Review of Carrier's OHJ, Part 1 of 12: Sections 1 thru 3, What I liked and didn't like

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Leucius Charinus
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Re: Review of Carrier's OHJ, Part 1 of 12: Sections 1 thru 3, What I liked and didn't like

Post by Leucius Charinus »

GakuseiDon wrote: Sat Mar 18, 2023 2:27 amI'll be interested in people's feedback of my draft. If there is anything unclear or wrong, please don't hesitate to let me know.

Thank you!
I'd like to ask you if any part of your review deals with the mechanics of Bayes Theorem as applied by Carrier. The reason I ask is because I believe (perhaps erroneously) that Carrier uses a cut-off date for his evidence that is directly used to argue his case, and AFAIU this cut-off date is c.150 CE. I notice your Part 2 introduces his treatment of Epiphanius who is a later 4th century "master heresiologist" who is obviously way past the 150 CE cut-off. I do understand that Bayes Theorem uses explicit terminology (see below) and that somehow this 4th century evidence is included even though this 150 CE cut-off date is also used.

I am happy to wait until a further more appropriate Part of your review is introduced in order to answer my question. The answer may relate to b and e (below) but atm I am not sure.

Thanks G'Don

7. Explanation of the Terms in Bayes’ Theorem

P = Probability (epistemic probability = the probability that something stated is true)

h = hypothesis being tested

~h = all other hypotheses that could explain the same evidence (if h is false)

e = all the evidence directly relevant to the truth of h (e includes both what is observed
and what is not observed)

b = total background knowledge (all available personal and human knowledge about
anything and everything, from physics to history)

P(h|e.b) = the probability that a hypothesis (h) is true given all the available evidence (e)
and all our background knowledge (b)

P(h|b) = the prior probability that h is true = the probability that our hypothesis would
be true given only our background knowledge (i.e. if we knew nothing about e)

P(e|h.b) = the posterior probability of the evidence (given h and b) = the probability
that all the evidence we have would exist (or something comparable to it would
exist) if the hypothesis (and background knowledge) is true. = [consequent probability]

P(~h|b) = 1 – P(h|b) = the prior probability that h is false = the sum of the prior
probabilities of all alternative explanations of the same evidence (e.g. if there is
only one viable alternative, this means the prior probability of all other theories is
vanishingly small, i.e. substantially less than 1%, so that P(~h|b) is the prior
probability of the one viable competing hypothesis; if there are many viable
competing hypotheses, they can be subsumed under one group category (~h), or
treated independently by expanding the equation, e.g. for three competing
hypotheses [ P(h|b) x P(e|h.b) ] + [ P(~h|b) x P(e|~h.b) ] becomes [ P(h1|b) x
P(e|h1.b) ] + [ P(h2|b) x P(e|h2.b) ] + [ P(h3|b) x P(e|h3.b) ])

P(e|~h.b) = the posterior probability of the evidence if b is true but h is false = the
probability that all the evidence we have would exist (or something comparable to
it would exist) if the hypothesis we are testing is false, but all our background
knowledge is still true. This also equals the posterior probability of the evidence if
some hypothesis other than h is true—and if there is more than one viable
contender, you can include each competing hypothesis independently (per above)
or subsume them all under one group category (~h). = [consequent probability]

EXTRACTED FROM: Richard C. Carrier, Ph.D.
“Bayes’ Theorem for Beginners: Formal Logic and Its
Relevance to Historical Method — Adjunct Materials
and Tutorial”
The Jesus Project Inaugural Conference
“Sources of the Jesus Tradition: An Inquiry”
5 December 2008 (Amherst, NY)

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Re: Review of Carrier's OHJ, Part 1 of 12: Sections 1 thru 3, What I liked and didn't like

Post by GakuseiDon »

Leucius Charinus wrote: Sun Mar 19, 2023 5:52 pmI'd like to ask you if any part of your review deals with the mechanics of Bayes Theorem as applied by Carrier.
Yes, Section 5 will be about how Carrier is using Bayes Theorem to compare two theories that aren't their direct negation of the other.

The classic Bayes Theorem example is "Suzie is getting married on Saturday. Will it rain?" The answer is "Yes, it will rain" or "No, it won't rain." These make up 100% of the probability space. But if it becomes "Suzie is getting married on Saturday. Will it rain or will it be sunny?" Then it becomes trickier, since "cloudy day" -- so neither rain nor sun -- may take up most of the probability space.

Carrier's approach runs into the same issue. "MinM" and "MinH" aren't the negation of each other. Let's say there is a third option on the board, and --taking this example completely at random! -- all literature up to the Fourth Century is forged. Then there needs to be an evaluation of that option before we can get to MinM and MinH.

