Probability about Jesus (Christ) existence on earth

[timhendrix]

Hi Bernard,

I didn't want to but into this debate but perhaps this is an okay point.
I am not sure I fully understand your argument (I got a bit lost in the P's over the past pages) so perhaps I can illustrate the principle that Peter is mentioning.

Suppose you consider a sequence of four horseraces (r1, r2, r3, r4) which will take place over the next year with 5 different horses (Horse A, B, C, D, E). Suppose you don't know anything about the horses, the chance that horse A wins the first race is then 1/5, that horse A wins the second race 1/5 and so on for all the races and all the horses (you don't know anything so what could the probability otherwise be?).
We write this formally as P(A wins r3) = 1/5 to say that there is a 20% chance horse A wins race 3 and therefore also P(B wins r4) = 20% to say there is a 20% chance that horse B wins race 4. I hope you are with me so far.

Then we can ask what the chance is that horse A wins ALL four races. Well, one way to do this is to say:

P(A wins r1 & A wins r2 & A wins r3 & A wins r4) = P(A wins r1)P(A wins r2)P(A wins r3)P(A wins r4) = 1/5^ 4 = 0.16%.

What Peter and I are saying is that this is false. In reality, one of the horses are all things considered better than the other, and if we assume that the best horse usually wins then the chance horse A wins all races is really the chance the best horse wins all races and A is that horse. There is a 20% chance A is the best horse (all horses have an equal chance of being the best insofar as we know) and a chance somewhere less than 100% the best horse win all races. So in reality:

P(A wins r1 & A wins r2 & A wins r3 & A wins r4) ~~ 20% (less than 20% as the best horse might not win all races)

If you doubt this conclusion on an intuitive level I suggest the following: Instead of considering four races, consider four competitions about who has the heaviest horse. Obviously, if A is heaviest in the first competition, it will win all four competitions and so, in this case, there is trivially a 20% chance that horse A wins all four competitions.

How do we account for this mathematically? This is where conditional probabilities come in. What Peter is saying is that we should use conditional probabilities all times. For instance:

P(A wins r1 & A wins r2) = P(A wins r2 | A wins r1) P(A wins r1)

and even though P(A wins r1) = 20%, you would obviously conclude that P(A wins r2 | A wins r1) > 20% (if A just won a race, that would increase your confidence it would win the next race).

Let us get to the case of interpolations. The example relates to interpolations because (as I understand Peter) the interpolations are like a horse winning a race: If you know interpolation r1 happened, that increase your confidence that r2 happened.
Can we prove that mathematically? No! If it is actually true that

P(Interpolation 2 took place | Interpolation 1 took place) > P(Interpolation 2 took place)

is something we got to determine based on our knowledge about interpolations, however, it would seem like a reasonable assumption. This is the assumption Peters illustrates in his pie charts.

I might be misunderstanding you, however in that case we could perhaps first determine if you agree with me in the horse-race example, and then we can discuss if that example is really appropriate. Please keep in mind I am not entirely sure what your original argument is.

[Bernard Muller]

to Peter,

(Or maybe all the mathematicians in the world are confused, and you've got it figured out.) In any case, there doesn't seem to be any trust in the fact that I am representing the subject faithfully and accurately.

You are the one who put me straight initially on the equation about resulting probability:

Suppose we have six independent events. Independence means that we can simplify many calculations... suppose that each of these events has a certain probability p = 0.2 to occur. Let "X" be the number of such events that do actually occur. This is a binomial distribution, and the probability that a certain number of them occur is given by:

Binomial distribution
Image

Where n = 6, p = 0.2, k = the number that actually occur (that we want the probability of), and "(n k)" = "n choose k" = n! / (k! (n-k)!).

Checking the probability that X >= 1 is especially simple. We just find the probability that X = 0 and compute the complement, i.e., 1 - Pr(X=0).

Pr(X=0) = ("6 choose 0") * (0.2)^0 * (0.8)^6 = (0.8)^6 = 0.262144.

1 - Pr(X=0) = 0.737856

So if you have six independent events with probability 0.2 each, the probability that at least one occur is 0.737856.

That got confirmed later by some amateur mathematicians, answering my question:

If I have 5 independent arguments which are deemed for each at 20% probability to prove the same point, what would be the resulting probability of the 5 arguments together to prove my point.

