# The Bible, History, and Bayes' Theorem

(This is posted in Biblical Errancy because it is sparked by discussion from these threads: The awkward fact of the baptism of Jesus, What Abe finds wrong with "The God Who Wasn't There", and The failed prophecies of the historical Jesus)

**ApostateAbe wrote:**

The first very big issue concerns the use of "evidence." You keep repeating your demand for evidence, and I repeat my answer that the primary evidence is contained in the set of the early Christian sources. I know you think this is very bad, very unreasonable, so I would like to explain.

To me, evidence isn't even the final destination. The final goal is to find the best explanations for the evidence, or to find explanations for the evidence that are most probable. The methods of finding the best explanations are such criteria as explanatory power, explanatory scope, plausibility, consistency, and minimum ad hoc. This set of criteria is known as the "Inference to the Best Explanation" or "Argument to the Best Explanation." It is designed for critical New Testament scholarship, but it can actually be applied to anything, and it is a great way to model debates in any subject of deciding beliefs concerning the objective reality.

Anything can be evidence if it relates to the origins of Christianity. The origins of Christianity are best reflected in the manuscripts of the Pauline epistles and the synoptic gospels (earliest compositions). Therefore, the most relevant evidence for any explanation relating to the origins of Christianity are the Pauline epistles and the synoptic gospels.

There is a continuing widespread error in the way we talk about "evidence." We conflate two very different principles of empiricism in our everyday language: evidence and explanations. When we talk about evaluating the evidence, it should be about evaluating the various explanations for the evidence. The "evidence" is actually somewhat fixed. It is the directly-observed objective reality. The evidence does not change, unless it is destroyed or if a researcher discovers something new about it. The evidence does not actually have values on a scales of quality. We should not be ranking some evidence as better than other evidence (though some evidence can be more relevant than others). If evidence in any form exists, then we are terribly misleading ourselves if we think of the evidence as non-existent, even if a hypothesis is extraordinary and the conclusions are extremely unlikely. I know that is generally the way everyone talks, but it can lead to a lot of unnecessary confusion, especially in a subject where evidence is scarce and ambiguous. Instead, the explanations for the evidence have values on a scale of quality. We can rank some explanations for the evidence as better than others.

So, when you say, "(By the way, have you ever wondered why John the Baptist, who by all accounts is a much less important and historically significant person than Jesus, nevertheless has more evidence for his existence than Jesus himself???)", I think it is a big mistake to quantify evidence like that, because the sources found in the Christian canon count as evidence! They are evidence that can have a bunch of explanations, and our goal should be to find the best explanation.

Let me give you an example. When Earl Doherty makes his case that the earliest Christians believed that Jesus was merely spiritual, he can't possibly do it by starting out with, "The Christian sources are not evidence." Anyone who says that can not possibly have any knowledge about how Christianity may have begun. Instead, he does and should use the Christian sources--the Pauline epistles and the synoptic gospels--as evidence. That evidence directly reflects what the earliest known Christians believed. Based on what Christians apparently believed, then we can try to find the best explanations for those beliefs.

# Yes, Basically...

Abe,

Point taken, and I basically agree with your essential point that 'anything can be evidence'. I admit I was using the sloppy language of colloquial English when making my points about your evidence 'not being evidence'.

It is true that the way most people usually speak about evidence is problematic and can introduce confusion and ambiguity.

Also, I agree with you that what must be evaluated are the 'explanations' of the evidence that we have. The evidence usually stands on its own and doesn't change much (except in certain cases, such as forgeries, when previously accepted evidence must be directly questioned).

So, for the purpose of clearing the debris, I would like to introduce to you the idea of Bayesian probability theory, since it directly applies to the topics you raised in a crucial, fundamental way.

I hope to do this as a discussion, rather than an essay with a wall-o-text (you can be the judge of whether this prophecy has failed ). However, this topic will almost inevitably require a little extra reading work on your part. I'll try not to over-load you, though. I'm good at responding to questions, too, so if any material here seems too dense or abstract, let me know and I think I'll be able to bring it down to Earth and cut it down to size for you. That's why I think a discussion will work best, as I will tailor my points to your specific concerns and areas of interest.

(Also, forgive me if at times I sound pedantic. I'm writing this assuming that there will be some people reading this who are averse to math and/or statistics, even if you personally might be very comfortable with them. If the math is too slow and easy for you, just skim along and you'll do fine. It IS actually very easy math, to be honest.)

# Introduction to Bayes' Theorem with An Easy Example

I believe the best way to start on this issue is to simply jump the first hurdle which is to understand the basic idea behind Bayesian probability calculation. So, here goes.

It's your birthday, and a friend Alice has just given you a present. "Guess what it is before you open it!" she says.

Now, it just so happens that you had made a wish list before your birthday, with only two things on it: A watch, and a keychain.

It also just so happens that your other friend Bob, who is 100% reliable and trustworthy, has told you that, "Alice definitely got you one of the two things on your wish list."

