Probability about Jesus (Christ) existence on earth

[Peter Kirby]

Perhaps there could be a quantitative, rather than merely categorical, rating of evidence.

... a system that allowed for more fine-grain control over the rating of evidence.

Yes. That would be "conditional probability" ??

Currently, the way we've used the terms "evidence" and "no evidence" is fully described by this set of relationships:

P(N1 | ~X1) = 0.95 - "95% chance of no evidence if not interpolated"
P(~N1 | ~X1) = 0.05 - "5% chance of evidence if not interpolated"
P(N1 | X1) = 0.8 - "80% chance of no evidence if interpolated"
P(~N1 | X1) = 0.2 - "20% chance of evidence if interpolated"

These express various conditional probabilities, but there is only room for "off" and "on," "no evidence" or "evidence," as Bernard observed.

We could either create more categories "for more fine-grain control" (more categories allowed to be chosen, each with different shades of "strength" of evidence) or we could define the numbers specifically for each individual item (a quantitative choice - as "fine-grained" as you like it).

[Bernard Muller]

to Peter,
From the writings of a same ancient author, there are 10 statements implying the same thing.
Each one of these statements has a 10% probability to be an interpolation. I want to know the overall probability of all of them are interpolations.
Is the following valid mathematically: 0.1^10 = 0.0000000001 = 0.00000001%
If it is valid, is there some restrictions for its application?

Cordially, Bernard

[Peter Kirby]

It really is easier to use other examples, to build understanding. Using controversial examples to build understanding, invites misunderstanding.

Suppose you wanted to know the probability that you pull ten Aces from a deck, assuming that the selection is random and with replacement. Suppose you know that the chance that any given card is an Ace is 1 out of 13.

(1) You can consider the events independent in the case where an ordinary deck is chosen, and cards are replaced and shuffled before each selection. In this case, the general form:

P(A1) * P(A2 | A1) * P(A3 | A1, A2) ....

Is equivalent to the special form:

P(A1) * P(A2) * P(A3) ....

Because of the fact of what it means to be independent events, which implies that the conditional probability is identical to the non-conditioned probability:

P(A2) = P(A2 | A1)
P(A3) = P(A3 | A1, A2)
etc.

(2) But suppose instead that one of twenty-six decks are chosen, at random. Thirteen of them are ordinary decks of all 52 playing cards. Thirteen of them are special decks that contain only a single card in them: a deck of all 2, a deck of all 3, ... , and a deck of all Aces. Here your chance of pulling an Ace remains the same: 1 in 13. However, your chance of pulling all Aces (ten Aces) just got much higher. And the special form (applied naively) would give a wrong answer that is extremely small.

Here is the correct answer (using the law of total probability and, for convenience, the conditional independence of events after conditioning on the deck selection):

Chance of All Aces = (Chance of Ordinary Deck) * (Chance of All Aces with Ordinary Deck) + (Chance of Special Deck, Non-Ace) * 0 + (Chance of Special Deck, Ace) * 1

Chance of All Aces = 1/2 * (1/13)^10 + 1/26

Or just a hair above the 1/26 chance that the special deck of Aces was chosen.

(3) The answer for the last question was from the perspective of not having been dealt any cards yet. But suppose you were allowed to peek at the first five cards, and then make a decision regarding whether the remaining five will be Aces. I.e., you get:

Ace, Ace, Ace, Ace, Ace...

This is a very interesting thing, no? It's very unlikely to be pulled from an ordinary deck. The chances that you are being dealt from the special deck are quite high, which means that your chances of getting five more Aces (conditioned on the first five being Aces) is quite high. This intuition can be expressed with specific numbers (but I will spare the reader).

From the writings of a same ancient author, there are 10 statements implying the same thing.
Each one of these statements has a 10% probability to be an interpolation. I want to know the overall probability of all of them are interpolations.
Is the following valid mathematically: 0.1^10 = 0.0000000001 = 0.00000001%
If it is valid, is there some restrictions for its application?

From the feedback posted in this thread, it seems that most people don't believe we should assume that these are "independent events" in the sense that your answer should be exactly 0.1^10. I would agree, that is a very bold assumption, and it leads to extreme conclusions that don't gel with what we would expect. Imagine that this isn't some ancient author, but rather a will and testament. Imagine that one of the hands through which it has passed, is one of the inheritors. Imagine that the ten items in the text are all items granting the inheritor vast amounts of property. And imagine that it seems only 5-10% likely that this person perpetrated a wholesale interpolation of the ten statements. It's consistent with that, that we could consider the individual statements to have, themselves, approximately a 10% chance of being interpolated. But that's before conditioning on any other events. And we need to condition on the other events, if we're going to use the formula for computing the probability of the intersection of several events. If we don't, we'll get an answer much lower than 5%, which contradicts our earlier statement that there is a 5-10% chance that this person interpolated everything.

If this is confusing, I'd recommend not focusing on the topic of interpolations, and instead thinking more about the topic of probability itself.

[Bernard Muller]

Thank you on your reply, Peter.

From the feedback posted in this thread, it seems that most people don't believe we should assume that these are "independent events" in the sense that your answer should be exactly 0.1^10.

I rebuked all the arguments about interdependence in the case of the 10 statements from the Pauline epistles.
I personally don't think they made sense. And they were not according to your idea of dependence either.
And even if the 0.1^10 is not exact, it still would come close to 0, even if the probabilities are raised to 0.5 for each. In that case, we would have 0.5^10 = 1%

Imagine that this isn't some ancient author, but rather a will and testament. Imagine that one of the hands through which it has passed, is one of the inheritors. Imagine that the ten items in the text are all items granting the inheritor vast amounts of property. And imagine that it seems only 5-10% likely that this person perpetrated a wholesale interpolation of the ten statements. It's consistent with that, that we could consider the individual statements to have, themselves, approximately a 10% chance of being interpolated

I think the 5-10% should be much higher, as also your 10% in order for a potential inheritor to be suspected of fraud on all the items.
Are they interpolations? Just 10% of probability is simply not enough to make that assumption for all the 10 items.
Most likely, with 10%, only one item could be an interpolation because [(9*0)+(1*1)]/10 = 10%
Anyway, that would not be enough to make a case against the individual except if other (& more conclusive) pieces of evidence are put forward.

