difficulty of the project, not the inapplicability of the rule..
I disagree.
smijer: Plug this into BT and tell me what you get:
If all the world were paper
and all the seas were ink
and all the trees were bread and cheese
what would we have to drinK?
It should be fairly simple. Refer it out if you need to. On the other hand, if you see that there are difficulties getting from this to BT: welcome to the world of critical historical scholarship.
Biblical scholarship is already, even close to its very essence, a vast but disordered and informal accumulation of probabilities.
Most of the central questions of traditional religious studies imply rough, informal calculations of probability. For example? 1) Who wrote the epistles of Paul = what is the probability that a given epistle attributed to Paul, was really written by him. 2) Then : what is the probability that this or that physical miracle occured? 3) Then the authority of the gospels: How certain is the testimony of any single synoptic gospel, relative to the other gospels?
And especially? 4) The search for the root of the Gospels, in Mark or Q, already involves scholars roughly using calculations of Probability: how consistant are certain elements of the gospels.
Therefore, rough assessments of Probability have always been used as a core part of traditional religious study. So? Why not begin to use this dialogue on Bayes, 1) to recognize this aspect of what is already been done in an uncontrolled way, in the field? To raise an already-implicit calculation in textual studies, to consciousness. And 2) begin to systematize, what textual critics already do?
To be sure, as Joe Hoffmann’s remarks here suggest or show, the first effect might be to foreground the already-existing looseness of traditional scholarship and its assessments, it assignments of findings; the first clarification is to acknowledge the huge number of variables. At the same time however, this effort begins to at last acknowledge that there were already, always, rough internal calculations in the field; calculations that have already long been at the core of traditional textual study. While once we see this more clearly? We can begin the hard and useful work of at last listing the vast number of such probabilities, and systematizing them. And then? Improving them somewhat, at least.
At last acknowledging and listing the vast number of calculations of probability already made, in fact, should turn out to be extremely fruitful, due to a particular feature of Bayes. In that as it turns out that in Bayes, in effect, part of the reason it is useful, is that it begins to systematically assemble many points of data, MANY probabilities. This is useful in itself partially; as it begin to give us a better picture of the whole. While indeed one of the main features of Bayes, is that it very good in assembling more and more probabilities, of more and more related events … to compare and add them up. And increase the overall accuracy of each individual elements. By allowing us to systematically cross-references and refine, any single given prediction, calculating its own individual probability better, by seeing it as a part of a larger, corroborating system.
Any such massive system, should be advanced with all due cautions and humility to be sure; warning that after all, the whole field is highly speculative. However? This effort now seems timely and necessary. Given the increasing use of computers. And given that the field by now is already dominated by half-conscious, wild, native, uncontrolled, and unsystematic probability calculations. So that any systematization of this side of the field, would be an improvement over what is already being done in an uncontrolled way.
But one thing that one must keep in mind in this whole discussion is that texts are not unbiased snapshots of history. Texts themselves have a history. And in the case of certain texts like those of the NT this is sometimes impossible to discover. This leaves us with all manner of possible or plausible conjectures. For some time now, despite Schwietzers famous observations which every introductory textbook on the issue notes, scholars have been painting self portraits and calling them ‘Jesus’ (as dale Allison notes). Is the ‘reality’ (as opposed to myth) within a text like the gospels like the cake which can be seperated from the icing on it? Or is it like a pudding where myth and fact mix seamlesslty and nothing is easily recoverable? How much Mishnah, Haggadah, typology etc. are we dealing with? What is the genre of the NT literature? Because answers to questions like these can alter our interpretations completely when it comes to making judgements here. Which leads to the question, can probability be applied to these issues meaningfully? Will any ‘numerical probabilities’ suggested in such a context ever be immune to the charge of being the purely speculative reflections of our own dispositions? Or will there now be a Bayesian excuse to continue to create Jesus (or lack thereof) in our own images?
