Ch. 6: The Prior Probability (On the Historicity of Jesus by Richard Carrier)

[Tim Hendrix]

Well, I am aware that Carrier writes that. Here is the example I had in mind: Carrier defines h as the hypothesis that Jesus existed (OHJ, p. 30). Then ~h would (formally) be the logical negation of h, however in OHJ "~h" is defined as the list of propositions in OHJ, p.53. From a formal point of view, that is false as the list of propositions are not logically equivalent to the negation of h. Carrier is aware of this abuse of notation and mentions it in OHJ.

This is getting repetitive. I already showed here that this is not false because Carrier does not need mythicism [according to Carrier's hypothesis] to be logically equivalent to the negation of historicity [according to Carrier's hypothesis]. He only needs it to be numerically equivalent. He has clearly stated the assumptions he makes that make this true. So there is no formal error. You responded to me saying you agreed. And now you are back claiming he made a formal error.

I am a bit lost for words here. An example of a formal error is when you use a mathematical symbol or rule different from it's definition. For instance, if I say that 2 + 2 = 5 that is a formal error because that is not how "+" is defined for integers.
The negation of a proposition means something particular in Boolean logic. When Carrier writes "~h", but defines that as something else than the negation of h, that is a formal error according to my above description of what a formal error is. You can claim something is not a formal error if, in subsequent computations, it has no effect. For instance, you could say that 2+2=5 assuming it was part of some computation where it would not matter if we used 4 or 5 in terms of some goal or pragmatic consideration --- however, you would be completely alone in that definition of what it means to be formally correct or not.
As a further point, I suggest you are affected by confirmation bias if you are seriously arguing that it is formally correct to re-define the rules of Boolean logic so as to maintain OHJ are free of formal inaccuracies.

The use of a particular theory of historicity, therefore (plausibly) affect all terms in the computation as I think it is self-evidently true elements of the 5-point hypothesis make some of the evidence easier to explain. For instance, it is easier to explain the gospels (stories of a man on earth) if you assume that early Christian communities believed in such a man on earth than if you do not make such an assumption. The use of a particular hypothesis (rather than a specific) must carefully be accounted for when the prior is estimated and therefore any issues with the prior potentially bias the entire computation.

Bias the computation? How? Yes, obviously if your hypothesis is: "Some people believed that Jesus was a man" that explains stories of a man called Jesus better than if your hypothesis is "Bread is a planet made of jellyfish".

I have explained how it bias the computation several times here and elsewhere. Please notice you are again changing my argument to something ridiculous: I claim (or rather, propose) that the assumption "Later Christian communities came to believe (or teach) Jesus was a historical person" better explains stories about a historical Jesus than the bare assumption that "originally Jesus existed". You can disagree with that suggestion and I am rather convinced I can't change your mind one bit, however, I am still free to point out the consequences of such an assumption being true.

I am happy you bring up a concrete example we can discuss. The problem with your example is that you are not using Carriers estimates of the probabilities, but rather consider another, unrelated, example. If we use the actual computation Carrier uses, and your way of defining "bias" as additive, then it does invert the conclusion. I think this graph is correct but be aware I have not checked it very well:

You could at least check it well enough to see that neither Bob or Sue appear in Carrier's estimates of the probabilities or in his computation. I'm using Carrier's formula in the same way he uses it. If I use Carrier's numbers, of course, I will get Carrier's results. We can't use his numbers because we do not know what the correct estimates of the probabilities are. So I use a thought experiment of a hard case where we know the correct estimates, which allows us to see the effect of error and bias.

What do you mean that Bob or Sue does not appear in his estimates?.
You are using a formula structured as Carriers, but with completely different numbers. If you want to examine the effect of systematic bias on Carriers computations then at the very least the case of no bias has to agree with Carriers numbers!.
Your example is like studying the effect of having unusually heavy cars pass over a bridge, and then starting out by assuming each car weights 5kg and conclude that a 5% increase in the cars weights have no effect -- if you allow yourself to replace Carriers numbers by something completely different to prove a point about small changes in Carriers numbers then, well, I don't know what to say.

But I think I can see what you're doing: you're simply assuming that every argument Carrier uses is always wrong, therefore the more arguments that are brought into the discussion, the more wrong Carrier is, and the more certain can we be that the opposite of what Carrier argues must be correct.

