Biblical Criticism & History Forum - earlywritings.com

to Ben,

One statement is not dependent on the other in the sense that Paul had to write one first. That is not what independence means here. Independence means that, if Paul was thinking of a real human in one statement, then he was probably thinking of a real human in the other. That is, both statements probably imply the same thing for Paul. When you, Bernard, suggest that these statements are independent when it comes to the probabilities, you are suggesting that Paul may have easily gone back and forth on the matter, being a mythicist in one chapter and an historicist in another. Is that what you really think? I suspect you do not understand the concept of independence of events, rather than that you really, truly think that Paul could have changed his mind in a fashion as random as a coin flip.

I was trying to say Paul was very unlikely to mean his statement about "descendant of David" was "purely metaphorical or spiritual". From that, it is very unlikely his statement about "descendant of Jesse" was meant by Paul to be also "purely metaphorical or spiritual". So the dependence possibility on "descendant of Jesse" is very small and therefore unsignificant.
No, I never thought one statement can be mythicist and the other one historicist.

Are you serious, Bernard? Are you humanly incapable somehow of thinking in terms of hypotheticals? Tell me truly, and stop this stupid posturing. You know full well that I do not follow Carrier here; I have told you before explicitly that I think those passages demonstrate that Paul was thinking of an historical man (if they are not interpolations, of course). Unless you think me as unthinking as your Paul is, who writes his opinions on the historical Jesus randomly, now a mythicist but then an historicist a few minutes later. So please waste no more time on this nonsense. Please grasp the concepts of probability before you start hammering away at me. You are better than this, Bernard.

So if you do not follow Carrier, what is the case for "descendant of David" being "purely metaphorical or spiritual"?
Why would that little possibility prevent "descendant of Jesse" to be mostly independent from "descendant of David"?

Let's say there is a 5% probability that "descendant of David" is "purely metaphorical or spiritual". If it is so (the 5% probability), what would be the probability that "descendant of Jesse" is also "purely metaphorical or spiritual"? I calculate 0.05 * 0.8 = 0.04 = 4%
This 4% can be part of the 20% of IID that I allow for "descendant of Jesse'.

An example: the weather forecast is for sun all day with blue sky. But in the morning somebody in an outdoorsy group say: "but wait, there is a small chance it is going to rain". Then the group would say: OK, better not go hiking today.
Yes we would have full dependence of "hiking today" on that small possibility, but is the reaction of the group realistic? No, of course.
Rather, they will go hiking, showing no dependence on what that somebody said (or maybe a little bit of it, by making sure they have rain gear with them).

Do you understand the concept that all these people have been trying to convey to you now, or do you not? Do you see how "descendant of Jesse" and "descendant of David" are probably not, in terms of how to use the equations, independent statements?

I do not agree.

Cordially, Bernard

Bernard Muller wrote:to Ben,

One statement is not dependent on the other in the sense that Paul had to write one first. That is not what independence means here. Independence means that, if Paul was thinking of a real human in one statement, then he was probably thinking of a real human in the other. That is, both statements probably imply the same thing for Paul. When you, Bernard, suggest that these statements are independent when it comes to the probabilities, you are suggesting that Paul may have easily gone back and forth on the matter, being a mythicist in one chapter and an historicist in another. Is that what you really think? I suspect you do not understand the concept of independence of events, rather than that you really, truly think that Paul could have changed his mind in a fashion as random as a coin flip.

I was trying to say Paul was very unlikely to mean his statement about "descendant of David" was "purely metaphorical or spiritual". From that, it is very unlikely his statement about "descendant of Jesse" was meant by Paul to be also "purely metaphorical or spiritual".

This is exactly what interdependence means. If it is unlikely that "descendant of David" is metaphorical or spiritual, then it is also unlikely that "descendant of Jesse" is metaphorical or spiritual. The statements are, therefore, interdependent: do not ask any more questions about it, because now you know how to use the equation (and which equation to use, if you are not using the general one already).

So the dependence possibility on "descendant of Jesse" is very small and therefore unsignificant.

No! Exactly the other way around. The interdependence is so heavy that it is extremely unlikely for one to be literal while the other is strictly figurative. That is a huge degree of interdependence; the statements are so interdependent that they virtually cannot mean different things!