Everything was fine up to the time I applied that equation to the issue of the existence of Jesus according to pre-gospels and non-Christian early texts.
Then everything went havoc because of the possibility of interpolations among the statements implying the existence of Jesus.
Suddenly, the equation which you deliver to me became WRONG.

You did not supply any evidence that any of these statements were interpolations by just analyzing them separately. In my view, very few are candidate for interpolation.

Also, considering these alleged interpolations had to be made logically after Paul wrote his epistles, you are assuming there were no statements about historicity written by Paul, because if they were, that would kill your argumentation: only a few (like only three at 80% probability) authentic ones would raise the overall probability to close to 100%.
And when the alleged interpolations would be incorporated later, that would not change a thing. They would not interfere with what Paul wrote earlier.
But what is your evidence that Paul wrote nothing or very little about statements implying historicity and all the other ones are later interpolations?
If you are so sure about your application of conditional probability equation in that case, why don't you go to a forum about math (just like I did) and explain the problem and how you resolve it?

Cordially, Bernard

[Peter Kirby]

to Peter,

(Or maybe all the mathematicians in the world are confused, and you've got it figured out.) In any case, there doesn't seem to be any trust in the fact that I am representing the subject faithfully and accurately.

You are the one who put me straight initially on the equation about resulting probability:

Suppose we have six independent events. Independence means that we can simplify many calculations... suppose that each of these events has a certain probability p = 0.2 to occur. Let "X" be the number of such events that do actually occur. This is a binomial distribution, and the probability that a certain number of them occur is given by:

Binomial distribution
Image

Where n = 6, p = 0.2, k = the number that actually occur (that we want the probability of), and "(n k)" = "n choose k" = n! / (k! (n-k)!).

Checking the probability that X >= 1 is especially simple. We just find the probability that X = 0 and compute the complement, i.e., 1 - Pr(X=0).

Pr(X=0) = ("6 choose 0") * (0.2)^0 * (0.8)^6 = (0.8)^6 = 0.262144.

1 - Pr(X=0) = 0.737856

So if you have six independent events with probability 0.2 each, the probability that at least one occur is 0.737856.

That got confirmed later by some amateur mathematicians, answering my question:

If I have 5 independent arguments which are deemed for each at 20% probability to prove the same point, what would be the resulting probability of the 5 arguments together to prove my point.

Everything was fine up to the time I applied that equation to the issue of the existence of Jesus according to pre-gospels and non-Christian early texts.
Then everything went havoc because of the possibility of interpolations among the statements implying the existence of Jesus.
Suddenly, the equation which you deliver to me became WRONG.

It's interesting that you see things this way, but it also shows (again) that you didn't understand what I've said in this thread.

The conditional statement is true: IF these assumptions hold (including the assumption of independence), THEN...

My stance on the math has never changed. Unfortunately, your understanding has not improved either, in the course of this thread.

(I'd like to leave the thread alone, but the above speaks to character, and I don't think I should have to leave statements impeaching my character alone.)

This was your original comment:

to Ben,
I made some revisions on why I think 1 Th 1:10 in an interpolation. However it is not why I want to talk about on this post, but about the math I used in order to call an interpolation from several independent arguments (6 in the case of 1 Th 1:10).

I do not expect any one of my arguments to be a "killer" demonstrating I am be right without any doubt. Far from that. I certainly not list my arguments for that reason.
However if I list 6 independent arguments, and each one of them can be weighted as having 20% chance to show it is an interpolation, then my 6 arguments collectively would put me over 100 %.
So what about the other 80% for each argument? Would that mean it shows there is 80% chance it is NOT an interpolation? NO, it shows there is 80% chance it does not show it is an interpolation.
Of course, that can be demonstrated by throwing dices. Let's use 6 dices. Throw them many times together then let's look if any of those shows a 1 on top. Well, for each dice, there is 16.7 % chance the result will be 1. But for the 6 dices together, the average result will be close to 16.7 X 6 = 100%.
I said close, that is not quite 100 %, because there will be times none of the 6 dices will show a 1 on top.

In both cases, they regarded conclusions that I would not necessarily agree with. In both threads, I commented at first in order to be helpful and in order to clarify the math, because you really did (and do) need some help with this.

I've repeatedly emphasized that I didn't care to argue over the particular numbers, as long as the general concepts were conveyed. It's interesting to know that you think I'm both dishonest about that and dishonest about the math. Not particularly nice, but interesting.