You claim to not have read what I am actually doing and then you proceed to argue from your strawmen. I agree: If my claims were anything like that they would have no validity, however, I have never said any such thing. Studying bias simply means studying what happens if we are systematically too optimistic or too pessimistic in terms of the numerical stability of the computation.

In this example they are guessing that the probability that a newborn baby is female is described by a binomial model. This is a good enough guess for most purposes, but it is not precisely true. In reality, it is much more complicated than that. Indeed, it is in the modelling that the guesswork usually happens. It's no different for Carrier.

I do not claim statistics (as all science) is not based on assumptions. I claim those assumptions are of a very different nature. The example should make that evident as rather than guessing the terms in the likelihood, the model introduces a parameter that describes the probability of the two outcomes that are being modeled, i.e. as for the likelihood there is no guesswork aside the initial assumption that such a parameter exists and an exchangeability assumption. That, by the very nature, is different from what Carrier is doing. If you wish to say two examples of applied math make assumptions of the same validity if just they both make assumptions I don't think you understand what applied math is.

On to Carrier. Carrier claims that the highest, and lowest, estimate of the probability of the Gospels agree (i.e. the ratio is 1 in both cases). That is what I don't think is fair.

Then make an argument for that. Someone might say that kittens are a valid argument. It is clearly not Carrier's job to make everyone elses argument for them. He is simply stating which probabilities he personally finds to be within reason.

How about the person who makes the rather remarkable claim the upper and lower bounds exactly agree provides the argument? I did, by the way, provide reasons, namely that people such as your or scholars like Ehrman assigns a wider range to these values. This is again like looking at a tree and saying: I think the ratio of the trees weight to its height is 0.1. And the upper limit of that value is 0.1, and the lower limit is 0.1. The person who makes such a claim surely bear the burden of proof even if I cannot say exactly what those limits are.

I have at all times recognized that these statements are about ratios, simply see my very own quote above where I state exactly that. What Carrier assumes is that the ratio of P(Gospels|h) / P(Gospels|~h) = 1 in both the optimistic and pessimistic scenario. Mathematically that is equal to the assumption P(Gospels|h) = P(Gospels|~h) in both the optimistic and pessimistic scenario.

What this means is simply that Carrier has not found any argument that he believes holds any water for why the Gospels would either prove or disprove historicity. Now, if you think there is any argument that he has either overlooked, or that he is treating wrongly, then it is very easy for you to put in some different numbers, and Carrier is inviting you to do exactly that. But, really, you need to bring some argument, and it should better be one that Carrier hasn't already treated (or a rebuttal to his counter-arguments, etc).

See my above answer: Your assertion here is equivalent to saying that if you can provide no arguments for why the trees height/weight ratio should be above 0.1, or below 0.1, I am justified in claiming the upper and lower limit coincide. Meanwhile, experts believe those ratio takes a wide range of values, as do even yourself do. You are simply shifting the burden of proof onto me to prove Carriers subjective estimate wrong even while you yourself say Carriers subjective estimate likely is wrong(!).

(...)Your simulations do not use his probabilities as you write yourself, mine does. If we do use Carriers probabilities, your conclusion simply does not hold as you can check yourself. Once again I stress this is a basic point of error analysis.

It's not error analysis at all, but just bogus numbers thrown into a hat. If you apply that 'method' to any subject, you will find that the more reasons we actually have to believe that something is true, the more easily we are just victims of bias. If we have 1000 independent samples of DNA from the crime scene, analyzed by 1000 different labs, well, then in your model that makes the conclusion more uncertain than if we have only 1 sample, because any 'bias' will inflate the error.

Firstly, it boggles the mind you can so flatly accuse me of using "bogus numbers" when I use Carriers exact numbers and you do not.

Secondly, You are simply asserting your DNA example agrees with your conclusion with absolutely no reasons given. To substantiate your claim about the DNA example you would first have to provide a relevant statistical analysis of the DNA example, define Bias in that context and show the effect you speak of is true. I hope you will try to do this as I am sure you will learn relevant differences in how statistics are applied to DNA compared to how Carrier applies it.

