Probability about Jesus (Christ) existence on earth

[spin]

My cat also has problems with probability. Fortunately, she's given up worrying about it and now goes with the flow.

[Peter Kirby]

The numbers are completely made up, and emotions seem to get in the way. Try a different domain, to talk about the subject.

Let's say Bob might have committed murder.
Alice testifies against Bob and says that she saw him do the crime.
Carl testifies against Bob and says that he saw him do the crime.
David testifies against Bob and says he saw it too.
Alice and Carl are married and say that they were together at the time. David is their son.

Now let X be the probability of a murder being witnessed.
Let A be the probability that Alice witnessed the murder.
Let C be the probability that Carl witnessed the murder.
Let D be the probability that David witnessed the murder.

Suppose A and C and D all have a probability of 50% considered alone, because none is particularly trustworthy.

Do you believe that there is a full 87.5% chance that either Alice or Carl or David (one or more) witnessed the murder?

If not, that's an illustration of a basic idea here.

If so, you'll need to read more and come up with more examples to feed your intuition on the subject.

(Please don't argue with me about your OP. I'm not interested. If you want to say that this example of a concept is lame and you're 100% right about whatever your point is, go ahead. Just leave me out of it...)

[Bernard Muller]

to Peter,

I'd like to mention that I considered this to be a starting point, not a rebuttal.

It's entirely possible to make the kind of argument that you want to make, while trying to take into account conditional probability.

In fact, it's the only mathematically valid way to do so... (and assuming independence is not the only way to do so...)

But I think I took care of that by lowering my probabilities down to 50% (as an average). And I do not know what would be conditional about these probabilities. Would that matter much?

Cordially, Bernard

[Peter Kirby]

to Peter,

I'd like to mention that I considered this to be a starting point, not a rebuttal.

It's entirely possible to make the kind of argument that you want to make, while trying to take into account conditional probability.

In fact, it's the only mathematically valid way to do so... (and assuming independence is not the only way to do so...)

But I think I took care of that by lowering my probabilities down to 50% (as an average). And I do not know what would be conditional about these probabilities. Would that matter much?

Cordially, Bernard

Thank you for being cordial, since I know that my own comments can be very harsh-sounding. I'll try to be clear.

The real question to ask first is: what is probability? This is a really deep and complex topic, but I'll just try to stay practical and less precise. When speaking of probability and discussing a finite number of outcomes, each of those outcomes can be characterized as the occurrence or non-occurrence of different events. So if you are dealing with the events of the murder, let's say that (made up numbers!) the possible outcomes are:

(A, C, D) - all events occurred - probability 0.4
(~A, ~C, ~D) - none occurred - probability 0.3
(A, ~C, ~D) - Alice witnessed only - probability 0.1
(~A, C, ~D) - Carl witnessed only - probability 0.1
(~A, ~C, D) - David witnessed only - probability 0.1

So the rest of the outcomes have probability zero for whatever reason.

Based on this set of outcomes, you can talk about the individual probabiities:

P(A) = P(C) = P(D) = 0.5

You can also talk about conditional probabilities:

P(C | A) = P(C and A) / P(A) = 0.4 / 0.5 = 0.8 ("Carl, given Alice")
P(D | A and C) = P(D, C, and A) / P(A and C) = 0.4 / 0.4 = 1 ("David, given Alice and Carl")

And these conditional probabilities:

P(C | ~A) = P(C and ~A) / P(~A) = 0.1 / 0.5 = 0.2 ("Carl, given not Alice")
P(D | ~A and ~C) = P(D, ~A, and ~C) / P(~A and ~C) = 0.1 / 0.4 = 0.25 ("David, given not Alice and not Carl")

And you can use the conditional probability version of the formula at the top of the thread:

P(A or C or D) = 1 - (1 - P(A)) (1 - P(C | ~A)) (1 - P(D | ~A and ~C)) = 1 - (0.5) (0.8) (0.75) = 1 - 0.3 = 0.7

And this matches the probabilities that you would obtain by inspecting all the outcomes directly.

So, if we're going to talk about probability, we're going to need to think deeply about what kind of "outcomes" we're dealing with and how we'd describe the space of their probabilities. We seem to be talking about our uncertainty in the interpretation of the artifacts of history, interpreted as best as we can guess. So we'd need to talk about the "outcomes" in terms of the various scenarios for the historical past. Our intuition, if it is going to be useful, needs to be able to work in terms of connections between events and broad-strokes pictures of what-could-have-been, and how we imagine their relative strength / merit / likelihood.

It may be a task too much for us, since we aren't designed to be able to have good and precise intuition about things like that, but it's the least we can try to do if we're going to attempt to work with such figures mathematically. (We don't necessarily have to try to do that...)

Would that matter much?