Here are two truly independent statements:

1. Ben C. Smith is a Caucasian male in his forties.
2. Santa Claus exists and lives at the North Pole.

Imagine that the first one is true (and it is). What is your estimate of the odds of the second one being true? Now, in a leap of imagination that you seem to be finding difficult, imagine that the first one is false (imagine, in other words, that Ben C. Smith is not a Caucasian male in his forties; imagine that I am an elderly Asian woman pretending to be a white male). Does that change your estimate of the second one? I hope not. I hope my sex, race, and age have nothing to do with the odds you give to Santa being a real person.

Now, here are two interdependent statements:

1. Paul thought that Jesus was the literal descendant of David.
2. Paul thought that Jesus was the literal descendant of Jesse.

Imagine that the first one is true. What is your estimate of the odds of the second one being true? Now, in another leap of imagination, imagine that the first one is false (imagine, in other words, that we know for a fact that Paul did not think of him as literally Davidic). NOW what is your estimate of the second one being true? Did it remain the same? I hope not! It should have plummeted. If we know that the first one is false, we ought to be pretty sure that the second one is false, too. That is what dependence means in this context: knowledge of the result (in this case the truth value) of one event changes things for the other event. That is what tells us how to properly use the equations.

No, I never thought one statement can be mythicist and the other one historicist.

Of course not, because you are not an idiot. BUT THAT IS WHAT YOUR MATH IS SAYING. When you claim that the events are independent, and when you use the equation accordingly, you are saying that Paul may have been changing his mind about Jesus' historicity every other chapter, like a flipping coin.

So if you do not follow Carrier, what is the case for "descendant of David" being "purely metaphorical or spiritual"?

Tiny. Or huge. Or nonexistent. It does not matter, because I am using this example only to demonstrate the interdependence. If you were convinced (somehow) that Carrier was right about "seed of David" pointing to a big spiritual sperm bank in the sky, would that not change your estimate of what "seed of Jesse" means?? It would have to, right? If, before somebody convinced you Carrier was right about "seed of David", your estimate about what "seed of Jesse" meant was high, now it should be much lower (now that somebody has convinced you that Carrier is right about the first one).

(Please note the "if" above. IF you were convinced that Carrier is right. I know that you are not, and you know that I am not. But imagine that contingency just so that you can see exactly how interdependent the statements are.)

Why would that little possibility prevent "descendant of Jesse" to be mostly independent from "descendant of David"?

Because the possibility that both statements are mythicist or that both statements are historicist, over and against the possibility that one is mythicist and the other is historicist, is not "little"; it is huge.

An example: the weather forecast is for sun all day with blue sky. But in the morning somebody in an outdoorsy group say: "but wait, there is a small chance it is going to rain". Then the group would say: OK, better not go hiking today.
Yes we would have full dependence of "hiking today" on that small possibility, but is the reaction of the group realistic? No, of course.
Rather, they will go hiking, showing no dependence on what that somebody said.

This is an example of using the term "dependence" in a sentence, but with no connection to what it means to the equations we are dealing with. Here, let me give another example of this term used in a sentence, but with no connection to what it means to the equations we are dealing with:


So what? How is either sentence helping us? Neither has anything to do with the term "dependence" in the sense that we are using it on this thread.

to Ben,

Paul thought that Jesus was the literal descendant of David.
Paul thought that Jesus was the literal descendant of Jesse.

That might be a matter of detail, but I have to say I do not think that exactly. By "descendant of David" and "descendant of Jesse", Paul implied Jesus had been an earthly human. Because all known descendants of David & Jesse and even those who pretend(ed) to be, are/were earthly humans. That's what matter. And that's the normal condition indicated by regular reading, consequently the basis P = 100% but minus possibilities of interpolation, interpretation (against historicity, including Mythicist ones), and dependence (on gospels or other items).

No! Exactly the other way around. The interdependence is so heavy that it is extremely unlikely for one to be literal while the other is strictly figurative. That is a huge degree of interdependence; the statements are so interdependent that they virtually cannot mean different things!