[MrMacSon]

Let's say we give 50% probability that the following shows that Jesus called Christ existed as a man on earth:

1) Descendant of Abraham (Gal 3:16)
2) Descendant of Israelites (Ro 9:4-5)
3) Descendant of Jesse (Ro 15:12)
4) Descendant of David (Ro 1:3)
5) Having brothers by blood, one of them being James (1 Cor 9:5, Gal 1:19)

6) becoming from a woman (Gal 4:4)

7) From the tribe of Judah (Heb 7:14)

8) Tacitus' Annals 15.44
9) Josephus' Antiquities XX, IX, 1

As Peter has alluded, a lot of these points are not independent - points 1-5, & 7.

Hardly any can be considered facts.

Surely (1) 'Descendant of Abraham (Gal 3:16)', (2) 'Descendant of Israelites (Ro 9:4-5)', (3) 'Descendant of Jesse (Ro 15:12)', (4) 'Descendant of David (Ro 1:3)', 5) 'Having brothers by blood, one of them being James (1 Cor 9:5, Gal 1:19)', and (7) 'From the tribe of Judah (Heb 7:14') are inter-related concepts and unrelated to the others -ie. unrelated to (5), (6), (8), and (9).

Surely (5) 'Having brothers by blood, one of them being James (1 Cor 9:5, Gal 1:19)' and (6) 'becoming from a woman (Gal 4:4)' (and perhaps (9) Josephus' Antiquities XX, IX), could be inter-related to each other, but the notion those premises are inter-related is fraught b/c there is no clear relationship between the various James (plural) of the Bible (in the Synoptics) and Mary, the mother of Jesus or Joseph (the supposed father of Jesus)!!! Moreover, some of the Synoptic commentary is not only unclear about the genealogy of the other James, but actually gives other parents!!

You do realise the gospels give various accounts of various mothers and various fathers to various James? None fully line up to be Jesus' sibling?

Are you confusing James, the son of Mary & Joseph with James, the brother of John, whose father is Zebedee? There are also other James in the gospels but that does not prevent one of these James to be the brother of Jesus, as in gMark 6:3.

Mark 6:3
"Is not this the carpenter, the son of Mary and brother of James and Joses and Judas and Simon, and are not his sisters here with us?”

is similar to Matt 13:55 -
Is not this the carpenter’s son? Is not his mother called Mary? And are not his brothers James and Joseph and Simon and Judas?

Yet Mark 15:40 has
"Some women were watching from a distance. Among them were Mary Magdalene, Mary the mother of James the younger and of Joseph, and Salome."

and Mark 16:1 has
"When the Sabbath was over, Mary Magdalene, Mary the mother of James, and Salome bought spices so that they might go to anoint Jesus' body."

Matthew 27:56 has
Among them were Mary Magdalene, Mary the mother of James and Joseph, and the mother of Zebedee's sons.

Yet

Roman Catholic interpretation generally holds that James, the younger is the same James mentioned in Mark 16:1 and Matthew 27:56 and is to be identified with James, the son of Alphaeus and James, the brother of Jesus. http://www.newadvent.org/cathen/08280a.htm

The pseudepigraphical Second Apocalypse of James names James's father Theudas rather than Joseph

Eusebius of Caesarea reported the tradition that James the Just was the son of Joseph's brother Clopas and therefore was of the "brothers" of Jesus described in the New Testament (which he interprets as "cousin").

This is echoed by Jerome (c. 342 – 419) in De Viris Illustribus ('On Illustrious Men') – James is said to be the son of another Mary, wife of Clopas and the "sister" of Mary, the mother of Jesus – in the following manner:

• James, who is called the brother of the Lord, surnamed the Just, the son of Joseph by another wife, as some think, but, as appears to me, the son of Mary, sister of the mother of our Lord of whom John makes mention in his book.

(8) Tacitus' Annals 15.44 is un-related & unconditional on the other premises.

.

[Bernard Muller]

to MrMacSon,

Surely (1) 'Descendant of Abraham (Gal 3:16)', (2) 'Descendant of Israelites (Ro 9:4-5)', (3) 'Descendant of Jesse (Ro 15:12)', (4) 'Descendant of David (Ro 1:3)', 5) 'Having brothers by blood, one of them being James (1 Cor 9:5, Gal 1:19)', and (7) 'From the tribe of Judah (Heb 7:14') are inter-related concepts and unrelated to the others -ie. unrelated to (5), (6), (8), and (9).