Indeed it can. In the "worst case" (when this one event occurs, it occurs in outcomes where all the other events also occurred), all of your 'arguments' (events) 'combined' could be only and exactly as strong (likely) as the strongest single 'argument' (event). This can make the whole idea of accumulation of evidence very questionable. On the other hand, a single strong fact can be much better than a million little cuts, for these very reasons (even though you quickly hit "certainty" even with just a dozen of these little things, if you assume their independence ... which hopefully sets off alarms).

[Ben C. Smith]

to Ben,

In probability theory, two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of the other.

I still do not see why any of my 9 points would be dependent on each others. Maybe somebody can explain that to me & us.

Here is your original list:

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

You do not see how, to take but one example, numbers 3 and 4 are not independent of one another? David is the putative descendant (son) of Jesse; therefore every single descendant of David is also a descendant of Jesse. Also, I think according to your reconstruction Paul wrote both Romans 1.3 and Romans 15.12, so even the authors are not independent here: they are the same guy. Do you really think that a person supposing someone to be the descendant of Jesse has nothing to do with that same person supposing that same someone to be the descendant of David? If you met a random person on the street, I imagine you would assign no strong probability (yet) in favor of him/her being either a descendant of David or a descendant of Jesse. But now imagine that it were proven to you that s/he is a descendant of David. Would not your assessment of the odds in favor of him/her being a descendant of Jesse change now? Whatever probability you mentally assigned before, surely now it is 100%, since it is impossible to be a descendant of David without also being a descendant of Jesse. Right?

[Bernard Muller]

to Peter,

The numbers are completely made up, and emotions seem to get in the way. Try a different domain, to talk about the subject.

Let's say Bob might have committed murder.
Alice testifies against Bob and says that she saw him do the crime.
Carl testifies against Bob and says that he saw him do the crime.
David testifies against Bob and says he saw it too.
Alice and Carl are married and say that they were together at the time. David is their son.

Now let X be the probability of a murder being witnessed.
Let A be the probability that Alice witnessed the murder.
Let C be the probability that Carl witnessed the murder.
Let D be the probability that David witnessed the murder.

Suppose A and C and D all have a probability of 50% considered alone, because none is particularly trustworthy.

Do you believe that there is a full 87.5% chance that either Alice or Carl or David (one or more) witnessed the murder?

I have no problem with the 87.5% conclusion except I would prefer if it was about Bob doing the crime. That's what an investigator would want to solve, that's the common point. Of course it might be a collusion between members of the same family (if they have motives to hate Bob), which would lower the 87.5%. But I do not see how that would apply to Paul, the author of Hebrews, Tacitus and Josephus.
And if there were about eight very similar cases, there is a good chance than the suspect would be innocent in one of these cases.

Cordially, Bernard

[Bernard Muller]

to Ben,

You do not see how, to take but one example, numbers 3 and 4 are not independent of one another? David is the putative descendant (son) of Jesse; therefore every single descendant of David is also a descendant of Jesse. Also, I think according to your reconstruction Paul wrote both Romans 1.3 and Romans 15.12, so even the authors are not independent here: they are the same guy. Do you really think that a person supposing someone to be the descendant of Jesse has nothing to do with that same person supposing that same someone to be the descendant of David? If you met a random person on the street, I imagine you would assign no strong probability (yet) in favor of him/her being either a descendant of David or a descendant of Jesse. But now imagine that it were proven to you that s/he is a descendant of David. Would not your assessment of the odds in favor of him/her being a descendant of Jesse change now? Whatever probability you mentally assigned before, surely now it is 100%, since it is impossible to be a descendant of David without also being a descendant of Jesse. Right?

I do not see how that family relationship between Jesse & David would matter:
Number 4, as understood Paul implying Jesus had been an earthly human being, confirms, many chapters later, number 3, also as understood Paul implying the same a different way, and therefore strengthening the fact Paul telling us Jesus had been an earthly human.
If, taking in account all the mythicist (far-fetched) arguments trying to show otherwise and setting a probability of 50% for each, we still would have 75% for the ensemble of the two.

Cordially, Bernard

[Peter Kirby]

to Ben,

You do not see how, to take but one example, numbers 3 and 4 are not independent of one another? David is the putative descendant (son) of Jesse; therefore every single descendant of David is also a descendant of Jesse. Also, I think according to your reconstruction Paul wrote both Romans 1.3 and Romans 15.12, so even the authors are not independent here: they are the same guy. Do you really think that a person supposing someone to be the descendant of Jesse has nothing to do with that same person supposing that same someone to be the descendant of David? If you met a random person on the street, I imagine you would assign no strong probability (yet) in favor of him/her being either a descendant of David or a descendant of Jesse. But now imagine that it were proven to you that s/he is a descendant of David. Would not your assessment of the odds in favor of him/her being a descendant of Jesse change now? Whatever probability you mentally assigned before, surely now it is 100%, since it is impossible to be a descendant of David without also being a descendant of Jesse. Right?