Carrier does address the problem of a third option, so Section 5 is about how Carrier addresses it. Spoiler alert: he addresses it badly!
Leucius Charinus wrote: Sun Mar 19, 2023 5:52 pmBut " The reason I ask is because I believe (perhaps erroneously) that Carrier uses a cut-off date for his evidence that is directly used to argue his case, and AFAIU this cut-off date is c.150 CE. I notice your Part 2 introduces his treatment of Epiphanius who is a later 4th century "master heresiologist" who is obviously way past the 150 CE cut-off. I do understand that Bayes Theorem uses explicit terminology (see below) and that somehow this 4th century evidence is included even though this 150 CE cut-off date is also used.
Carrier also looks at the Talmud, which is dated from the Third to Fifth Centuries. From memory, the reason he restricts the texts to about 150 CE is everything starts getting dominated by the Gospels and proto-orthodoxy from mid-Second Century so aren't useful for questions of historicity. I don't see a problem with his reasoning there. Both Epiphanius and the Talmud are later documents, true, but they are referencing apparent early beliefs. In those cases, it makes sense to allow later texts.
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Leucius Charinus
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Re: Review of Carrier's OHJ, Part 1 of 12: Sections 1 thru 3, What I liked and didn't like

Post by Leucius Charinus »

GakuseiDon wrote: Sun Mar 19, 2023 7:34 pm
Leucius Charinus wrote: Sun Mar 19, 2023 5:52 pmI'd like to ask you if any part of your review deals with the mechanics of Bayes Theorem as applied by Carrier.
Yes, Section 5 will be about how Carrier is using Bayes Theorem to compare two theories that aren't their direct negation of the other.

The classic Bayes Theorem example is "Suzie is getting married on Saturday. Will it rain?" The answer is "Yes, it will rain" or "No, it won't rain." These make up 100% of the probability space. But if it becomes "Suzie is getting married on Saturday. Will it rain or will it be sunny?" Then it becomes trickier, since "cloudy day" -- so neither rain nor sun -- may take up most of the probability space.

Carrier's approach runs into the same issue. "MinM" and "MinH" aren't the negation of each other.
That's an interesting point.
Let's say there is a third option on the board, and --taking this example completely at random! -- all literature up to the Fourth Century is forged. Then there needs to be an evaluation of that option before we can get to MinM and MinH.
Nice work. The example could be water down to say --- some literature up to the Fourth Century is forged. There are plenty of examples. (I list a few below)
Carrier does address the problem of a third option, so Section 5 is about how Carrier addresses it. Spoiler alert: he addresses it badly!
Well I will await your Section 5.
Leucius Charinus wrote: Sun Mar 19, 2023 5:52 pmBut " The reason I ask is because I believe (perhaps erroneously) that Carrier uses a cut-off date for his evidence that is directly used to argue his case, and AFAIU this cut-off date is c.150 CE. I notice your Part 2 introduces his treatment of Epiphanius who is a later 4th century "master heresiologist" who is obviously way past the 150 CE cut-off. I do understand that Bayes Theorem uses explicit terminology (see below) and that somehow this 4th century evidence is included even though this 150 CE cut-off date is also used.
Carrier also looks at the Talmud, which is dated from the Third to Fifth Centuries. From memory, the reason he restricts the texts to about 150 CE is everything starts getting dominated by the Gospels and proto-orthodoxy from mid-Second Century so aren't useful for questions of historicity. I don't see a problem with his reasoning there.
Well the problem I see is that this is an assumption that Carrier is making. It may be a correct assumption but it may be the opposite. We don't know.

I would make the point that what we do know (if we are being completely transparent in our logical processes -- explicitly stating our assumptions) is that we really have zero physical evidence prior to the 3rd century. Does Carrier make any distinction between the hypothetical evidence and the physical evidence. By hypothetical evidence I refer to that which is inferred from the NT and from the supposedly post 150 CE "Fathers" but for which we don't have physical evidence.

The first one of the core principles for determining reliability is this:

Human sources may be relics such as a fingerprint;
or narratives such as a statement or a letter.
Relics are more credible sources than narratives.

https://en.wikipedia.org/wiki/Historical_method

Does Carrier mention this principle of the historical method? I have not observed that he does. Neither does Doherty AFAIK.
Both Epiphanius and the Talmud are later documents, true, but they are referencing apparent early beliefs. In those cases, it makes sense to allow later texts.
Other later documents include:

* the letter exchange between Paul and Seneca
* the Historia Augusta
* the "church history" of Eusebius
* the festal letter of Athanasius which lists the canonical NT books
* the Arian controversy
* the entire collection of the NT Apocryphal literature (excluding the Ascension of Isaiah)

In summary although I think Bayes Theorem may be useful, Carrier is applying it in a specific manner by using various assumptions that may not necessarily be true. I am still interested to determine whether this c.150 CE cut-off date is a major problem. It has been essentially inferred on the basis of what is written post-150 CE by Justin, Irenaeus and others. That is, if we moved the cut-off date to c.367 CE (Athanasius' Festal Letter) this would introduce a great mass of other evidence.