I do not deny possible interdependence, as I already said. But they are already factored in the IID, including the probabilty of IID for "descendant of Jesse" (20%) as I explained previously.

Let's go back to "descendant of David". Let's say there is a probability of 5% the statement was meant by Paul to be "purely metaphorical or spiritual" (change the 5% if you do not find it realistic).
So what would be the probability that "descendant of Jesse" is also "purely metaphorical or spiritual" IF "descendant of David" is "purely metaphorical or spiritual"? Answer: 100%.

But we have to take in account this will happen only with a probability of 5%, because the answer has to be a reduction of 5% * 80% = 4%, so the probability for be true (as indicating Jesus' historicity) for "descendant of Jesse" becomes 76%.
But wait, because the IID is supposed to contain all elements which would be against the historicity probability, this 4% would be also included in the 20%. So no need of calculation. Like I said, this dependence factor is also already factored in the IID probability for "descendant of Jesse'.

Another way to understand it:
When "descendant of David" is "purely metaphorical or spiritual" then the probability of "descendant of Jesse" is also "purely metaphorical or spiritual" is 100%.
But that's only valid for the 5% of probability for David" is "purely metaphorical or spiritual" being true.

The other probability will be 95% for "descendant of David" being NOT "purely metaphorical or spiritual" then the probability of "descendant of Jesse" being "purely metaphorical or spiritual" is 0%.

I say the first condition is 5% out of 100%, the second 95% out of 100%, so the second condition is 19 times more likely to happen than the first one.
Let's calculate:
1*100% = 100%
19*0% = 0%
Average: 100%/20 = 5% for the overall average reduction of probability for the "descendant of Jesse" being true by taking in account the 5% probability that "descendant of David" being "purely metaphorical or spiritual".

Of course this math is approximative because obviously 4% is not 5% but that gives an idea on what to expect from that 5% chance that "descendant of David" being "purely metaphorical or spiritual" and its influence on the probabilty on "descendant of Jesse" being true or NOT.

I do not want to be subjected again to a barrage of rhetorical counter arguments. Tell me what's wrong with my calculations or come up with your own.

Cordially, Bernard

Bernard Muller wrote:I do not deny possible interdependence, as I already said. But they are factored in the IID, including the probabilty of IID for "descendant of Jesse" (20%) as I explained already.

Let's go back to "descendant of David". Let's say there is a probability of 5% the statement was meant by Paul to be "purely metaphorical or spiritual" (change the 5% if you do not find it realistic).
So what would be the probability that "descendant of Jesse" is also "purely metaphorical or spiritual" IF "descendant of David" is "purely metaphorical or spiritual". Answer: 100%.

Well, that feels like some progress to me. That even means that Peter's 1% was too high on the contingency that the first statement failed to demonstrate a Pauline belief in an earthly Jesus.

I do not want to be subjected again to a barrage of rhetorical counter arguments. Tell me what's wrong with my calculations or come up with your own.

Sorry; but no, thanks. I am going to leave the actual numbers in the equations to those who have already been haggling with you over them. My point was about the concept of interdependence, and I am going to leave that discussion where it stands, harboring no illusions that mutual understanding has been achieved, but also satisfied that I did my level best to explain why people are disagreeing with your approach.

to Ben, Peter & others,

Well, that feels like some progress to me. That even means that Peter's 1% was too high on the contingency that the first statement failed to demonstrate a Pauline belief in an earthly Jesus.

Is Peter infallible? I did oppose his views (including these 1%) with arguments (more so that interpolations came after the epistles were written and consequently could not have influenced what has been written earlier by Paul) but he did not comment on them specifically despite my requests.
Peter was talking about possibilities (of interpolations) and their consequences, I am dealing with overall probabilities.
viewtopic.php?f=3&t=2753&start=40#p61418
viewtopic.php?f=3&t=2753&start=110#p61571
viewtopic.php?f=3&t=2753&start=110#p61576

I would welcome Peter & yourself (and others) to comment on my whole last post, which I just edited to make it more precise & correct, or/and also this one.

