Here's the trick: You assign a number to it.Byron wrote:There's no inherent numerical value to questions like "what does 'the Lord's brother' mean?" One has to be assigned.
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Here's the trick: You assign a number to it.Byron wrote:There's no inherent numerical value to questions like "what does 'the Lord's brother' mean?" One has to be assigned.
Stein wrote:proudfootz wrote:I guess if you're happy to live with historians cloaking their bullshit in 'truthy' sounding phrases like 'probable' and 'likely' I will have to live with that.
Just as you'll have to live with the fact that others would like history to be a little less vague than all that.
Excuse me: likelihood even trumps other arguments in certain reaches of science. At the same time, just because we haven't found the missing link is no reason to view creationism as therefore more likely than evolution. Evolution is still far more likely than creationism because of a ton of additional evidence that makes the absence of the missing link incidental to the overwhelming data in favor of evolution.
logical bob wrote:proudfootz wrote:This is more than that one point, as you may notice the paper makes many other points as well - this is about a comprehensive method of testing hypotheses. ... If you bother to read the paper there are many points than the one you cherry picked.
I've commented on six extracts so far, but if you'd like to highlight a point that actually does make use of Bayes' Theorem to shed light on the HJ question I'd be happy to talk about that one.
proudfootz wrote:... as I pointed out earlier for those who missed reading it.
There's no inherent numerical value to questions like "what does 'the Lord's brother' mean?" One has to be assigned. It's telling that Carrier's example is a statistical question (the likelihood of Jerusalem having a public library).
Formula only work with what you put in, and that's a judgment call. Claiming that abstract systems transfer to empiricism is just the ontological arguments rehashed.
logical bob wrote:Even though it was presented to a conference called Sources of the Jesus Tradition: An Inquiry?
proudfootz wrote:Obviously there's judgement calls. No one ever said otherwise.
Using Bayes Theorem to check hypotheses in history will help make those judgement calls more explicit and the logic behind them more amenable to analysis and correction where necessary.
It's just a logical tool to help weed out the invalid arguments.
Byron wrote:proudfootz wrote:Obviously there's judgement calls. No one ever said otherwise.
Using Bayes Theorem to check hypotheses in history will help make those judgement calls more explicit and the logic behind them more amenable to analysis and correction where necessary.
It's just a logical tool to help weed out the invalid arguments.
How? So far this is mere assertion.
1. Bayes’ Theorem will help you determine how to tell if your theory is probably true
rather than merely possibly true.
It achieves this
(a) by forcing you to compare the relative likelihood of different
theories of the same evidence (so you must think of other reasons the evidence we have
might exist, besides the reason you intuitively think is most likely), and
(b) by forcing you to examine what exactly you mean when you say something is ‘likely’ or ‘unlikely’
or is ‘more likely’ or ‘less likely’. With Bayes’ Theorem you have to think in terms of
relative probabilities, as in fact must be done in all sound historical reasoning, which
ultimately requires matching numbers (or ranges of numbers) to your vocabulary of
likelihood.
2. Bayes’ Theorem will inspire a closer examination of your background knowledge,
and of the corresponding objectivity of your estimates of prior probability.
Whether you are aware of it or not, all your thinking relies on estimations of prior
probability. Making these estimations explicit will expose them to closer examination and
test. Whenever you say some claim is implausible or unlikely because ‘that’s not how
things were done then’, or ‘that’s not how people would likely behave’, or ‘other things
happened more often instead’, you are making estimates of the prior probability of what
is being claimed. And when you make this reasoning explicit, unexpected discoveries can
be made.
For example, as Porter and Thiessen have both observed, it’s inherently unlikely
that any Christian author would include anything embarrassing in a written account of his
beliefs, since he could choose to include or omit whatever he wanted. In contrast, it’s
inherently likely that anything a Christian author included in his account, he did so for a
deliberate reason, to accomplish something he wanted to accomplish, since that’s how all
authors behave, especially those with a specific aim of persuasion or communication of
approved views. Therefore, already the prior probability that a seemingly embarrassing
detail in a Christian text is in there because it is true is low, whereas the prior probability
that it is in there for a specific reason regardless of its truth is high.
3. Bayes’ Theorem will force you to examine the likelihood of the evidence on
competing theories, rather than only one — in other words, forcing you to consider
what the evidence should look like if your theory happens to be false (What evidence can
you then expect there to be? How would the evidence in fact be different?). Many
common logical errors are thus avoided. You may realize the evidence is just as likely on
some alternative theory, or that the likelihood in either case is not sufficiently different to
justify a secure conclusion.
For example, Paul refers to James the Pillar as the Brother of the Lord, and to the
Brothers of the Lord as a general category of authority besides the Apostles. It is assumed
this confirms the historicity of Jesus. But which is more likely, that a historical (hence
biological) brother of Jesus would be called the Brother of the Lord, or that he would be
called the Brother of Jesus? In contrast, if we theorize that ‘Brother of the Lord’ is a rank
in the Church, not a biological status, then the probability that we would hear of19
authorities being called by that title is just as high, and therefore that Paul mentions this
title is not by itself sufficient evidence to decide between the two competing theories of
how that title came about.