One such difference is that the frequency of the alleles used in DNA evidence is something that is estimated reliably and with quantifiable errors. In other words, this alone put us outside the realm of simply guessing the various factors as in OHJ. Now, you can claim that statistical analysis is still based on some assumptions: True, but again those assumptions can be examined experimentally, they do not take the form of one long sequence of "My subjective estimate of the probability of X is ...".

[Harry Marks]

I think those are the kinds of perspectives which mainline historians (e.g. Ehrman) have treated as most credible.

Ehrman is simply not an historian at all. He is a theologian by education, degree and publication history.

Fair enough. I retract my use of the title, with apology. His assessment on historicity, however, aligns with typical historians of the period and topic, though I would not argue that there are no respected dissenters.

I am an economist. When we overlap with a field, such as psychology or history, then we are usually pretty scrupulous about policing the boundaries by disciplinary qualifications and background. However, the arguments given are fair game for anyone with relevant material to add. And an expert in a relevant area may be able to assess a topic more sensibly than others with disciplinary qualifications but no mastery of the relevant details.

Scholars who are familiar with the Near East of the time, and with the relevant languages and evidence about available texts, may have more to contribute on a topic than scholars whose training is more appropriate in use of technique but who have not familiarized themselves with the specifics of the topic.

[Tim Hendrix]

I think those are the kinds of perspectives which mainline historians (e.g. Ehrman) have treated as most credible.

Ehrman is simply not an historian at all. He is a theologian by education, degree and publication history.

Fair enough. I retract my use of the title, with apology. His assessment on historicity, however, aligns with typical historians of the period and topic, though I would not argue that there are no respected dissenters.

I am an economist. When we overlap with a field, such as psychology or history, then we are usually pretty scrupulous about policing the boundaries by disciplinary qualifications and background. However, the arguments given are fair game for anyone with relevant material to add. And an expert in a relevant area may be able to assess a topic more sensibly than others with disciplinary qualifications but no mastery of the relevant details.

Scholars who are familiar with the Near East of the time, and with the relevant languages and evidence about available texts, may have more to contribute on a topic than scholars whose training is more appropriate in use of technique but who have not familiarized themselves with the specifics of the topic.

Regarding this issue of Ehrman not being a historian, what I keep thinking is that if we agree Ehrman not being a historian mean we should not put much weight in what he has to say about history, would that not imply we should not trust Carrier that much on probability theory?

The difference is, of course, that when Ehrman writes on history he is making unremarkable claims from the perspective of mainline history (insofar as I know). Carrier, on the other hand, claims to offer a new foundation of probability theory (his version of frequentism; this is a claim based on him not understanding what a foundation of probability theory is and I am certainly not the only one with that opinion) and applies BT in ways that other experts believe is misleading.

So does a degree matter or does it not?

[JohanRonnblom]

An example of a formal error is when you use a mathematical symbol or rule different from it's definition. For instance, if I say that 2 + 2 = 5 that is a formal error because that is not how "+" is defined for integers.
The negation of a proposition means something particular in Boolean logic. When Carrier writes "~h", but defines that as something else than the negation of h, that is a formal error according to my above description of what a formal error is.

In my view, a formal error is something beyond just a spelling error or some other minor mistake that is of no consequence.

To say that 2+2 = 5 would result in serious confusion (at best). In this case, what you refer to is probably that carrier writes [OHJ p. 30]:
2. ¬h = 'Jesus was a mythical person historicized'
when, to be perfectly clear and correct, he could have written something like:
2. m = 'Jesus was a mythical person historicized', m = ¬h

But since Carrier is clearly explaining why, according to his clearly made assumptions, 'Jesus was a mythical person historicized' really is equal to ¬h, the omission of an intermediary such as m is obviously not of any consequence.

This is an example of nitpicking in the extreme, and it is usually a sign that someone is desperate to find 'errors' in a text, rather than trying to contribute something of value.

There is no doubt that OHJ is in some parts painfully poorly edited and has serious layouting errors that make some sections much more difficult to understand than they should have been. I mention some of this in my review of the book btw.

Please notice you are again changing my argument to something ridiculous: I claim (or rather, propose) that the assumption "Later Christian communities came to believe (or teach) Jesus was a historical person" better explains stories about a historical Jesus than the bare assumption that "originally Jesus existed".

And this would be relevant exactly how? You can have any assumptions you like. If you make unreasonable assumptions without giving evidence, people will not find your reasoning convincing. But as long as your assumptions are reasonable, there is no problem here.