Sorry; but no, thanks. I am going to leave the actual numbers in the equations to those who have already been haggling with you over them. My point was about the concept of interdependence, and I am going to leave that discussion where it stands, harboring no illusions that mutual understanding has been achieved, but also satisfied that I did my level best to explain why people are disagreeing with your approach.

Yes, that board in mostly about people opposing any historical Jesus or having sympathy for mythicism, so a lot of disagreements can be expected. But did I get comprehensive alternatives to my math and rating of probabilities? I do not think so.
I accepted the principle of dependence. I just do not think it is significant enough to change much about my rating of probabilities except, as I said already, for Tacitus' testimony.

Another example:
Let's say I heard somebody making an argument (aA) showing something (sA) is true. But I think that argument has a 5% probability not to be valid, that is not showing that something (sA) is true.
Then I make an argument trying to prove something else (sB) is true. I think my probability to be right on sB is about 80% (without considering any dependence). But because my argument is fully dependent of argument aA showing sA is true, I have to make that calculation:

P(sB being true considering dependence on sA) = P(sA being true) * P(sB being true without considering dependence on sA) = 95% * 80% = 76%
So there is only a reduction of 4% (from 80%) for sB being true because of dependence on sA.

What's wrong with that?

Cordially, Bernard

Howling in the wind:

It is saying that P(B | A) = P(A) P(B), which is not true in general.

Fortunately, this is a solved problem.

P(B | A) = P(A and B) / P(A)

This is purely a statement about math. If you were using math to make a point in politics or about culture, instead of religion, we'd be accused of political motives or cultural differences. But that is just 'rhetoric.' The problem is ignorance of the math. The question remaining is whether it is vincible ignorance or invincible ignorance, in the Catholic turn of phrase.

I wouldn't mind being surprised.

(I may not stay for an argument... But if you have specific questions to be able to understand the math better... That might be the best approach, instead of having me irritate you by pointing out that almost all your statements about the math are wrong.)

Bernard Muller wrote:Is Peter infallible?

Of course Peter is infallible. Popes always are.

Bernard Muller wrote:iid or IID stands for probability of Interpolation, Interpretation (against historicity) or Dependence (on gospels).

You also have to consider the relationship of each statement/premise to each other.

Ben C. Smith wrote: This is exactly what interdependence means. If it is unlikely that "descendant of David" is metaphorical or spiritual, then it is also unlikely that "descendant of Jesse" is metaphorical or spiritual. The statements are, therefore, interdependent: do not ask any more questions about it, because now you know how to use the equation (and which equation to use, if you are not using the general one already).

So the dependence possibility on "descendant of Jesse" is very small and therefore insignificant.

No! Exactly the other way around. The interdependence is so heavy that it is extremely unlikely for one to be literal, while the other is strictly figurative. That is a huge degree of interdependence; the statements are so interdependent that they virtually cannot mean different things!

to Peter,

Peter Kirby wrote:Howling in the wind:

It is saying that P(B | A) = P(A) P(B), which is not true in general.

Fortunately, this is a solved problem.

P(B | A) = P(A and B) / P(A)

This is purely a statement about math. If you were using math to make a point in politics or about culture, instead of religion, we'd be accused of political motives or cultural differences. But that is just 'rhetoric.' The problem is ignorance of the math. The question remaining is whether it is vincible ignorance or invincible ignorance, in the Catholic turn of phrase.

I wouldn't mind being surprised.

(I may not stay for an argument... But if you have specific questions to be able to understand the math better... That might be the best approach, instead of having me irritate you by pointing out that almost all your statements about the math are wrong.)

That, I understand (from http://davidmlane.com/hyperstat/A129515.html):

Probability of A and B (2 of 2)
previous
Next section: Probability of A or B

If A and B are Not Independent
If A and B are not independent, then the probability of A and B is:

p(A and B) = p(A) x p(B|A)

where p(B|A) is the conditional probability of B given A.

If someone draws a card at random from a deck and then, without replacing the first card, draws a second card, what is the probability that both cards will be aces? Event A is that the first card is an ace. Since 4 of the 52 cards are aces, p(A) = 4/52 = 1/13. Given that the first card is an ace, what is the probability that the second card will be an ace as well? Of the 51 remaining cards, 3 are aces. Therefore, p(B|A) = 3/51 = 1/17 and the probability of A and B is:

1/13 x 1/17 = 1/221

But that does not look to be applicable for the statements about Pauline epistles implying the existence of an earthly human Jesus.