The present is in a small, non-descript box, wrapped in bright paper with a bow on it.

Having no further clues, you ask yourself, "What is the probability that she got me a watch vs. a keychain?"

Again, having no further clues, you decide that it is reasonable to give both options equal odds, and so you calculate correctly that this would imply that the probability that the present is a watch is 1/2 or 50%, and likewise the probability that it's a keychain is equally 1/2 or 50%.

You decide to see if you can figure out what's inside by shaking the box and listening to whether it rattles or not.

But first, prior to shaking the box, and based on 100% reliable information from Bob, you know that IF the box contains a watch, THEN there is only a **20%** chance that the box will rattle. You likewise know that IF the box contains a keychain, THEN there is a **60%** chance that the box will rattle.

You shake the box, and it rattles! The question is, given this new clue, what is the actual probability that the box contains a keychain?

### Intuition?

It is intuitively obvious that a rattling sound should more strongly indicate that the box contains a keychain, so the probability should be more than 50%, but how much more?

You almost want to say that it should be 60%, but quickly catch yourself, because you realize that by the same reasoning there would be a 20% chance of a watch, but 60% + 20% doesn't add up to 100%, so that can't be right.

It's also intuitively obvious that the best explanation for the rattling sound is a keychain, since that has the highest likelihood of making a rattling sound. But it doesn't prove it's a keychain, because a watch could technically also make a rattling sound. If someone asked you to bet on it, you would bet on a keychain, but it would depend on the gambling odds of the wager, wouldn't it? If the pay-off was stacked heavily in favour of the watch, it might be worth betting on the watch even though it is not as likely as the keychain. Would it be worth, say at a 10 to 1 pay-off, taking the risk on that bet?

What would be fair odds for this bet? Given only the clues above, what is the best estimate of the actual probability that it really does contain a keychain and not a watch?

You have an intuitive feeling that there should be a way to figure out this probability question, but intuition alone is not enough to give a solid, definitive answer, even if that solid answer happens to be a probability estimate. Is it 60%? 70%? 80%? 90%?

Human intuition alone can only give a rough answer. But there's a better way.

## How to Solve It!

### State the Assumptions

There are two competing 'explanations', or 'hypotheses'. Trusty Bob's clue told you that either the box contains a watch, or it contains a keychain. Let's give these hypotheses names/symbols to make it easier to talk about them:

W - The box contains a watch.

K - The box contains a keychain.

Now, before you shook the box, you had a nice, clear idea that both hypotheses were equally likely, and so you (correctly, according to the assumptions of this example) determined these probabilities are also equal:

P(W) = 50% = 1/2 = 0.5

P(K) = 50% = 1/2 = 0.5

And also before you shook the box, you had reliable information about the likelihoods of hearing a rattle in each of the cases where one hypothesis or the other are true.

If W is true (a watch), then the probability of hearing a rattle (let's give a 'rattle sound' the name/symbol R) should be 20%. In the lingo of probability, you can state this as, "The probability of R, given that W is true," or:

P(R|W) = 20% = 0.2

And likewise, if K is true (a keychain), then the probability of R (a rattle sound) should be 60%. Or, "The probability of R, given that K is true":

P(R|K) = 60% = 0.6

Following so far? These are just symbols. I haven't said anything new yet. I've only put the assumptions of the example into math lingo. Now let's look at how to use these math symbols to get a solid answer to the probability question.

### Make the Predictions

We don't know which hypothesis, W or K, is actually true yet, but we do have some information about what we should expect if the alternative hypotheses were true. (Side-note: Another word for 'expectation' is 'prediction'.)

Let's examine the possible cases:

1. There is a 50% chance that W is true. If W is true, then there is a 20% chance that the box will rattle when shaken, and an 80% chance it won't.

2. There is a 50% chance that K is true. If K is true, then there is a 60% chance that the box will rattle when shaken, and a 40% chance it won't.

Hmm. The 50% and 50% add up to 100%, the 20% and 80% add up to 100%, and the 60% and 40% add up to 100%.

Case 1 and Case 2 are mutually exclusive. Either W is true or K is true, and not both at the same time. And, within Case 1, where W is true, the possibilities are also mutually exclusive. Either the box rattles (R) or it doesn't (which we'll call ~R, or 'not R'). So within Case 1, the likelihoods 20% and 80% add up to 100% of the possible outcomes.

Likewise, within Case 2, where K is true, again R and ~R are mutually exclusive, and 60% plus 40% adds to 100% of the possible outcomes.

So, there are only four possible, mutually exclusive outcomes in this example:

W and R - There is a watch, and the box rattles.

W and ~R - There is a watch, and the box doesn't rattle.

K and R - There is a keychain, and the box rattles.

K and ~R - There is a keychain, but the box doesn't rattle.

