Bayesian Historicity

[Bertie]

Because of this, Carrier essentially tables several questions that are a matter of considerable "devil in the details" debate, such as the dating of the letters of Ignatius (early 2nd century or mid 2nd century), etc. He elects to work on the assumption that either dating could be correct and attempt to discern the state of the evidence on the historicity question either way.

This right here gets at an important point: when evaluating Carrier's (or any other) probability based argument, you must not only apply your skepticism to the numbers being plugged into the formula but to what is allowed to count as evidence at all. For example, Carrier uses a 120 C.E. cut-off date for evidence. Now, the general idea of a cut-off can certainly be defended because of the chance that later and later texts reflect independent evidence goes down and because the amount of texts starts exploding. But I remember when reading the book I thought it a bit convenient that this date let Carrier dismiss Aristides, Quadratus, and the Epistle of Barnabas in footnotes — all three of these, if I remember right, would nudge the dial towards historicity and fall just on the wrong side of Carrier's cut-off.

Maybe that is pretty minor, but I had more problems with the way evidence considered by Carrier to be interpolated or hearsay is treated (you know, the Tacitus, Josephus, Suetonius, etc. that we are always arguing about). Once this stuff is argued to to be interpolated or hearsay, it counts for nothing. No attempt is made to do something like, say, giving these sources a probability of being interpolated or hearsay and working from there. No attempt is made, as when dealing with texts that Carrier does accept as evidence, to toss the other side a bone and come up with a "best case for historicity" number.

Now OK, maybe you're totally on board with assigning Josephus and company with a big fat zero on the Jesus historicity relevance scale, and you don't care about those texts that fall just on the wrong side of that 120 C.E cut-off. But look at some of the other stuff that Carrier does allow to move the numbers: Epiphanius. The Talmud. Hegesippus. (Carrier lets these late, and in the case of the Talmud, way late sources in under the possibility that they reflect older independent traditions). I mean, doesn't that sound weird to anyone: Josephus, totally worthless even though we're constructing a probability based argument here that can assign probabilities to interpolation or hearsay that are no worse than these magic numbers that were coming up with for the evidence we do accept. Hegesippus and the Talmud, on the other hand, at least counts for something.

[Leucius Charinus]

Thanks for these discussions: I am finding them very thought provoking.

There is no doubt that the Bayesian method is useful. The question is whether it is being used in an appropriate manner for the task at hand. The hammer analogy hits the nail on the head. Carrier is certainly breaking new ground here to arrive at a new description of Jesus as a 32% chance of historicity.

Peter Kirby thanks for the second post which answered all my questions. Do you mind a question .... Did you (or FWIW anyone else here) study mathematics (particularly statistical mathematics) at a university level? Also thanks Mac for an outline of the basics.....

Formalization of an argument refers to the identification of premises, conclusions, and inferences in discrete, formal steps or calculations. It has little to do with the validity of the argument, although it can be used to help identify whether the argument is ultimately valid or invalid by clarifying the structure of the argument.

The two main forms of formal argument are

• deductive arguments where the premises lead to the conclusion (the conclusion is deduced from the premises)
• inductive arguments where the conclusion is induced or inferred from the premises

Arguments may be valid, but their conclusions not true if the premise are not true (Invalid arguments has poor or no logical ties between the premises).

A sound deductive argument is one with a true conclusion deduced from true premises.

A cogent inductive argument is one with a reasonable/convincing conclusion inferred by true or reasonable premises.

There is also the issue of major, minor and middle terms (and the 'predicate')

[Leucius Charinus]

Because of this, Carrier essentially tables several questions that are a matter of considerable "devil in the details" debate, such as the dating of the letters of Ignatius (early 2nd century or mid 2nd century), etc. He elects to work on the assumption that either dating could be correct and attempt to discern the state of the evidence on the historicity question either way.