But that's before conditioning on any other events. And we need to condition on the other events, if we're going to use the formula for computing the probability of the intersection of several events. If we don't, we'll get an answer much lower than 5%, which contradicts our earlier statement that there is a 5-10% chance that this person interpolated everything.

The 5-10% chance that this person interpolated everything is arbitrary. Different persons might have vastly different opinions on that chance, from less of 1% to 100%. But all of that motivated by different belief or personal interest.
Furthermore, if different persons made interpolations to their advantage, that would allow thinking some of the items are genuine.

And in order to make your earlier case with 8 items, for an end result of near 100%, you had to assume 100% evidence of interpolation for 7 items out of 8. Which would make the average probability of interpolation at [(7*1)+(1*0)]/8 = 87.5% which is much higher than these 10% probability for each of these 8 items.

So I think your scenario B is highly unrealistic, except if the average probability for interpolation for all the items is very high.

Cordially, Bernard

[Peter Kirby]

The gods are laughing.

[MrMacSon]

• I rebuked all the arguments about interdependence in the case of the 10 statements from the Pauline epistles.
  I personally don't think they made sense.

These 10 statements? -

• 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) "poor, in poverty" (2 Cor 8:9) (can anyone be poor in heaven?)
  
  8) "The first man out of the earth, earthy; the second man the Lord out of heaven" (1 Co 15:47)
  
  9) "the one man Jesus Christ" (Ro 5:15)
  
  10) The crucifixion happening in the heartland of the Jews

it would seem that

• 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)
  
  and, to a certain extent, (6) becoming from a woman (Gal 4:4)

are being used to assert "(9) 'the one man Jesus Christ' (Ro 5:15)", yet they^ are very aligned concepts, so they are interdependent.


and, "(8) 'The first man out of the earth, earthy; the second man the Lord out of heaven' (1 Co 15:47)" somewhat negates "(9) 'the one man Jesus Christ' (Ro 5:15)"


Also, 1 Cor 9:5 (5) does not affirm one of the brothers was James

.

[Peter Kirby]

And even if the 0.1^10 is not exact, it still would come close to 0, even if the probabilities are raised to 0.5 for each. In that case, we would have 0.5^10 = 1%

Just 10% of probability is simply not enough to make that assumption for all the 10 items. Most likely, with 10%, only one item could be an interpolation because [(9*0)+(1*1)]/10 = 10%

I think you need to start by discarding the assumption that you know what is true and not true about this subject? To learn.

Here's a stab at helping you understand that what you've been saying above here is wrong (almost everyone else seems to get it...). I have chosen a sexy example involving ancient authors and interpolations, as you seem to believe it's easier to reason about those examples.

There are 89 words in the Testimonium and (if I recall) about 63 words in a reconstruction a la Meier.

We can choose any numbers we like for the probability that some individual words are interpolated. For example, let's choose 99% for the unconditioned probability of interpolation for the 26 words that Meier excises. And let's choose 95% for the unconditioned probability of interpolation for the 63 words remaining. Just to demonstrate here.

If we use the naive but wrong approach of assuming independence of events for no reason other than sheer bloody-mindedness:

0.99^26 * 0.95^63 = 0.030416

And we're supposedly reduced to a 3% chance that all the words have been interpolated. Supposedly! But that's a lot of nonsense.

Reductio ad absurdum. Quod erat demonstrandum. Sic transit gloria mundi - Amen!

(Na, just kidding. I have no hope. I expect this to get mangled.)

PS -- what we've learned: if you interpolate anything, do it 100 times, and nobody will ever be able to suspect you!

[Ben C. Smith]

PS -- what we've learned: if you interpolate anything, do it 100 times, and nobody will ever be able to suspect you!

[Bernard Muller]

to Peter,

If we use the naive but wrong approach of assuming independence of events for no reason other than sheer bloody-mindedness:

0.99^26 * 0.95^63 = 0.030416

A word is not an event.
1st event: words discarded by Meier as interpolation (rated 99% probability of interpolation).
2nd event: words kept by Meir as genuine but regardless considered most likely interpolation (rated 95% probability of interpolation).

Then, we have:
0.99^1 * 0.95^1 = 0.9405 = 94.05%
And that result makes lot of sense in view the 99% and 95% implies some small doubts against the possibility of interpolations.

According to the input data, the probability the whole TF if genuine is:
1 - [(1-0.99)^1 * (1-0.95)^1] = 1 - 0.9405 = 0.0595 = 5.95%

We can even do better and weight the events according to the number of words for each event:
26/63 = 0.4127
For event 1: 0.99^(1+0.4127) = 0.9859
For event 2: 0.95^1 = 0.95

P = 0.9859 * 0.95 = 0.09366 = 93.66%

Cordially, Bernard

[Bernard Muller]

PS -- what we've learned: if you interpolate anything, do it 100 times, and nobody will ever be able to suspect you!

As long as you have strong evidence for each one of these 100 alleged interpolations being true (at least for most of them), someone will be suspected.
But if you have little evidence for each one of these 100 alleged interpolations being true (at least for most of them), at best a few interpolations can be expected, but not necessarily by the same interpolator.

Cordially, Bernard