It's actually quite straightforward to calculate the probabilities of these four, mutually exclusive outcomes:

P(W and R) = P(W) x P(R|W) = 0.5 x 0.2 = 0.1 or 10% chance

P(W and ~R) = P(W) x P(~R|W) = 0.5 x 0.8 = 0.4 or 40% chance

P(K and R) = P(K) x P(R|K) = 0.5 x 0.6 = 0.3 or 30% chance

P(K and ~R) = P(K) x P(~R|K) = 0.5 x 0.4 = 0.2 or 20% chance

Now we're getting somewhere. Note that 10% + 40% + 30% + 20% = 100%. We've covered all the possibilities.

But wait! We know something specific about these possibilities. We did shake the box, and it did rattle. So, using the process of elimination, we can rule out the 2 cases where the box didn't rattle. We are left with only two cases:

P(W and R) = 0.1 = 10%

P(K and R) = 0.3 = 30%

We already know that the box rattled, so in fact, R is a given. R is a clue, a piece of information that narrows down the possibilities.

Hmm... Unfortunately, these probabilities don't add up to 100% either.

But wait! They must somehow 'add up' to 100% because we already know that the box rattled! We are already in a universe where a non-rattling box is no longer possible, because that test was already done, and the results are in: It rattled. R is true. It no longer makes sense to talk about the 'possibility' of ~R. Those possibilities applied to the universe before we shook the box.

R is a given. What we want to determine now is the probability that the box contains a keychain (K) **given** that the box rattled (R)! This is the question in math-speak:

P(K|R) = ???

The probability that K is true, given that we know R is true, is what exactly?

### Bayes' Theorem: The Better the Prediction, the Better the Hypothesis

Another way of thinking about the four mutually exclusive outcomes before we shook the box is that they are predictions, and perhaps it is intuitively easier to think about the problem in terms of what the hypotheses predict. The W hypothesis has predicted that R will occur 20% of the time, and prior to that, we predicted that W itself has a 50% probability. So, naturally, we predict that 'W and R' together should have a 50% x 20% = 10% joint probability.

Likewise, the K hypothesis predicts R with a probability of 60%, and K itself is predicted with 50% probability, so we predict that 'K and R' should have a 50% x 60% = 30% joint probability.

Well, we shook the box, and the prediction of R has come true! But wait, compared to K's prediction at 30%, W's prediction was pretty darn weak at a mere 10%.

It stands to reason that the hypothesis that made the best, most accurate prediction should be the one we favour at the end of the day. And not only that, but the stronger and better its prediction was, compared to the other competing hypotheses, the more favourably we should judge the hypothesis.

And that's where Bayes' Theorem comes in. We are only one step away from getting the correct answer to our probability question.

Bayes' Theorem basically says that we should update our initial estimates of the probabilities of competing hypotheses in a way that is proportional to the strengths of their predictions: The better the prediction, the better the hypothesis.

The proportion between 10% and 30% is the same proportion as the ratio 1:3. It is 3 times more likely that the box contains a keychain (K) than that it contains a watch (W). Converting the ratio 1:3 into a fractional probability for K, we divide P(K and R) by the total probability of P(K and R) plus P(W and R):

P(K|R) = P(K and R) / [ P(K and R) + P(W and R) ]

= 30% / [ 30% + 10% ]

= 30% / 40%

= 3/4

= 0.75

= 75%

At last, we have a solid answer. After hearing the rattling sound, we can conclude that the probability that the box contains a keychain is 75%, and likewise the probability that it contains a watch is only 25%.

Prior to shaking the box, we were justified in claiming that the probability of a keychain was 50%, but after shaking the box and hearing the rattle, we realize that the keychain hypothesis had predicted that outcome 3 times better than the watch hypothesis. And so, we are justified in updating our probability estimates in a proportion of 3 to 1. Whereas, prior to shaking the box the probabilities were 1 to 1 even, after shaking the box they are now 3 to 1 in favour of the keychain hypothesis, which works out to a 75% chance of a keychain, which is 3 times bigger than the 25% chance of a watch.

### Clean Up

The only thing left to do for this example is to wrap it all up in a nice little package (oh god, not another crappy metaphor....). Okay I won't go there. But seriously, the above example makes sense, but it's awfully messy. Seems like a lot of work for not much.

The nice thing about math is once you've worked out a solution to a problem, you can often generalize it so that it works for any problem of a similar kind. And this is what Bayes' Theorem is in practice:

P(H_{1}|E) = P(H_{1}) x P(E|H_{1}) / [ P(H_{1}) x P(E|H_{1}) + P(H_{2}) x P(E|H_{2}) + ... + P(H_{n}) x P(E|H_{n}) ]

Which reads, basically, in English: The probability of a particular hypothesis H after observing some new evidence E is equal to the strength of H's prediction of E proportioned against the strengths of all the competing hypotheses' predictions combined. Where "the strength of H's prediction of E" is calculated as the joint probability of both H and E, which is equal to the prior estimated probability of H times the predicted likelihood that E would occur if H were true.