No, they are different ways for implying Jesus had been an earthly human being. Sure, in that way they are related.
And in the same way, they are also related to the others, referring to my updated list of evidence from Paul's epistles, that is 6, 7, 8, 9 & 10:

1) 90% Descendant of Abraham (Gal 3:16) http://historical-jesus.info/18.html
2) 80% Descendant of Israelites (Ro 9:4-5) http://historical-jesus.info/25.html
3) 80% Descendant of Jesse (Ro 15:12) http://historical-jesus.info/60.html
4) 70% Descendant of David (Ro 1:3) http://historical-jesus.info/70.html
5) 85% Having brothers by blood, one of them being James (1 Cor 9:5, Gal 1:19). See Notes 1 and 2
6) 90% becoming from a woman (Gal 4:4) http://historical-jesus.info/18.html
7) 80% "poor, in poverty" (2 Cor 8:9) (can anyone be poor in heaven?) http://historical-jesus.info/21.html
8) 70% "The first man out of the earth, earthy; the second man the Lord out of heaven;" (1 Co 15:47)
9) 80% "the one man Jesus Christ" (Ro 5:15)
10) 60% The crucifixion happening in the heartland of the Jews http://historical-jesus.info/19.html

11) 80% From the tribe of Judah (Heb 7:14) http://historical-jesus.info/40.html
12) 60% "... For surely it is not with angels that he is concerned but with the descendants of Abraham.
Therefore he had to be made like his brethren in every respect, ..." (Heb 2:14-17) http://historical-jesus.info/40.html
13) 50% "In the days of his flesh," (Heb 5:7) http://historical-jesus.info/40.html

14) 30% Tacitus' Annals 15.44 (low because possibly heard from Christians then, which would make it dependent on the gospels)

15) 80% Josephus' Antiquities XX, IX, 1

there is no clear relationship between the various James (plural) of the Bible (in the Synoptics) and Mary, the mother of Jesus or Joseph (the supposed father of Jesus)!!!

"Mary the mother of James the less and of Joses" (Mk 15:40), most likely meant to be another Mary than the mother of Jesus.
"Mary the mother of Joses" (Mk 15:47), probably the same Mary as in my quote of part of Mk 15:40.
"and Mary the mother of James", again probably the same Mary as in my quotes of parts of Mk 15:40 & Mk 15:47. I think if the author meant that Mary was also the mother of Jesus, he would have said "Mary, the mother of Jesus".
"Mary the mother of James and Joseph," (Mt 27:56) The Greek does not have "Joseph" but "Joses".
And "Joses" ('Ἰωσῆς') is not the same name than "Joseph" ('Ἰωσήφ'). Likely "copied" from Mk 15:40. And again, I think if the author meant that Mary was also the mother of Jesus, he would have said "Mary, the mother of Jesus".

So, I do not see any problem here.

Please note I did not check for variants.

Cordially, Bernard

[Bernard Muller]

to Peter,

I'd like to leave the thread alone, but the above speaks to character, and I don't think I should have to leave statements impeaching my character alone.

I have the most complete respect for you and I don't (and did not) want to leave statements impeaching your character.

But I also notice you did not answer my new comments and questions of my previous post.

I want to refine them here:
Let's say there are 8 statements (as I indicated already) showing that Paul implied the past existence of an earthly human Jesus. Let's say that if these statements are independent, they have each a probability of 80% to be right (that's a simplification from my ratings). The other 20% would be about interpolation.
Through math, there is a probability of about 1 to 2 statements are an interpolation among the 8 (as I explained on my previous post for 80% probabilities).
Which means that 6 to 7 statements were likely written by Paul. There is no interpolation here and your conditional probability equation cannot apply for these statements.
Using the equation about the resulting probability for the sum of independent probabilities P = 1 - [(1-0.8)^6.5] then the overall result is practically 100%.

The interpolations (1 or 2) had to be done after Paul wrote his epistles, so they would not affect the 100% overall result.

Also, since the 6 to 7 statements out of 8 are deemed without a chance of interpolation, their probabilities should be raised considerably, let's say to 90% average.
So I would see P = 1 - [((1-0.9)^6.5)*((1-0)^1.5)] = 100%

I would value your comments on each of these points.

Cordially, Bernard

[Peter Kirby]

to Peter,

I'd like to leave the thread alone, but the above speaks to character, and I don't think I should have to leave statements impeaching my character alone.

I have the most complete respect for you and I don't (and did not) want to leave statements impeaching your character.

But I also notice you did not answer my new comments and questions of my previous post.