What do you mean that Bob or Sue does not appear in his estimates?.
You are using a formula structured as Carriers, but with completely different numbers. If you want to examine the effect of systematic bias on Carriers computations then at the very least the case of no bias has to agree with Carriers numbers!.

If you are arguing that Carrier is biased, it makes no sense to construct an argument assuming that he is not biased (unless it is an argument ad absurdum, which this is not).

I can put Carrier's numbers into my simulation but the graphs will basically look the same. This is because we are examining different things. I am examining what happens when we add more evidence to resolve disagreements in the presence of bias and error.

You are examining what happens when someone is really, really wrong. Your conclusion is that if someone is sufficiently wrong on every argument, they will also be wrong on the conclusions. This is painfully obvious without any use of mathematics or Bayes' Theorem whatsoever. If you want to claim that this is a property of Bayes' Theorem, or Carrier's use of it, then tell me: what alternative method could someone who is wrong on all the arguments use to arrive at the correct conclusion?

Your example is like studying the effect of having unusually heavy cars pass over a bridge, and then starting out by assuming each car weights 5kg and conclude that a 5% increase in the cars weights have no effect -- if you allow yourself to replace Carriers numbers by something completely different to prove a point about small changes in Carriers numbers then, well, I don't know what to say.

Nope. You clearly have not even looked at the x-axis of my graphs.

I do not claim statistics (as all science) is not based on assumptions.

Actually, you did.

I claim those assumptions are of a very different nature. The example should make that evident as rather than guessing the terms in the likelihood, the model introduces a parameter that describes the probability of the two outcomes that are being modeled, i.e. as for the likelihood there is no guesswork aside the initial assumption that such a parameter exists and an exchangeability assumption. That, by the very nature, is different from what Carrier is doing. If you wish to say two examples of applied math make assumptions of the same validity if just they both make assumptions I don't think you understand what applied math is.

There is no difference in nature. For something such as the sex of newborns, we certainly have a lot more data and the ability to conduct experiments to see to which degree a certain model fits actual outcomes. But it really is the same thing: based on some observations, we 'guess' at some mathematical representation of reality. Further observations, or reinterpretation of the data, could be used by others to claim that our model is wrong. Of course, Carrier uses an extremely simple model: it's just a number. Something like a binomial model is obviously much more complex, and therefore in itself a more risky guess to make. But, because the available data is much better, we can easily show that this is warranted.

In any way, Carrier is not doing anything different than other historians here. Pick any disagreement among historians you like, you certainly won't see many cases of historians constructing some advanced mathematical model. Rather, they evaluate the evidence and weigh them together into a conclusion. This is usually the best we can do in history.

How about the person who makes the rather remarkable claim the upper and lower bounds exactly agree provides the argument?

He does, read the book!

I did, by the way, provide reasons, namely that people such as your or scholars like Ehrman assigns a wider range to these values.

Then if you think Ehrman makes any valid points not refuted by Carrier, please bring them up. Because if he does not, then it would be wrong for Carrier to have a wider range.

Again, imagine that someone claims arsenic is healthy because kittens are cute, and also because puppies are cute, and capybaras are cute, and so forth. Yes, we will dismiss all these arguments. We will say that the reasonable upper and lower bounds of probabilities here on both hypotheses is 1. You can't just, without arguments, claim that we should really allow some range of 'uncertainty', without any argument for that. Because that would just allow us to invalidate any conclusion by adding enough spurious arguments. No, to warrant a range, there needs to be an argument, and we have to judge that argument as having at least some merit.

See my above answer: Your assertion here is equivalent to saying that if you can provide no arguments for why the trees height/weight ratio should be above 0.1, or below 0.1

We just fundamentally disagree about the merits of these hypothetical arguments against Carrier. You assume that they are strong. But you have not brought any of these arguments up. That is like assuming the planet Mars really could be made of chocolate so we should not assume it isn't, because someone out there may have an argument supporting this theory.

No, we should not leave any room for hypothetical arguments that theoretically could exist but which we have not, despite careful examination, been able to find.

Secondly, You are simply asserting your DNA example agrees with your conclusion with absolutely no reasons given. To substantiate your claim about the DNA example you would first have to provide a relevant statistical analysis of the DNA example, define Bias in that context and show the effect you speak of is true. I hope you will try to do this as I am sure you will learn relevant differences in how statistics are applied to DNA compared to how Carrier applies it.