### Translation from math to English

P(H_{1}|E) -Probability of H_{1} given E. The probability that H_{1} is true, given that E is true. The posterior probability of H_{1}, given E. The estimated probability of the hypothesis after having observed the new evidence.

P(H_{1}) - Probability of H_{1}. The probability that H_{1} is true. The prior probability of H_{1}.The estimated probability of the hypothesis before having observed the new evidence.

P(E|H_{1}) - Probability of E given H_{1}. The probability that E is true, given that H_{1} is true. The conditional probability of E given H_{1}. The likelihood of the new evidence under the hypothesis. The predicted probability that the new evidence would be observed, in the case where the hypothesis is assumed to be true.

P(H_{1}) x P(E|H_{1}) - The joint probability of both E and H_{1}. The "strength of H_{1}'s prediction of E".

H_{1}, H_{2}, ..., H_{n} - The competing, mutually exclusive hypotheses.

[ P(H_{1}) x P(E|H_{1}) + P(H_{2}) x P(E|H_{2}) + ... + P(H_{n}) x P(E|H_{n}) ] - The marginal probability of E. The sum of the joint probabilities of E across all of the Hs. The "combined strengths of all the competing hypotheses' predictions".

### How Is This Relevant?

The thing about Bayes' Theorem is that it is a theorem. Given the extremely basic postulates of probability, it can be and has been proven as axiomatically true as any other fundamental mathematical theorem.

The basic postulates of probability cover a lot of ground: All science, all statistics, all profitable casinos and lotteries, all applications of math to any form of speculation. This includes the study of history, and specifically the study of the Bible and the historicity of Jesus.

The above discussion of a mundane situation like guessing a birthday present is not just a matter of speculation, it is a strictly logical consequence of the assumptions of the problem. It is a logically valid argument: If the premises are true, then the conclusion is inescapable.

It may sound strange to speak of probability as having 'inescapable conclusions', and this is why I took the time to explore this simple example in detail and why I am emphasizing this point right now.

Imagine that you got the present, shook the box, heard the rattle, and concluded that the box contained a keychain with a probability of 75%. And then you open the box, and sure enough, it's a ... WTF!? It's a fucking watch! I thought you said it would be a keychain!

The inescapable conclusion of Bayes' Theorem is not that there is definitely a keychain in the box. It is that there is a 75% probability of a keychain in the box. There is still a chance that it's a watch, it's just not an even money bet. In fact, it's a bet with 3:1 odds in favour of the keychain. But 3:1 favoured horses can still lose the race. In fact, they will lose the race about 25% of the time in the long run.

Again, how is this relevant? Just that Bayes' Theorem is the axiomatically correct tool to use to judge how we should modify our probability estimates of various competing hypotheses.

Historical studies of the Bible have gotten along fairly well with the standard, accepted criteria for judging explanations (hypotheses) of different types of evidence. But for the particularly thorny and politically-tinged issue of the historicity of Jesus, they have so far failed to resolve the issue definitively. Although most scholars will dismiss the competing hypothesis of mythicism, they really do not have solid grounds to do so. While some of the standard historicity criteria are indeed good criteria (and they are supported by Bayes' Theorem when they are), others are weak and/or problematic (and Bayes' Theorem can help explain why).

In the case of Jesus' historicity, it doesn't require one to hold a mythicist position in order to see clearly that the standard criteria have failed miserably. All one need do is look at the plethora of conflicting and/or contradictory 'historical' Jesus hypotheses put forth by various supporters of Jesus' historicity.

Is Jesus a doomsday cult leader? Yes! Is Jesus a freedom fighter? Yes! Is Jesus a teacher? Yes! A rabbi? Yes! Unknown? Yes! Famous? Yes! Crucified? Yes! Not crucified? Yes!

You name it, Jesus was it, depending on which historian you're asking.

This is, not surprisingly, exactly the same situation that theists are in when they try to tell us who 'God' is. And it is exactly as suspicious as theism is. When the evidence does not clearly point in one direction, it is easy to imagine it pointing in whichever direction you happen to be looking. Jesus 'is' whoever you want him to be.

It doesn't require positing a mythicist hypothesis to see that this confusion is a problem that cannot be resolved with the intuitive tools of the standard historicity criteria, precisely because they are based only in intuition, and different historians with different perspectives (and undoubtedly different agendas in some cases) cannot agree based on intuition alone.

There is really only one way out of this in the long run, and that is to take a more principled, rational approach to the evidence and hypotheses in question. Hypotheses must be judged according to consistent, justifiable criteria, not according to fuzzy rules of thumb and personal guesses, however educated those guesses may be.

Bayes' Theorem can be applied to this situation to sort the wheat from the chaff.