This right here gets at an important point: when evaluating Carrier's (or any other) probability based argument, you must not only apply your skepticism to the numbers being plugged into the formula but to what is allowed to count as evidence at all. For example, Carrier uses a 120 C.E. cut-off date for evidence. Now, the general idea of a cut-off can certainly be defended because of the chance that later and later texts reflect independent evidence goes down and because the amount of texts starts exploding. But I remember when reading the book I thought it a bit convenient that this date let Carrier dismiss Aristides, Quadratus, and the Epistle of Barnabas in footnotes — all three of these, if I remember right, would nudge the dial towards historicity and fall just on the wrong side of Carrier's cut-off.

Thanks for these reflections Bertie. Do you know whether Carrier uses this 120 CE cut-off date for all the evidence or just the historical hypothesis evidence. The reason that I ask this is because AFAIK quite a large amount of the weight being contributed to the mythicist hypothesis evidence (particularly as treated and evaluated by Doherty and Carrier ... "celestial being") seems to be derived from the text of the "Ascension of Isiah" and AFAIK to quote WIKI ..... "theories as to the date of its composition place it in a range from the late 1st century to the beginning of the 3rd century CE", which of course places it on the cut-off side of 120 CE..

The question is of course is this 120 CE cut-off date for all evidence, or just some evidence? Thanks for any info.


LC.

[Leucius Charinus]

And on the subject of how Carrier and the Bayesian model caters for forgeries, interpolations, corruptions, etc ....

Maybe that is pretty minor, but I had more problems with the way evidence considered by Carrier to be interpolated or hearsay is treated (you know, the Tacitus, Josephus, Suetonius, etc. that we are always arguing about). Once this stuff is argued to to be interpolated or hearsay, it counts for nothing. No attempt is made to do something like, say, giving these sources a probability of being interpolated or hearsay and working from there. No attempt is made, as when dealing with texts that Carrier does accept as evidence, to toss the other side a bone and come up with a "best case for historicity" number.

Now OK, maybe you're totally on board with assigning Josephus and company with a big fat zero on the Jesus historicity relevance scale, and you don't care about those texts that fall just on the wrong side of that 120 C.E cut-off. But look at some of the other stuff that Carrier does allow to move the numbers: Epiphanius. The Talmud. Hegesippus. (Carrier lets these late, and in the case of the Talmud, way late sources in under the possibility that they reflect older independent traditions). I mean, doesn't that sound weird to anyone: Josephus, totally worthless even though we're constructing a probability based argument here that can assign probabilities to interpolation or hearsay that are no worse than these magic numbers that were coming up with for the evidence we do accept. Hegesippus and the Talmud, on the other hand, at least counts for something.

WOW. Well I kind of agree. I had hoped Carrier might develop some sort of Bayesian approach to indicate the likelihood of forgery, perhaps even on the model of the "TF" and then use that in his work. But from what you say he does not do this, but essentially just dismisses the evidence. Interesting. Not that I agree that the "TF" (for example) might not be dismissed, its the principle Berties states above. The authenticity of the "TF" (eg) would itself be a probability to be plugged in to a very large Bayesian probability equation. The "TF" probability might be quite small when Carrier plugs it in, but it should not be zero. I guess Carrier does a cut-off with his assessment of this.

But of course this is the whole point of the OP - to understand how the Bayesian historicity equation is "loaded up" for the test-run. In theory there should be one massive general historicity equation which can be "loaded up" by opponents. Those who think (for various reasons) that the "TF" is partially authentic or even completely authentic could allocate their own value of "historicity" for it, and then push the button to compute again.


On a lighter note, if Carrier got 32 % would Douglas Adams have got 42 % :) ?

[bcedaifu]

My take on Bayesian historicity calculations is that they result in a false assumption of objectivity.
In the end, you just shift the subjectivity from formulating the result to assigning probabilities to your premises.

Agree.

They help with drawing the right conclusions from your presuppositions, but the main problem of the historicity question is those presuppositions.