Yes, and you are simply asserting that Carrier might be biased. This is like the accused person in the trial jumping up and down and screaming "but all the 1000 DNA samples might be biased!". Ok, it could be true. But you need arguments for that. When you do not provide any arguments. Your 'analysis' only shows that if someone is wrong, then they are wrong. Which is trivially true, and equally so for Carrier, Ehrman, me and you. It has no relevance at all to OHJ.

[JohanRonnblom]

Regarding this issue of Ehrman not being a historian, what I keep thinking is that if we agree Ehrman not being a historian mean we should not put much weight in what he has to say about history, would that not imply we should not trust Carrier that much on probability theory?

No one said we should not put much weight in what Ehrman says. However, misrepresenting someone's competence is not trivial. Even less so in this case because on this issue non-historians are very frequently said to be historians. This happens often enough that it cannot really be a random mistake.

Moreover, I certainly would not recommend someone to read Carrier for learning about probability theory. In that case you should read a book written by an expert on that subject. Carrier has written a book (Proving History) on applying probability theory to history. It is a much better (and shorter) read than OHJ and I would recommend it, because it might inform you about what Carrier is doing and why.

The difference is, of course, that when Ehrman writes on history he is making unremarkable claims from the perspective of mainline history (insofar as I know).

Then you know absolutely nothing. There is virtually no scholar out there who agrees very much with Ehrman. Sure, you can find someone agreeing on some point here, some point there. But he is definitely highly controversial. As are, in fact, all authors in this genre.

[JohanRonnblom]

His assessment on historicity, however, aligns with typical historians of the period and topic, though I would not argue that there are no respected dissenters.

It does? Can you name one of these 'typical' historians who agree with Ehrman? I would be very interested in reading any article or monograph written by such a scholar on this topic. Something peer-reviewed would be preferable, but really anything satisfying minimal standards of publication would do.

I will warn you however that I have been searching for over ten years for such a scholar, and have not been able to find one.

[Tim Hendrix]

An example of a formal error is when you use a mathematical symbol or rule different from it's definition. For instance, if I say that 2 + 2 = 5 that is a formal error because that is not how "+" is defined for integers.
The negation of a proposition means something particular in Boolean logic. When Carrier writes "~h", but defines that as something else than the negation of h, that is a formal error according to my above description of what a formal error is.

In my view, a formal error is something beyond just a spelling error or some other minor mistake that is of no consequence.

To say that 2+2 = 5 would result in serious confusion (at best). In this case, what you refer to is probably that carrier writes [OHJ p. 30]:
2. ¬h = 'Jesus was a mythical person historicized'
when, to be perfectly clear and correct, he could have written something like:
2. m = 'Jesus was a mythical person historicized', m = ¬h

Once more you are simply ignoring what is actually in OHJ. As I already wrote: ~h is not simply "Jesus was a mythical person historizised", but rather "~h" is defined as the list of propositions in OHJ, p.53. By that definition "~h" is not the negation of h. This is not formally correct because it violates how the negation operator functions in Boolean logic. Now, you can adopt another standard of what a formal error is and in that case we must just agree to disagree:

IF it is not a formal error to use a mathematical symbol different from how it is defined THEN OHJ is free of formal errors.

One question though: I assume you have/are taking classes at a university, was that the standard that you were made familiar with in your introductory math course?

This is an example of nitpicking in the extreme, and it is usually a sign that someone is desperate to find 'errors' in a text, rather than trying to contribute something of value.

There is no doubt that OHJ is in some parts painfully poorly edited and has serious layouting errors that make some sections much more difficult to understand than they should have been. I mention some of this in my review of the book btw.

Rather than nicpicking, I was answering your point about formal errors and asides correcting the notation I don't have much to say about the misuse of the negation operator. But let us summarize: Every single conclusion I write is wrong (for so far undisclosed reasons), and I am nitpicking by pointing out the negation operator is used incorrectly. However, you are providing an apt critique by discussing the layout of the book. Oh dear.

Please notice you are again changing my argument to something ridiculous: I claim (or rather, propose) that the assumption "Later Christian communities came to believe (or teach) Jesus was a historical person" better explains stories about a historical Jesus than the bare assumption that "originally Jesus existed".