If you think the conditional equation solves the problem, please provide an example how it would work for "descendant of David" (A) and descendant of Jesse" (B) in Romans, taking in account that "descendant of David" might have been interpolated?
I propose 80% probability for both A & B (without dependence on A). Change that if you please. Show me what happens mathematically when B is dependent on A.
I know this result already: if A is an interpolation, then B is (likely) also one.

Note: I said "likely", because the interpolator might have added "descendant of David", not for implying the historicity of Jesus, but to "upgrade" Paul's Christology after gLuke & gMatthew were known. In that case B would not be dependent on A, that is Paul could have written B with A being interpolated much later.

But what happens for B if the probability of A being an interpolation (affecting B) is rated at 10%?

How you manage that mathematically (that is with numerical values) would be worth thousand of words. Certainly, that would cut down on "howling in the wind".

I do understand your viewpoint: if one of the Pauline statement implying Jesus' historicity is an interpolation, then likely all other statements to the same conclusion are also interpolations.
The problem is most of these statements do not look to be interpolations. And it is rather difficult to make a good case for one of this statement to be interpolation.

Cordially, Bernard

Bernard Muller wrote:to Peter,

Peter Kirby wrote:Howling in the wind:

It is saying that P(B | A) = P(A) P(B), which is not true in general.

Fortunately, this is a solved problem.

P(B | A) = P(A and B) / P(A)

This is purely a statement about math. If you were using math to make a point in politics or about culture, instead of religion, we'd be accused of political motives or cultural differences. But that is just 'rhetoric.' The problem is ignorance of the math. The question remaining is whether it is vincible ignorance or invincible ignorance, in the Catholic turn of phrase.

I wouldn't mind being surprised.

(I may not stay for an argument... But if you have specific questions to be able to understand the math better... That might be the best approach, instead of having me irritate you by pointing out that almost all your statements about the math are wrong.)

That, I understand (from http://davidmlane.com/hyperstat/A129515.html):

Probability of A and B (2 of 2)
previous
Next section: Probability of A or B

If A and B are Not Independent
If A and B are not independent, then the probability of A and B is:

p(A and B) = p(A) x p(B|A)

where p(B|A) is the conditional probability of B given A.

If someone draws a card at random from a deck and then, without replacing the first card, draws a second card, what is the probability that both cards will be aces? Event A is that the first card is an ace. Since 4 of the 52 cards are aces, p(A) = 4/52 = 1/13. Given that the first card is an ace, what is the probability that the second card will be an ace as well? Of the 51 remaining cards, 3 are aces. Therefore, p(B|A) = 3/51 = 1/17 and the probability of A and B is:

1/13 x 1/17 = 1/221

But that does not look to be applicable for the statements about Pauline epistles implying the existence of an earthly human Jesus.

If you think the conditional equation solves the problem, please provide an example how it would work for "descendant of David" (A) and descendant of Jesse" (B) in Romans, taking in account that "descendant of David" might have been interpolated?
I propose 80% probability for both A & B (without dependence on A). Change that if you please. Show me what happens mathematically when B is dependent on A.
I know this result already: if A is an interpolation, then B is (likely) also one.

Note: I said "likely", because the interpolator might have added "descendant of David", not for implying the historicity of Jesus, but to "upgrade" Paul's Christology after gLuke & gMatthew were known. In that case B would not be dependent on A, that is Paul could have written B with A being interpolated much later.

But what happens for B if the probability of A being an interpolation (affecting B) is rated at 10%?

How you manage that mathematically (that is with numerical values) would be worth thousand of words. Certainly, that would cut down on "howling in the wind".

I do understand your viewpoint: if one of the Pauline statement implying Jesus' historicity is an interpolation, then likely all other statements to the same conclusion are also interpolations.
The problem is most of these statements do not look to be interpolations. And it is rather difficult to make a good case for one of this statement to be interpolation.

Cordially, Bernard

I think you're asking good questions. Thanks! I will come back to this in a bit.