Nope

What was the main problem with Plato and Aristotle's theory of geocentrism: "presuppositions"??? No. They used geometric analysis in the tradition of Ἱπποκράτης ὁ Χῖος,
Is it our "presuppositions" that explain recognition that Jimmy Olsen had not functioned as a reporter for a major newspaper in New York City? We understand that "Paul" and Jimmy, were both fictional characters, not because of "presuppositions" but because humans don't interact with supernatural entities, as both "Paul" and Jimmy claimed to have done.

What is the main problem of historicity? Is that problem amenable to analysis by application of Bayes' theorem?

In my view, the main problem of historicity is absence of meaningful data. Facts. Truth. Unambiguous detail. Absent genuine data, there can be no historicity, only legend, rumors, and gossip. Disgruntled academicians can cloak the glaring absence of data in a mathematical sweater, in a vain attempt to improve acceptance of some tenet. In essence, that is precisely what Plato and Aristotle did, when explaining the mathematical basis underlying geocentrism.

At last, a perfectly fair and insightful criticism. This is the long and short of it.
The Bayesian approach changes nothing really important to the discussion and ends up becoming, in practice, a self-inflicted red herring for Carrier.
I'm sure Carrier would blame sophism, mathematical illiteracy, and other foibles for the fact that it's become so distracting... oh well.

I acknowledge that Ulan's comment is well written. He errs, however, in identifying, as principal issue preventing assertion of historicity, an author's opinion. Claim for historicity depends only on reliable data, not on presuppositions--fact 1; ancient city of Troy existed: contemporary excavations in Turkey. Fact 2: Achilles was not granted divine protection in war. Fact 3: there are no divine entities.

[Bertie]

Thanks for these reflections Bertie. Do you know whether Carrier uses this 120 CE cut-off date for all the evidence or just the historical hypothesis evidence. The reason that I ask this is because AFAIK quite a large amount of the weight being contributed to the mythicist hypothesis evidence (particularly as treated and evaluated by Doherty and Carrier ... "celestial being") seems to be derived from the text of the "Ascension of Isiah" and AFAIK to quote WIKI ..... "theories as to the date of its composition place it in a range from the late 1st century to the beginning of the 3rd century CE", which of course places it on the cut-off side of 120 CE..

The question is of course is this 120 CE cut-off date for all evidence, or just some evidence? Thanks for any info.
LC.

The exact quote regarding the 120 CE date is on page 258, "I will consider only texts that are known to have been written (or probably written) before 120 CE (or that record information from an identifiable source before that date)". Following this is a justification for this date: the death of all surviving witnesses to the 30s CE and the explosion of "bogus" texts about Jesus.

The Ascension of Isaiah, however, is not used as evidence in the book but as background knowledge. The evidence is interpreted in light of all the background knowledge; as Peter Kirby mentioned upthread, the collection of background knowledge relevant to the historicity of Jesus is a strength of this book. In particular, the AoI is used a fair amount when Carrier evaluates the evidence from the Epistle to the Hebrews.

It would be valid to say, I think, that if the AoI (or the relevant parts of it) did date that late, that would compromise to some extent its suitability as background knowledge for the argument in this book, and its value for interpreting (say) the Epistle to the Hebrews reduced.

[MrMacSon]

.
In my view, the main problem of historicity is absence of meaningful data. Facts. Truth. Unambiguous detail. Absent genuine data, there can be no historicity, only legend, rumors, and gossip.

By 'data' you really mean information: primary [contemporary] sources ('data' is essentially what has been document (or is documented in the present) in a series of targeted, objective or structured observations or experiments).

Non-contemporary information may be useful, as for, say, Alexander the Great, especially when there is large amounts of information. But gleaning legend from fact can still be difficult.