And this would be relevant exactly how? You can have any assumptions you like. If you make unreasonable assumptions without giving evidence, people will not find your reasoning convincing. But as long as your assumptions are reasonable, there is no problem here.

That would be relevant because of stories of Jesus, and how easily they are explained by the two hypothesis, directly influence Carrier's numerical result.

What do you mean that Bob or Sue does not appear in his estimates?.
You are using a formula structured as Carriers, but with completely different numbers. If you want to examine the effect of systematic bias on Carriers computations then at the very least the case of no bias has to agree with Carriers numbers!.

If you are arguing that Carrier is biased, it makes no sense to construct an argument assuming that he is not biased (unless it is an argument ad absurdum, which this is not).

I can put Carrier's numbers into my simulation but the graphs will basically look the same. This is because we are examining different things. I am examining what happens when we add more evidence to resolve disagreements in the presence of bias and error.

I am investigating how a slight bias affects Carrier's computations according to which no bias, of course, must agree with Carriers numbers. Also, your graphs will not look the same using the same numbers I use (i.e. Carriers numbers from OHJ).

What you are doing is that you are examining what happens if we consider a completely separate situation in which we add pieces of evidence that each confirms a particular conclusion, and then you compare that to a similar situation where each piece of evidence confirms the conclusion albeit slightly less strongly: Of course in both cases the conclusion is confirmed as more evidence is added; this has nothing to do with the numerical stability of Carriers computation as you are simply never using his numbers.

I do not claim statistics (as all science) is not based on assumptions.

Actually, you did.

Well, then I was wrong. However, I am interested in the quote because I suspect another reading issue.

I claim those assumptions are of a very different nature. The example should make that evident as rather than guessing the terms in the likelihood, the model introduces a parameter that describes the probability of the two outcomes that are being modeled, i.e. as for the likelihood there is no guesswork aside the initial assumption that such a parameter exists and an exchangeability assumption. That, by the very nature, is different from what Carrier is doing. If you wish to say two examples of applied math make assumptions of the same validity if just they both make assumptions I don't think you understand what applied math is.

There is no difference in nature. For something such as the sex of newborns, we certainly have a lot more data and the ability to conduct experiments to see to which degree a certain model fits actual outcomes. But it really is the same thing: based on some observations, we 'guess' at some mathematical representation of reality. Further observations (..)

Well, you write the difference in nature yourself in that quote: We have data (i.e. replicated observations) and we have the ability to perform experiments and validate the model by observing how it fit future data, and finally "actual outcomes" that can be observed.

If you belive we have something similar from Carriers computation, i.e. that the two situations are not different, can you please tell me how as for the historicity of Jesus I would go about obtaining new data, how we can make predictions to see how the model fit actual outcomes and what those future outcomes are. And please don't change the meaning of those words as you provide such examples.

In any way, Carrier is not doing anything different than other historians here (..) you certainly won't see many cases of historians constructing some advanced mathematical model.

So Carrier is doing nothing different than other historians...but he is doing something different.

He is doing something quite different from e.g. what Aviazer Tucker is doing in his book on applying BT to the historical method (which is the only other book I have read or know of that discusses the historical method and BT. Have you read it?), and he is certainly doing something very different from statistics which is my claim.

Again, imagine that someone claims arsenic is healthy because kittens are cute, and also because puppies are cute, and capybaras are cute, and so forth. Yes, we will dismiss all these arguments. We will say that the reasonable upper and lower bounds of probabilities here on both hypotheses is 1.

I can't tell which probabilities you are referring to here.

See my above answer: Your assertion here is equivalent to saying that if you can provide no arguments for why the trees height/weight ratio should be above 0.1, or below 0.1

We just fundamentally disagree about the merits of these hypothetical arguments against Carrier. You assume that they are strong. But you have not brought any of these arguments up. That is like assuming the planet Mars really could be made of chocolate so we should not assume it isn't, because someone out there may have an argument supporting this theory.

Whenever you want to write "that is like", please pause and consider if what you are thinking off bear any resemblance at all to what the other person is saying.