I want to refine them here:
Let's say there are 8 statements (as I indicated already) showing that Paul implied the past existence of an earthly human Jesus. Let's say that if these statements are independent, they have each a probability of 80% to be right (that's a simplification from my ratings). The other 20% would be about interpolation.
Through math, there is a probability of about 1 to 2 statements are an interpolation among the 8 (as I explained on my previous post for 80% probabilities).
Which means that 6 to 7 statements were likely written by Paul. There is no interpolation here and your conditional probability equation cannot apply for these statements.
Using the equation about the resulting probability for the sum of independent probabilities P = 1 - [(1-0.8)^6.5] then the overall result is practically 100%.

The interpolations (1 or 2) had to be done after Paul wrote his epistles, so they would not affect the 100 % overall result.

Also, since the 6 to 7 statements out of 8 are deemed without a chance of interpolation, their probabilities should be raised considerably, let's say to 90% average.
So I would see P = 1 - [((1-0.8)^6.5)*((1-0)^1.5)] = 100%

I would value your comments on each of these points.

Cordially, Bernard

I have no comment on the New Testament aspects.

I also don't have much more to say on the math, other than that I can confirm that you are doing it incorrectly.

Consider asking someone else, whom you trust to give you a true answer, about why it doesn't make much sense.

I have the most complete respect for you and I don't (and did not) want to leave statements impeaching your character.

Well, thank you for this. So, I will say this...

As I said earlier, my intent was to remove the problem where you don't use "my" (?!?!) the general multiplication rule. This equation is always true and always applicable. There is no need to justify it empirically. By the fact of what you were attempting to calculate, it must be used.

Unlike the special form for "independence," the general form doesn't require any particular assumptions. When events are known to be "independent," use of the general multiplication rule provides the same answer (as the "special" version for independence). If they don't, that is actually considered a proof of non-independence. By refusing to use the general form, because of concern that it could provide a different answer, you are actually confirming the fact that you would yourself consider the events non-independent (at least if you were thinking it all through) ... and the necessity of the general form.

Since you are not using the general multiplication rule, my effort was in vain. Part of the reason for that seems to be that you don't trust me to be truthful. So I think you need to ask people you trust more to be truthful, in order to understand the math here.

I'm confident you could reach a figure of 99% or higher with the multiplication rule and without trampling over probability theory. But you seem to think I'm attacking your conclusion, instead of helping with an error of method, so you don't seem to see that either.

PS -- Perhaps a word to the wise is sufficient. Go back and look at the pie charts again. In 100% of the probability space remaining, after multiplying by the probability of A (which is 0.2), "A" is true. That makes sense, because we're using multiplication, and we've already excluded the 80% of the probability space where "~A" is true. Once we've already multiplied by the 0.2, it is completely silly to consider any possibility at all of "~A" being true. We're considering only what would be once "A" is true with a 100% probability of being true (because multiplying by 0.2 "cuts out" the rest of the probability space, that 80%, already). Please study it, using real resources (like math books and math professor videos and so on), if you don't believe me.

[MrMacSon]

Let's say there are 8 statements (as I indicated already) showing that Paul implied the past existence of an earthly human Jesus. Let's say that if these statements are independent, they have each a probability of 80% to be right (that's a simplification from my ratings).

Bernard, they're not independent [of each other]!!

The probability that they're right is probably about 10% to 30% [each varies]

[Bernard Muller]

to MrMacSon,

Bernard, they're not independent [of each other]!

Yes, they are independent from each other, because if you eliminate one, that does not change the others.

The probability that they're right is probably about 10% to 30% [each varies]

Even if the 8 of them have a probability to be true of 20%, then the overall probability of the 8 together to be true is:
P = 1 - (1 - 0.2)^8 = 83.22%

Cordially, Bernard

[timhendrix]

to MrMacSon,

Bernard, they're not independent [of each other]!

Yes, they are independent from each others, because if you eliminate one, that does not change the others.

The probability that they're right is probably about 10% to 30% [each varies]

Even if the 8 of them have a probability to be true of 20%, then the overall probability of the 8 together to be true is:
P = 1 - (1 - 0.2)^8 = 83.22%

Cordially, Bernard

Hi Bernard,

Your last example with the 83.22% is equivalent to the horse-race example I posted above which (hopefully) illustrate why that inference does not hold in general.
If you prefer not to discuss this subject with me because you are already discussing it with several other that is fine, however, I just wished to make you aware of it.