### Links

**Required reading** is *Bayes' Theorem for Beginners*, by Richard C. Carrier, Ph.D. (from http://www.richardcarrier.info/jesus.html)

Recommended reading is *An Intuitive Explanation of Bayes' Theorem* by Eliezer S. Yudkowsky

I think I'll stop here for now. I have much more to say, but it's better if I wait for your response on this one tidbit, I think.

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#1Yes, clearly the gospels are evidence about what the respective authors of the gospels believed when they were written. Claiming that they believed something else is bizarre. Gnostic interpretations of Jesus did not show up until the 2nd century, which indicates that some Xtians at that [later] time believed that Jesus was purely spiritual.

#2Very good post, I enjoyed reading that and learned something

My two cents and just my opinion from what I've read. Jesus as the bible portrays him, did not exist. The character is based on a number of Jesus like characters that trolled around the first century claiming to teach wisdom and aspects of previous religions. Not one document has been more bastardized than the bible in all of human history. The countless translations and transcriptions of the stories, coupled with the deliberate vetoing of certain sections by a group of religion leaders with unknown political and moral inclinations, makes the bible a very poor piece of evidence for anything.

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc

#3natural, you have written a very good introduction to Bayes' Theorem, and I think it should be published somewhere. I got a very good understanding of Bayes' Theorem from what you wrote. Thank you.

Unfortunately, I don't have any confidence that Bayes' Theorem or any other method depending on numerical probability estimates will be helpful in making historical decisions. I wish Richard Carrier all of the best of luck in that, but I think the weaknesses are at a very fundamental level. Probability ratios simply are not appropriate for explanations of evidences that are almost entirely inter-subjective (linguistic). We can't even begin to use Bayes's Theorem because we have no way of estimating the probability ratios.

I think maybe the weaknesses can be best illustrated with an example of an historical debate where we may think that Bayes' Theorem could apply. Perhaps the most common debate between mythicists and historicists surrounds the evidence of Galatians 1:19. It is one of the simplest debates, though of course the complexity can magnify as the debate progresses. Paul wrote:

but I did not see any other apostle except James the Lord’s brother.

Basically, the standard interpretation of this evidence is that Paul wrote of meeting James, the brother of Jesus. If there is any doubt about what Paul means by "Lord's brother," it is clarified by Mark 6:3, Matthew 13:55 and Josephus' Antiquities of the Jews 20:9:1. Those sources reflecting Christian myth tell of a literal sibling relationship between Jesus and James.

The mythicists have objections, however. They point out that, almost any time Paul uses the word for "brother," it is meant metaphorically, as in religious kin. Of course, if Paul needed to describe a literal sibling relationship, he would have no choice but to use the same Greek word for it (adelfos), but the pattern counts for at least something. How much? Hard to say.

There is only one other time that Paul uses a phrasing similar to "Lord's brother," and that is in 1 Corinthians 9:5, where it is plural.

Do we not have the right to be accompanied by a believing wife, as do the other apostles and the brothers of the Lord and Cephas?

The historicists claim this as evidence, because Jesus reputedly had a plurality of literal brothers, and this passing verse seems to regard the "brothers of the Lord" as having special authority, but they are not quite the same as the apostles, much as we would expect for the literal siblings of Jesus. Mythicists often claim that "brothers of the Lord" are simply a small group of high status Christians, not necessarily the literal siblings of Jesus.

So, how do you use Bayes' Theorem to sort this stuff out? What is the probability ratio that Paul was referring to a literal brother of Jesus? What is the numerical probability that there was a small group of Christian leaders separate from the apostles with the title, "brothers of the Lord"? How much weight do you give the patterns of Paul's use of the word "adelfos" relative to the weight you give to the known Christian myth that existed very shortly afterward concerning the brothers of Jesus? What is the probability estimate for Christians misinterpreting the status of these high-ranking Christians and changing them into literal brothers of Jesus? When the evidence is ambiguous and interpreted subjectively, then so will the probability estimates. If you can do it, then by all means go for it. I would love to see it done.

I am not saying that the concept probability has no place in historical debates. But, I much prefer probability

ranking, where estimates of probability for competing explanations are donerelativeto one another. One explanation for the evidence isbetterorworse thanthis other rival explanation. The rankings are necessarily ambiguous and subjective, and I do believe that very much follows from the evidence being inherently ambiguous and subjective--such is all language, especially ancient historical religious mythical language. That certainly isn't to say that one explanation is generally just as good as another. There are still ways to determine the rankings. As I alluded to before, I prefer the Argument to the Best Explanation, outlined on Wikipedia here.#4ApostateAbe wrote:The theorem is not really useful in a yes or no scenario. Obviously the odds are 50/50 on any given claim. The theory can, however, be applied to a broader questions that has more options for outcomes. For example, did Jesus, as the bible portrays him, walk the earth?

Here you have a number of options, all of which are supported by their own evidence adding probability. You can build mathematically on the main options. Let's say you consider:

Jesus is the son of god.