You yourself believe that the upper and lower bounds disagree with respect to the gospels (i.e. your previous argument that the Gospels could be seen as providing evidence in favor of mythicism, "I also think that it is possible to conclude something using evidence from the Gospels..."). In conclusion, you are at the same time claiming that the upper and lower bounds agree and if I want to claim anything else I better damn well provide a bullet proof argument simultaneous asserting these limits disagree on your view. Now only is this shifting the burden of proof, it is a gigantic double standard.

Secondly, You are simply asserting your DNA example agrees with your conclusion with absolutely no reasons given. To substantiate your claim about the DNA example you would first have to provide a relevant statistical analysis of the DNA example, define Bias in that context and show the effect you speak of is true. I hope you will try to do this as I am sure you will learn relevant differences in how statistics are applied to DNA compared to how Carrier applies it.

Yes, and you are simply asserting that Carrier might be biased. This is like the accused person in the trial jumping up and down and screaming "but all the 1000 DNA samples might be biased!". Ok, it could be true. But you need arguments for that. When you do not provide any arguments. Your 'analysis' only shows that if someone is wrong, then they are wrong. Which is trivially true, and equally so for Carrier, Ehrman, me and you. It has no relevance at all to OHJ.

If a person wished to discuss bias in the context of a trial case he would have to go into the relevant computation, define what bias means, argue which of the terms could potentially be affected by bias and show how that affects the computation in terms of numerical stability.
I have argued why the terms can be affected by bias (we have no external means of checking them and they relate to our subjective judgement), you yourself seemed to accept that bias could exist in such subjective judgements, and I have provided a computation, using Carriers numbers, to show the numerical stability of the result in the presence of Bias. Now I simply ask you to do so yourself in the DNA example if you feel they are actually similar.

[Tim Hendrix]

Moreover, I certainly would not recommend someone to read Carrier for learning about probability theory. In that case you should read a book written by an expert on that subject.

When is a person considered an expert in your view?

Carrier has written a book (Proving History) on applying probability theory to history. It is a much better (and shorter) read than OHJ and I would recommend it, because it might inform you about what Carrier is doing and why.

I have read it quite careful and written about my opinion of it elsewhere.

Can you name one of these 'typical' historians who agree with Ehrman? I would be very interested in reading any article or monograph written by such a scholar on this topic. Something peer-reviewed would be preferable, but really anything satisfying minimal standards of publication would do.

Well, I will be happy to try. But just so I know what I should look for can you say what you use as the definition of a typical historian in this context?

[JohanRonnblom]

Once more you are simply ignoring what is actually in OHJ. As I already wrote: ~h is not simply "Jesus was a mythical person historizised", but rather "~h" is defined as the list of propositions in OHJ, p.53. By that definition "~h" is not the negation of h.

There is no ¬h on page 53. I don't know if you're pretending to be stupid in order to find "errors", or if you're really not getting it.

This is what needs to be done to fix it: On page 30, where it appears to define ¬h and also ¬h0 (which is not occurring beyond this page), it really should not use the ¬ symbol without an intermediary clarifying step. Rather, he could call his "¬h" say m and his "¬h0" m0. Then, he should go on to say that because of his assumption that h0=m0=0, it turns out that m = ¬h0. That is all we need to do to clarify this. Nothing on page 53 or any page beyond page 30 is affected by this in any way.

One question though: I assume you have/are taking classes at a university, was that the standard that you were made familiar with in your introductory math course?

It would definitely render a reduction in points, but since it does not affect the overall calculation in any way this reduction would be minor.

But really, I'm not interested in debating spelling errors or bad layout or whatever. I think it is quite obvious that you are wasting your time on such trivial nonsense because you know you have no real arguments here.

However, you are providing an apt critique by discussing the layout of the book. Oh dear.

Well, the layouting issues are simply much more relevant since they actually make the book significantly harder to understand.

That would be relevant because of stories of Jesus, and how easily they are explained by the two hypothesis, directly influence Carrier's numerical result.

Yes of course they would. Of course he wants to use good hypotheses rather than bad ones. It seems to me that you are accusing Carrier of cheating because he has chosen sensible hypotheses to defend, thus making his case easier!

this has nothing to do with the numerical stability of Carriers computation as you are simply never using his numbers.

This has nothing to do with numerical stability, period.

Well, you write the difference in nature yourself in that quote: We have data (i.e. replicated observations) and we have the ability to perform experiments and validate the model by observing how it fit future data, and finally "actual outcomes" that can be observed.