Firstly we have to swallow the notion that numerical values can be applied to our biases, prejudices, values etc. is accepted (and it appears it must be for this form of Bayesian application to be meaningful). This may seem ‘obvious’ to us today in an age where we all grow up in system where teachers and professors regularly attach ‘grades’ and numerical evaluations to our thoughts (in essays etc.). But this is only a very recent invention (going back to William Farish if I’m correct, although I may be wrong). And as far as I know, this system won out not because there was some obvious “truth” to it but because of practicality. The actual issue of whether such a course of action is legitimate remains unresolved.
But allowing this, will this really accomplish anything beyond changing the vocabulary of the current discussions? Today we may have two scholars arguing that “this is clearly a midrashic expansion” vs. “there is a clear echo of a historic remenisence here”, and tomorrow we may have them arguing “there is over a 80% chance that this is purely midrash” vs. “it is over 83% certain that this echoes authentic historical events.” Amongst two scholars who disagree on something, today they would dsiagree with the plausibility of the others assumptions. Tomorrow they will say “but I feel that she has not justified this probability as being 60%, and hold that it is no greater than 45%”
Apologies again for errors in English
That’s almost right – but not quite. We are not just assigning numbers, percentages of probability for speculations; we are then plugging all that into … a potentially massive system.
What we should build, is rather exactly like current computerized models of the economy. We will see hundreds of economic models, major factors, with thousands of items of data;… now finally all systematized and internconnected. All systematized and interconnected. To the point that? If we change one item of data … we can look and see what the rest of the whole system looks like, after that change.
It works in our models of the economy. And it allows flexibility; you are allowed to plug a different value into the model here and there.
But especially? We can begin to see and systematize the INTERCONNECTIONS between all the formerly all-too-disconnected speculations. So that finally? We can begin to see how factors once thought to be remote from our particular baliwick or monograph, can seriously affect and inform, our own limited findings.
That should be a revolution, a quantum leap, in this field.
“What we should build, is rather exactly like current computerized models of the economy. We will see hundreds of economic models, major factors, with thousands of items of data;… now finally all systematized and internconnected. All systematized and interconnected. To the point that?” You are seriously proposing we run historical studies on the model of the economy. Perfect. that way when everything crumbles we can blame it…on the model!!!!
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etter erotiske eventyr, og dette med noen som deler
samme preferanser som dem. Det er de tingene vi vanligvis tenner på og fantaserer om.
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opp med væske, helst tilsatt litt salt.
I read this article completely about the difference of most recent and earlier technologies, it’s awesome article.
It’s a joke article. Rabbi Hoffy has no idea how or where or when Bayes is used in the real world. Presumably he read a little tract somewhere on the web to inform him. In fact one of its most useful applications is in identifying what happened in the past when and where: http://www.amazon.com/The-Theory-That-Would-Not/dp/0300188226
Oh my. A little tract somewhere. I think the statute of limitations has expired on this article, but in case anyone is still bothering with it the court of public opinion has returned its verdict on Carrier’s absurd use of Bayes.
I couldn’t refrain from commenting. Perfectly written!
Reblogged this on The New Oxonian.
This is old, I know, and now largely irrelevant. However, the entire basis of this post displays a gross misunderstanding of how Carrier intended to apply BT to historical questions (as he laid out in his previous book “Proving History.’) Applying BT, according to Carrier, only encourages the historian to consciously expose the logic underlying the argument. One can do this without math. BT is not a magic formula. The historian must defend the assigned probabilities which are exposed rather than hidden behind imprecise language such as “In my view, it is unlikely that…” or “it is plausible…” Exposing the underlying assumptions allows critics to question the assigned probability (such as N. Covington has done in his own critique of Carrier’s latest effort).
Carrier is not arguing for some sort of mathematical voodoo, here.
Reblogged this on Daniel N. Gullotta and commented:
Basically sums up my thoughts on the use of Bayes’s Theorem within the Study of the Historical Jesus:
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