Jesus is the the son of a mortal

Jesus did not exist.

Jesus character was based on more than one person.

Now the probability that Jesus is the son of god is 25% or 1:4.

Of course they're not all equal in supported evidence, so this is where the theorem becomes a good tool to analytically asses the probability. Every piece of evidence would increase the odds of one being the case over others.

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc

#5Ktulu wrote:Great, that is a start. Obviously, we would not settle on the probability of each option being 100%/n. The probability of each option presumably would shift considerably depending on the nature of the explanations and the strengths of the arguments with respect to the evidence. So, how do we quantify those things? See if you can do it for the debate about James and Galatians 1:19.

#6You don't have to 'settle on' any specific values to apply Baye's theorem usefully.

It is useful wherever you have any desire to estimate probability where there are a series of interconnected assumptions, in calculating the effect of different estimates of the probability of each of the individual propositions. This allows you to find those factors which bear most strongly on the ultimate probability you are interested in.

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." -Sam HarrisThe path to Truth lies via careful study of reality, not the dreams of our fallible minds- meFrom the sublime to the ridiculous: Science -> Philosophy -> Theology

#7BobSpence1 wrote:Great. I don't know so much about how you would apply Bayes' Theorem, but I think that would make more sense. natural's explanation of Bayes' Theorem seems to require numerical probability estimates, which would seem to be a very bad start.

#8ApostateAbe wrote:You still require numerical estimates, just not required to settle on one. It only works with numerical values.

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." -Sam HarrisThe path to Truth lies via careful study of reality, not the dreams of our fallible minds- meFrom the sublime to the ridiculous: Science -> Philosophy -> Theology

#9BobSpence1 wrote:True, but you could have a set of agreed upon pieces of evidence. The whole system would still be subjective but less so than just intuition alone.

For example, you could consider 10 pieces of evidence that both parties would agree upon as having no reason to be false. Basically apply Occam's razor. Once the evidence has been gathered then you can consider the sum to be 100%, and count pro/con evidence to arrive at a percentage value.

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc

#10Ktulu wrote:Baye's theorem avoids any need to make yes or no decisions on which pieces of evidence to accept, and it then makes a more accurate calculation than a simple sum assumed to be 100%, especially if there is any level of connection or interdependence between different pieces of evidence.

You only need to apply various 'guesstimates' for each individual immediate interpretation from each piece of evidence, and see what that implies as to the likelihood of various possible conclusions.

For any given assessment of each piece of evidence, which will indeed typically be quite subjective, it calculates the precise implications of those assessments.Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." -Sam HarrisThe path to Truth lies via careful study of reality, not the dreams of our fallible minds- meFrom the sublime to the ridiculous: Science -> Philosophy -> Theology

#11I will believe it when I see it happen. Try applying Bayes' Theorem to help solve the debate about James and Galatians 1:19. That is maybe the simplest topic, and the debate compounds the complexity, but maybe exclude most of the points of evidence to keep it simple.

#12I would personally regard trying to resolve any of the mess that is Scripture as a total waste of time.

Just put it aside and move on to something that might have something useful/insightful/inspiring to convey.

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

The path to Truth lies via careful study of reality, not the dreams of our fallible minds- meFrom the sublime to the ridiculous: Science -> Philosophy -> Theology

#13ApostateAbe wrote:This wouldn't solve any debate, it will just calculate the odds of one outcome vs another, it's no different than saying that there is overwhelming evidence towards one outcome vs another. As bob pointed out, the value of the evidence is still subjective. What you can do, is give it a numerical value as in saying, the odds of this outcome is 1:4 vs this one being 1:6. It won't convince anyone

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc

#14OK, for anyone who does think that Bayes' Theorem is useful and relevant for debates about the origins of Christianity, the offer remains extended.

#15ApostateAbe wrote:For shits and giggles we can attempt it later tonight when I have more time.

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc

#16Ktulu wrote:Correct. They're getting waaaaaaaaaaaaay ahead of themselves if they try and use any sort of Bayesian logic, Boolean logic, or Fuzzy logic.

That's the part that theists

refuseto acknowledge, and try andjumpright over.It's a

dichotomyif god does/does not exist.Period.

The odds are

50/50that god does/does not exist.Noamount ofarguingis going to change that.None.Stringing together a number of

assumptionsisnotstrengthening a theory, in theslighest, because any additional assumptions are looked at assub-additive.The probability of 1 of the assumptions being accurate (true), is no greater than the sum of all the probabilties assumed (less than, or equal to, no better than 50/50). This is Boole's Inequality Theorum.

I keep asking myself " Are they just playin' stupid, or are they just plain stupid?..."

"To explain the unknown by the known is a logical procedure; to explain the known by the unknown is a form of theological lunacy" : David Brooks

" Only on the subject of God can smart people still imagine that they reap the fruits of human intelligence even as they plow them under." : Sam Harris

#17redneF wrote:I'm with redneF on this one, partly because I respect his judgement and partly because I'm too lazy to attempt something that seems futile, for the beauty of the exercise.