I do not see how that family relationship between Jesse & David would matter:
Number 4, as understood Paul implying Jesus had been an earthly human being, confirms, many chapters later, number 3, also as understood Paul implying the same a different way, and therefore strengthening the fact Paul telling us Jesus had been an earthly human.
If, taking in account all the mythicist (far-fetched) arguments trying to show otherwise and setting a probability of 50% for each, we still would have 75% for the ensemble of the two.

Cordially, Bernard

You are saying that it makes sense to model (e.g.) the interpretation of two passages in Paul as being independent events. As you have it, you just said there is (if 50% be the made up number):

25% chance both 'mythicist' interpretations are correct
25% chance the first 'mythicist' one only
25% chance the second 'mythicist' only
25% neither are correct

But the big incongruity here are those two things in the middle. Is it really so likely that Paul sometimes has a non-mythicist interpretation and other times has a mythicist interpretation?

Indeed, extending the same to more passages, it becomes 'extremely unlikely' that any 'pure' position on Paul is correct. But that is far from intuitive. The most likely scenarios should be 'historicist' with or without a couple interpolations, 'mythicist' with or without a couple interpolations (by 'interpretation'), and 'mythicist' by interpolations (at least, that is my intuition, in general).

This would involve a lot of 'correlated data' so to speak. If one passage has the weird interpretation, likely more do. If several passages are interpolated, likely more are.

But it would have been nice if this was all understood, at least, in the abstract. If you don't get it in the abstract, why should we discuss (using probability) the highly controversial topics that will be highly difficult for people to agree on in the first place? So yes I ask again that the math is studied a bit more seriously before it is pressed into service for (dubious) applications.

[Peter Kirby]

to Peter,

The numbers are completely made up, and emotions seem to get in the way. Try a different domain, to talk about the subject.

Let's say Bob might have committed murder.
Alice testifies against Bob and says that she saw him do the crime.
Carl testifies against Bob and says that he saw him do the crime.
David testifies against Bob and says he saw it too.
Alice and Carl are married and say that they were together at the time. David is their son.

Now let X be the probability of a murder being witnessed.
Let A be the probability that Alice witnessed the murder.
Let C be the probability that Carl witnessed the murder.
Let D be the probability that David witnessed the murder.

Suppose A and C and D all have a probability of 50% considered alone, because none is particularly trustworthy.

Do you believe that there is a full 87.5% chance that either Alice or Carl or David (one or more) witnessed the murder?

I have no problem with the 87.5% conclusion except I would prefer if it was about Bob doing the crime. That's what an investigator would want to solve, that's the common point. Of course it might be a collusion between members of the same family (if they have motives to hate Bob), which would lower the 87.5%.

This is not adequate. In fact, based on the given statements, all you know would be that the probability of at least one of them witnessing the event is somewhere between 50% and 100%. Greater than or equal to 50%, because that's true for the unconditioned probability of an event (which are equal in unconditioned probability). Less than or equal to 100%, because that's the maximum.

For example, this set of outcomes is also consistent with P(A) = P(C) = P(D) = 0.5.

Outcome (A, ~C, ~D) - probability 0.5
Outcome (~A, C, D) - probability 0.5

If this is the set of outcomes that define the probability space, then P(A or C or D) = 1.

Or, for example, this set of outcomes is also consistent with P(A) = P(C) = P(D) = 0.5.

Outcome (A, C, D) - probability 0.5
Outcome (~A, ~C, ~D) - probability 0.5

If this is the set of outcomes that define the probability space, than P(A or C or D) = 0.5.

Needless to say, you've failed to grasp this point, and I recommend you read about it more, especially in a context where you don't feel like you're being attacked and where you're inclined to have trust in the exposition.

[Ben C. Smith]

to Ben,

You do not see how, to take but one example, numbers 3 and 4 are not independent of one another? David is the putative descendant (son) of Jesse; therefore every single descendant of David is also a descendant of Jesse. Also, I think according to your reconstruction Paul wrote both Romans 1.3 and Romans 15.12, so even the authors are not independent here: they are the same guy. Do you really think that a person supposing someone to be the descendant of Jesse has nothing to do with that same person supposing that same someone to be the descendant of David? If you met a random person on the street, I imagine you would assign no strong probability (yet) in favor of him/her being either a descendant of David or a descendant of Jesse. But now imagine that it were proven to you that s/he is a descendant of David. Would not your assessment of the odds in favor of him/her being a descendant of Jesse change now? Whatever probability you mentally assigned before, surely now it is 100%, since it is impossible to be a descendant of David without also being a descendant of Jesse. Right?

I do not see how that family relationship between Jesse & David would matter:
Number 4, as understood Paul implying Jesus had been an earthly human being, confirms, many chapters later, number 3, also as understood Paul implying the same a different way, and therefore strengthening the fact Paul telling us Jesus had been an earthly human.

Then it is clear that you do not understand what is meant by the independence of events. The same author confirming a previously stated position is not a second, independent event (which is not the same thing as saying that it is worthless; but it does change which equation you use). Peter is right: you need to use completely innocuous cases to educate yourself on the math; you are apparently too close to this particular subject matter.