How is that a difference in nature? True, it is rare that we find a stash of new documents such as the Nag Hammadi scrolls, Dead Sea scrolls etc. But it happens. But we also get new data from other discoveries such as people finding errors in a translation, scholars reaching a (near) consensus on some previously hotly debated topic, or a new line of argument that has previously not been used. If you don't believe this, then you are basically saying that history is a useless subject because we can never hope to make any progress. You seem to be implying that hypotheses in the subject of history are not, by nature, falsifiable.

Again, imagine that someone claims arsenic is healthy because kittens are cute, and also because puppies are cute, and capybaras are cute, and so forth. Yes, we will dismiss all these arguments. We will say that the reasonable upper and lower bounds of probabilities here on both hypotheses is 1.

I can't tell which probabilities you are referring to here.

The probability that kittens etc would be cute given that arsenic is healthy, and the probability that they would be cute given that it is not healthy. To use anything else than 1 for these probabilities, we need arguments. Just as we need arguments to not use 1 for the probabilities you're complaining about. Bring such arguments, or stop complaining.

You yourself believe that the upper and lower bounds disagree with respect to the gospels (i.e. your previous argument that the Gospels could be seen as providing evidence in favor of mythicism, "I also think that it is possible to conclude something using evidence from the Gospels..."). In conclusion, you are at the same time claiming that the upper and lower bounds agree and if I want to claim anything else I better damn well provide a bullet proof argument simultaneous asserting these limits disagree on your view. Now only is this shifting the burden of proof, it is a gigantic double standard.

You are the one claiming that Carrier's method is somehow seriously flawed.

Carrier's method is correct to not take arguments (such as mine) that he has no knowledge of into account. It could not possibly do that!

Now, I can use Carrier's correct method and update it with results obtained by using additional evidence. How would that invalidate his method? Or we can update them with your evidence, should you have any. That's what it is all about.

If you know of a method that incorporates evidence that we do not have, then please describe that method. But please start by describing your method that will lead to correct conclusions based on incorrect arguments. Because I noticed you conveniently forgot to answer that question!

If a person wished to discuss bias in the context of a trial case he would have to go into the relevant computation, define what bias means, argue which of the terms could potentially be affected by bias and show how that affects the computation in terms of numerical stability.

Oh why, he could just copy your Bob and Sue graph and be done! Because your whole argument is to assume, without evidence, that all the evidence will be biased.

I have argued why the terms can be affected by bias (we have no external means of checking them and they relate to our subjective judgement), you yourself seemed to accept that bias could exist in such subjective judgements, and I have provided a computation, using Carriers numbers, to show the numerical stability of the result in the presence of Bias. Now I simply ask you to do so yourself in the DNA example if you feel they are actually similar.

No you have not argued why they would be biased. You have just assumed that they will be. You have concluded that given the possibility that there could be massive bias, the conclusions could be wrong. Yeah. DNA could be wrong too. Without an argument, this is completely irrelevant.

Carrier could be wrong, Ehrman could be wrong, anyone could be wrong. Yet, you think it is only Carrier who could be biased, even though you have no arguments in favour of that hypothesis. Just this: if he is wrong, then he is wrong. Sorry, but that is simply not a meaningful conversation to have.

[JohanRonnblom]

Well, I will be happy to try. But just so I know what I should look for can you say what you use as the definition of a typical historian in this context?

I have no idea what you meant by 'typical', but I would describe an historian as someone who:
a) Has a degree (Ph. D. or equivalent) obtained at a department of history at a university.
b) Has published peer reviewed scholarly articles in well reputed historical journals.
c) Has been employed as a lecturer, professor or researcher at a history faculty at a university.

Preferably all three of these criteria, but two would be fine and even one would be of interest. I would note that Carrier fails on c) and that makes him less than the 'ideal' historian from my point of view.

So feel free to list people who satisfy either of these criteria and have published any scholarly opinion on the historicity of Jesus whether in a peer reviewed article or monograph, or even just a published book. Even a somewhat reputable journal for popular history would be of interest. Or anything else that you might think should qualify. I'm not too picky, but if someone writes one thing in the bulletin of the local evangelical church and never seems to engage in the same debate when facing other reputable historians, I would consider that somewhat suspect.