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc

#18Boole's Inequality Theorem in no way implies that all possibilities have an equal probability of being true, nor is there any other theorem that would imply such a thing. Evidence and the nature of the claims strongly affect values of probabilities, even if we can't properly mathematically quantify them. At the very least, we can conclude that some claims are far more likely than other claims. What is the probability that Santa Claus delivers presents to all the good little children of the world on Christmas Eve? 50/50?

#19ApostateAbe wrote:That's not what the theorum addresses. It's a 'realization' than assumptions are as likely to be

incorrect, as they are likely to be correct.It addresses 2 things.

1- That with any a priori either/or assumption, the odds are no better than 50/50 either way, no matter how much you 'argue'.

2- That additional a priori either/or assumptions, will make the entire set of a priori assumptions lesser than, or equal to no better than 50/50, no matter how much you argue.

ApostateAbe wrote:That's a perfect example.

Someone assumes or argues that they 'believe' Santa Claus is/was (possibly and probably) real.

It's equally possible/probable that he is not (or was not) real.

The salient point being, that theists can 'argue' as

muchas they want, about the 'truth'that a god exists, but they areequallyas likely to be completely mistaken, because what they have is a 'belief' (hope), and not any 'evidence'( solid reasoning).Which translates into the

mostsensible position is to remain 'neutral' about what the 'truth' is, since there is no evidence, either way.I keep asking myself " Are they just playin' stupid, or are they just plain stupid?..."

"To explain the unknown by the known is a logical procedure; to explain the known by the unknown is a form of theological lunacy" : David Brooks

" Only on the subject of God can smart people still imagine that they reap the fruits of human intelligence even as they plow them under." : Sam Harris

#20There is an old and highly apocryphal story about proving the existence of God using mathematics.

The French philosopher Denis Diderot was visiting Russia on Catherine the Great’s invitation. However, the Empress was alarmed that the philosopher’s arguments for atheism were influencing members of her court, and so Euler was asked to confront the Frenchman. Diderot was later informed that a learned mathematician had produced a proof of the existence of God: he agreed to view the proof as it was presented in court. Euler appeared, advanced toward Diderot, and in a tone of perfect conviction announced, “Sir, (a+b

^{n})/n = x, hence God exists—reply!”. Diderot, to whom all mathematics was gibberish, stood dumbstruck as peals of laughter erupted from the court. Embarrassed, he asked to leave Russia, a request that was graciously granted by the Empress.Of course, the equation was nothing but bluster, but Diderot supposedly knew nothing about algebra, so he could do nothing but accept defeat. Historically, Diderot was a very well-versed mathematician, and this story was therefore completely made up, but it does illustrate some important truths--mathematical arguments seem much more authoritative, even when it is applied in places that it most certainly does not belong, and especially when you can't make good sense of mathematics.

Richard Carrier was not the first to try to convince people that we should be applying probability theories to decide conclusions for complex topics of history. William Lane Craig was in a debate with Bart Ehrman recently, and Craig brought up Bayes' Theorem to assert that he could prove the probability of the resurrection of Jesus. Bart Ehrman, who specialized in the field of New Testament history, mocked it and laughed at it, for good reason. Craig never provided any numerical values, and he never actually specifically applied the equation for his arguments. He merely presented the equation as a way to give his arguments an air of authority. How do you fairly estimate the probability of a miraculous event? Sure, reasonable people know that miracles are the most improbable explanations that we can conceive of, but one's perspective on miracles will be far different if you are convinced of the relative probability of miracles, such as through going to a Pentecostal church every Sunday when seeming "evidence" for miracles is recounted and put on display in every sermon. Any numerical estimate we place on the probability of any miraculous event--or any historical explanation, for that matter--will depend very much on our own personal judgment. Small pieces of evidence can drastically shift the probability of an explanation from improbable to very probable--but by how much exactly? How do you go about deciding those values?

Until Richard Carrier or anyone else provides a specific demonstration of applying Bayes' theorem for deciding any historical conclusion, and it is reviewed by people who know both the history and the math, my advice is: don't buy it.

#21redneF, I don't know if I understand your perspective correctly, because it seems damned ridiculous, and I am thinking that I am probably missing something. You apparently think that there is a 50/50 chance that Santa Claus delivers presents to all of the good children of the world on Christian Eve. 50% is a considerably high probability. Have you thought about getting a video camera and staying up all night in a good child's house on Christmas Eve so you can very potentially catch footage of Santa Claus?

#22Boole's inequality theorem does not imply anything about probabilities of unspecified events being '50/50'. It just sets an upper limit, which is based on the estimated probabilities of the individual events.

'50/50' only applies if we know absolutely nothing about the likelihood of either of two events other than that one, and only one, must be true. Any information bearing on the likelihood of either proposition being the 'true' one will likely shift it away from 50/50.