[MrMacSon]

.
The exact quote regarding the 120 CE date is on page 258, "I will consider only texts that are known to have been written (or probably written) before 120 CE (or that record information from an identifiable source before that date)". Following this is a justification for this date: the death of all surviving witnesses to the 30s CE and the explosion of "bogus" texts about Jesus.

Which text? Proving History? On the Historicity of Jesus?

[neilgodfrey]

The value of the Bayesian approach is that it forces one to think carefully about all one’s presuppositions and background knowledge and alternative explanations (especially alternative explanations) and serves almost as a mnemonic to “keep historians honest” as they evaluate evidence and formulate judgements (probabilities) from the available evidence.

Good history does not need Bayes’ but it is much harder to do bad history when one does use it.

(Understanding "doing history" in the sense of discovering what happened.)

[Peter Kirby]

Did you (or FWIW anyone else here) study mathematics (particularly statistical mathematics) at a university level?

My university coursework did include an upper-division course in "Probability and Statistics" as well as a course in "Statistical Methods" in the natural sciences taken at CSU Fullerton.

Like Bertie, I also observed that Carrier neglected at several places to attempt to score points for the historicity of Jesus. This is a pretty common failing (to neglect to find the strongest arguments against one's position), and the onus is ultimately on the proponents of the historicity of Jesus properly to state the best case available to them. Hopefully the challenge will be accepted by someone, even if it requires admitting that there is a genuine debate to be had.

There is a serious wrinkle in the use of Bayes' theorem as applied by Carrier. It is the same wrinkle someone once pointed out as an objection to my essay linked above. It is as follows:

Let's stipulate some made-up numbers:

In a year a country had domestic and foreign vehicle sales. All sales were truck or sedan, and had either a 4-cylinder or 6-cylinder engine. Breakdown:

15% were 6-cylinder domestic trucks.
5% were 4-cylinder domestic trucks.
5% were 6-cylinder foreign trucks.
10% were 4-cylinder foreign trucks.
25% were 6-cylinder domestic sedans.
5% were 4-cylinder domestic sedans.
5% were 6-cylinder foreign sedans.
30% were 4-cylinder foreign sedans.

Now let's use Carrier's Bayesian method and tell him that a vehicle bought this year had 6 cylinders and is a truck. What is the probability that it is domestic?

After assigning a 50/50 prior probability (half of sales are domestic), Carrier starts by looking at 6-cylinder vehicles. 80% of 6-cylinder vehicles were domestic, while 20% were foreign. The updated probability becomes an 80% chance it is domestic. Also, 62.5% of trucks were domestic, while 37.5% of trucks were foreign. Carrier thus arrives at an 87% chance that a 6-cylinder truck is domestic.

However, if you look at 6-cylinder truck sales, 75% were domestic and 25% were foreign. Thus the actual probability is 75% that it is domestic. What went wrong?

Carrier's application of Bayes' theorem doesn't take into account whether the terms/variables he uses are independent. When we speak of independence, we mean (for example) that a vehicle in general that is 6-cylinder is just as likely to be domestic as a truck that is 6-cylinder is likely to be domestic... but that isn't true. These aren't independent variables. And treating them as independent variables leads you to a greater confidence level than is actually justified.

I'm not sure how one would go about ensuring that the variables used by Carrier are independent, and I doubt that it can be done. This would be fine, perhaps, if Carrier admitted that his application of probability theory was merely heuristic and that he doesn't view it as anything other than a blunt tool for making guesstimates by stringing together intuitions regarding various bits of evidence. It's not completely clear that this is his stance on it (even though it seems to me the most plausible - and certainly the most defensible - interpretation of Carrier).

Note finally the extremely wide variation between Carrier's "a forteriori" estimates (giving the best benefit of the doubt to historicity) and his own judgments, which speaks in favor of the heuristic interpretation and not the realist interpretation of Carrier's application of probability theory. (I suppose you could also try asking Carrier what he's up to, since he's still around to send an e-mail to, unlike the church fathers!)