Anyway I will await Section 5.
Thanks G'Don.
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Re: Review of Carrier's OHJ, Part 1 of 12: Sections 1 thru 3, What I liked and didn't like

Post by Paul the Uncertain »

Leucius Charinus wrote: Sun Mar 19, 2023 5:52 pm
7. Explanation of the Terms in Bayes’ Theorem

P = Probability (epistemic probability = the probability that something stated is true)

h = hypothesis being tested

~h = all other hypotheses that could explain the same evidence (if h is false)

e = all the evidence directly relevant to the truth of h (e includes both what is observed
and what is not observed)

...

EXTRACTED FROM: Richard C. Carrier, Ph.D.
“Bayes’ Theorem for Beginners: Formal Logic and Its
Relevance to Historical Method — Adjunct Materials
and Tutorial”
The Jesus Project Inaugural Conference
“Sources of the Jesus Tradition: An Inquiry”
5 December 2008 (Amherst, NY)

It is worth noting early on that this is not what Carrier does in OHJ. He first performs a projection of the entire set of possible hypotheses down to a working set of just two hypotheses, h1 and h2 if you will rather than h and ~h. G'Don has said that he will be considering this aspect of the problem in a later thread. I'd like to say a few things about it now, since it has come up.

Reducing the working hypothesis is perfectly fine, but you have to keep track of what you're doing. In "match play" (in this case comparing just 2 hypotheses when more than 2 hypotheses are seriously possible), you are performing "eliminative induction" similar to the style of Karl Popper (which is amusing since he loathed Bayesian inference, but like so many critics of Bayes was doing a form of it anyway).

In brief compass: the Loser in match play (the one with lower final probability) cannot be the winner in the complete hypothesis set - hence we can eliminate it as the most likely explanation. The Winner in the twosome, however, need not be the winner in the complete set, nor do we get any hard information about the prospects for that from the margin of victory in match play.

Example: h1 and h2 are selected from a larger hypothesis set H. With background information b and after observing evidence e, we calculate that P(h1|e,b) / P(h2|e, b) = 12,000. We may conclude from this that h2 isn't the highest probability hypothesis in the larger hypothesis set H. We may also conclude that P(h1|e.b) and P(h2|e,b) are upper bounds on their respective probabilities among the hypotheses of H. We may not infer any positive lower bound on those probabilities among H, nor may we infer that h1 is the most probable hypothesis in H.

Also "e" need not be all the bearing evidence. Rather, e can be any portion of the evidence we wish to discuss at a given time. So, for example, we may wish, as Carrier does in OHJ, to consider the impact of each individual piece of evidence one by one, and from time to time consider the cumulative impact of all the evidence discussed so far.

There is nothing wrong with this, part of the usefulness of Bayesian analysis is that it allows us to isolate portions of the evidence, or even to analyze hypothetical evidence (e.g. what if we found such-and-such a document, what would we believe then?). But as with projections of the hypothesis set, we do need to keep track of what we're doing.
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Re: Review of Carrier's OHJ, Part 1 of 12: Sections 1 thru 3, What I liked and didn't like

Post by Leucius Charinus »

Paul the Uncertain wrote: Mon Mar 20, 2023 12:26 am
Leucius Charinus wrote: Sun Mar 19, 2023 5:52 pm
7. Explanation of the Terms in Bayes’ Theorem

P = Probability (epistemic probability = the probability that something stated is true)

h = hypothesis being tested

~h = all other hypotheses that could explain the same evidence (if h is false)

e = all the evidence directly relevant to the truth of h (e includes both what is observed
and what is not observed)

...

EXTRACTED FROM: Richard C. Carrier, Ph.D.
“Bayes’ Theorem for Beginners: Formal Logic and Its
Relevance to Historical Method — Adjunct Materials
and Tutorial”
The Jesus Project Inaugural Conference
“Sources of the Jesus Tradition: An Inquiry”
5 December 2008 (Amherst, NY)

It is worth noting early on that this is not what Carrier does in OHJ. He first performs a projection of the entire set of possible hypotheses down to a working set of just two hypotheses, h1 and h2 if you will rather than h and ~h. G'Don has said that he will be considering this aspect of the problem in a later thread. I'd like to say a few things about it now, since it has come up.

Reducing the working hypothesis is perfectly fine, but you have to keep track of what you're doing. In "match play" (in this case comparing just 2 hypotheses when more than 2 hypotheses are seriously possible), you are performing "eliminative induction" similar to the style of Karl Popper (which is amusing since he loathed Bayesian inference, but like so many critics of Bayes was doing a form of it anyway).