When we are considering the existence or otherwise of an imagined entity that stretches or violates well-established understanding of reality, such as a God, we can be pretty confident the possibility of existence is way below 50%, although it is true that it would be hard to put a figure on it.

If you allow for the infinite array of 'possible' Gods implied if you assume the 'supernatural', then the likelihood of any specific God is essentially zero...

Now can we go on to something more potentially useful, such as establishing how many angels can dance on the head of a pin?

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

The path to Truth lies via careful study of reality, not the dreams of our fallible minds- meFrom the sublime to the ridiculous: Science -> Philosophy -> Theology

#23ApostateAbe wrote:It means if you are playing a shell game with 2 shells, your odds of picking the 1 with the white ball inside it, are no better than 50/50, because you can

onlymake anassumption.You

cannotlogically deduce, andimproveyour odds.Theists are claiming they'

logically deduced'how the universe was formed, without every having seen a universe formed.Boole's Inequality demonstrates that they are (at the very least)

justas likely, to be wrong, as they are, to be right.50/50

Which means, that there is

noburden on anyone who dismisses their claims as beinghighlyunlikely.And why is it completely

irrationalto try andshiftburden on anyone todisprovea positive claim that is just as likely to be false, as it could be at being true.I've often used the example of how it was

assumed(for thousands of years) that'what goes up, must come down'.It

wascompletelylogicalto deduce that, from reality that it was 100% accurate that'what goes up, must come down'.But, it was an

assumption,and it waswrong.In reality, the odds were that it was just as likely to be innacurate, as it was to be accurate.

I've also used the example of 'Fool's Gold'.

How many people

assumedthat the gold colored nuggets they found were 100% sure to be gold?Bottom line.....anyone who tells you they know the 100% 'truth' about how the universe was formed, is:

1- A liar

2- A fool

3- Has at

least,a 50% chance of being completelywrongI keep asking myself " Are they just playin' stupid, or are they just plain stupid?..."

"To explain the unknown by the known is a logical procedure; to explain the known by the unknown is a form of theological lunacy" : David Brooks

" Only on the subject of God can smart people still imagine that they reap the fruits of human intelligence even as they plow them under." : Sam Harris

#24redneF, I would still like to know how you think about Santa Claus. Have you thought about setting up a video camera on a tripod in front of the fireplace on Christmas Eve, putting it on "record," and seeing if you get lucky and catch footage of Santa Claus? It is a 50/50 probability after all. Can you explain to me where I have gone wrong with such a proposition?

#25Boole's inequality, applied to the case where there are only two possibilities, simply says that the probability of either event occurring cannot exceed the sum of their individual probabilities, which in this case is

100%.It does not lead to '50/50', it simply says that the possibility cannot exceed 100%. D'uh.

Boole's inequality is not very useful in this case. It becomes useful where we have multiple possible events, which may or may not exhaust the possibilities, as a way of setting bounds.

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

The path to Truth lies via careful study of reality, not the dreams of our fallible minds- meFrom the sublime to the ridiculous: Science -> Philosophy -> Theology

#26Santa Claus is more manageable probabilistically than 'God' - at least he doesn't presume any infinities.

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

The path to Truth lies via careful study of reality, not the dreams of our fallible minds- meFrom the sublime to the ridiculous: Science -> Philosophy -> Theology

#27ApostateAbe wrote:You've gone wrong because you

gavethe benefit of the doubt, to something (Santa Claus existing) that had (at minimum) 50% chance of being incorrect.How

couldyou believe that Santa Clauscouldbe real, to begin with?I keep asking myself " Are they just playin' stupid, or are they just plain stupid?..."

#28ApostateAbe wrote:I wouldn't do that if I were you, if Santa finds out... you get a dildo shaped piece of coal. The futility of applying mathematics to proving the historicity of Jesus, rests in the subjective way we rate each piece of evidence. In order for this to work we have to create an objective rating system, that both parties in a debate agree upon. We need a preset amount of pieces of evidence. And then you just let the numbers do the work.

So, for example. We agree that we can use 10 pieces of evidence, five each. We also agree that we can rate these pieces of evidence from 1 to 10.

1. Jesus walked the earth because the bible says he did. Well I would rate that at 1 you will most likely rate it at 10 so we agree on 5.

2. No comprehensive historical account of Jesus is offered. I would rate that as 10 you as 1, again 5....

point is, it's all subjective, it's not going to change anyone's mind. If you get 5 pieces of evidence and I get 5, we're going to rate each one the highest, otherwise you lose the argument. As a result the odds are 50/50 which is silly.

We can apply the same methodology to Santa Claus and we would deduce a 50/50 chance that Santa shows his fat ass on camera. He's not getting any fucking cookies from me this time.

"Don't seek these laws to understand. Only the mad can comprehend..." -- George Cosbuc

#29Continued in Part 2!