In brief compass: the Loser in match play (the one with lower final probability) cannot be the winner in the complete hypothesis set - hence we can eliminate it as the most likely explanation. The Winner in the twosome, however, need not be the winner in the complete set, nor do we get any hard information about the prospects for that from the margin of victory in match play.

Example: h1 and h2 are selected from a larger hypothesis set H. With background information b and after observing evidence e, we calculate that P(h1|e,b) / P(h2|e, b) = 12,000. We may conclude from this that h2 isn't the highest probability hypothesis in the larger hypothesis set H. We may also conclude that P(h1|e.b) and P(h2|e,b) are upper bounds on their respective probabilities among the hypotheses of H. We may not infer any positive lower bound on those probabilities among H, nor may we infer that h1 is the most probable hypothesis in H.

Also "e" need not be all the bearing evidence. Rather, e can be any portion of the evidence we wish to discuss at a given time. So, for example, we may wish, as Carrier does in OHJ, to consider the impact of each individual piece of evidence one by one, and from time to time, consider the cumulative impact of all the evidence discussed so far.

There is nothing wrong with this, part of the usefulness of Bayesian analysis is that it allows us to isolate portions of the evidence, or even to analyze hypothetical evidence (e.g. what if we found such-and-such a document, what would we believe then?). But as with projections of the hypothesis set, we do need to keep track of what we're doing.
Thanks for these comments Paul the Uncertain.

Can you explain where the Carrier 150 CE cut-off date is defined? IDK. I assume it is a restriction on e - the evidence - by chronology. But I could be wrong.

Epiphanius, the Talmud and 4th century events are introduced as a different type of "evidence"? Is this something like what you describe as "isolate portions of the evidence"? Or is this b - background evidence?

What is Carrier doing?

Again, IDK but I can only assume that he firmly believes that Christian origins certainly appeared on planet Earth before c.150 CE. Does he make any statements about the degree of this certainty in OHJ?

Thanks for any ideas and/or assistance.

ETA: It occurs to me that Carrier also assumes Paul is an historical figure and composed at least some of the epistles attributed to him. Maybe that explains Carrier's 150 CE? Or is this the hypothetical 150 CE "NT Canonical Collection"?
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Re: Review of Carrier's OHJ, Part 1 of 12: Sections 1 thru 3, What I liked and didn't like

Post by GakuseiDon »

Leucius Charinus wrote: Mon Mar 20, 2023 1:05 amCan you explain where the Carrier 150 CE cut-off date is defined? IDK. I assume it is a restriction on e - the evidence - by chronology. But I could be wrong.
I found it. From 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), as after that time we can't reasonably expect there to have been any surviving witnesses to the original decade of the cult's creation (in the 30s CE), due to the limits of life expectancy (Element 22); and also because after that time the quantity of bogus literature about Jesus and early Christianity exploded to an immense scale, making the task of sorting truth from fiction effectively impossible (Element 44).

Carrier lists two criteria for what counts as relevant primary evidence. From page 254:

For something to count as 'relevant primary evidence', it must meet two criteria: it must be plausibly capable of being causally connected with the facts (persons, properties or events) whose existence is in question, and it must be relevantly independent of all other primary evidence

He spends quite a few pages describing examples of those two criteria.
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Re: Review of Carrier's OHJ, Part 1 of 12: Sections 1 thru 3, What I liked and didn't like

Post by Leucius Charinus »

GakuseiDon wrote: Mon Mar 20, 2023 1:28 am
Leucius Charinus wrote: Mon Mar 20, 2023 1:05 amCan you explain where the Carrier 150 CE cut-off date is defined? IDK. I assume it is a restriction on e - the evidence - by chronology. But I could be wrong.
I found it. From 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), as after that time we can't reasonably expect there to have been any surviving witnesses to the original decade of the cult's creation (in the 30s CE), due to the limits of life expectancy (Element 22); and also because after that time the quantity of bogus literature about Jesus and early Christianity exploded to an immense scale, making the task of sorting truth from fiction effectively impossible (Element 44).


Thanks G'Don. As I had suspected. Carrier is basically assuming an early (1st century) Christian origins theory. He sets up modelling for two theoretical kinds - one historical the other mythical.
Carrier lists two criteria for what counts as relevant primary evidence. From page 254:

For something to count as 'relevant primary evidence', it must meet two criteria: it must be plausibly capable of being causally connected with the facts (persons, properties or events) whose existence is in question, and it must be relevantly independent of all other primary evidence

He spends quite a few pages describing examples of those two criteria.
Thanks once again for clarifying this !! Good luck with your review(s).
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