Estimates of prior probability might then decide the matter, but one then must
undertake a total theory of the evidence (extending beyond just this one issue), since
there is no direct evidence here as to what was normal (since there is no precedent for
calling anyone “Brother of the Lord” as a biological category, and only slim or inexact
precedent for constructing such a title as a rank within a religious order).
4. Bayes’ Theorem eliminates the Fallacy of Diminishing Probabilities.
Bayes’ Theorem requires a total theory of the evidence, as all historical reasoning
should, rather than focusing on isolated pieces of information without regard for how
they all fit together. But it does this by balancing every term in the numerator with a term
in the denominator.
For example, in the public libraries argument we saw that adding two pieces of
evidence together reduced the probability of the conclusion, contrary to common sense. It
would have been even worse if we had ten items of evidence. But in Bayes’ Theorem, for
every element of P(e|h.b) there is a corresponding element of P(e|~h.b), producing the
mathematical result that the more evidence you add, the higher the probability of the
hypothesis, exactly as we should expect.
For instance, if we had four items of evidence, each 60% likely if h is true, on a
straight calculation the probability of having all four items of evidence on h is 0.6 x 0.6 x
0.6 x 0.6 = 0.64 = 0.1296 = 13%, which means the more evidence we have, the less likely
h is, contrary to reason.
But on Bayes’ Theorem we ask how likely that same evidence is
if h is false (and any other hypothesis is true instead). If each item of evidence in our
hypothetical case was only 40% likely on ~h, then Bayes’ Theorem would give us (for
simplicity’s sake assuming the prior probabilities are equal):
P(h|e.b) =
P(h|b) x P(e|h.b)
__________________________________
[ P(h|b) x P(e|h.b) ] + [ P(~h|b) x P(e|~h.b) ]
P(h|e.b) =
0.5 x [0.6 x 0.6 x 0.6 x 0.6]
__________________________________________________
[ 0.5 x [0.6 x 0.6 x 0.6 x 0.6] ] + [ 0.5 x [0.4 x 0.4 x 0.4 x 0.4] ]20
P(h|e.b) =
0.5 x 0.1296
_____________________________ =
[ 0.5 x 0.1296 ] + [ 0.5 x 0.0256 ]
0.0648
______________ =
0.0648 + 0.0128
0.0648
______ =
0.0776
P(h|e.b) = 0.835 = 84%
RESULT: The more evidence you have, the higher the probability of the hypothesis,
exactly as common sense would expect.
5. Bayes’ Theorem has been proven formally valid. Any argument that violates a valid
form of argument is itself invalid. Therefore any argument that violates Bayes’ Theorem
is invalid. All valid historical arguments are described by Bayes’ Theorem. Therefore any
historical argument that cannot be described by a correct application of Bayes’ Theorem
is invalid. Therefore Bayes’ Theorem is a good method of testing any historical argument
for validity.
6. You can use Bayesian reasoning without attempting any math (see below), but the
math keeps you honest, and it forces you to ask the right questions, to test your
assumptions and intuitions, and to actually give relative weights to hypotheses and
evidence that are not all equally likely. But above all, using Bayes’ Theorem exposes all
our assumptions to examination and criticism, and thus allows progress to be made, as
we continually revise our arguments in light of the flaws detected in our reasoning.
http://www.richardcarrier.info/CarrierDec08.pdf
logical bob wrote:proudfootz wrote:Carrier's not trying to resolve a dispute here, just talking about methodology.
OK, back up. My claim is that the conclusions of this paper are blindingly obvious and not derived from Bayesian probability, the maths being spewed around in order to look clever. I gave an example of this and you accused me of quote mining, so I asked you to highlight a conclusion in the paper that does require Bayesian probability.
I don't want to get sidetracked away from that. Let's therefore accept for the sake of argument that this paper, presented to a conference on the sources of the Jesus tradition by a man who has much to say about the origins of Christianity and the historicity of Jesus, which gives a list of criteria it wishes to question including similarity to Jewish and Christian precedent, Greek, Jewish and Aramaic context, a discourse criterion explained in terms of "J's speeches" and a bizarre criterion called crucifixion, which draws a high percentage of its examples from questions directly relevant to the historical Jesus question and promises more details in a forthcoming book to be called On the Historicity of Jesus Christ and which is here posted in the Christianity rather than the History subforum and mainly defended by one of the most active posters in the Historical Jesus thread - let us accept that this is about methodology with no bearing on any particular question.
Can you point out any conclusions in this paper which are significant for methodology and which are genuinely reliant on Bayesian probability?
Stanley Porter, The Criteria for Authenticity in Historical-Jesus Research: Previous
Discussion and New Proposals (Sheffield Academic Press: 2000).
Christopher Tuckett, “Sources and Methods,” The Cambridge Companion to Jesus,
edited by Markus Bockmuehl (Cambridge University Press: 2001): pp. 121-37.
Gerd Theissen and Dagmar Winter, The Quest for the Plausible Jesus: The Question of
Criteria (John Knox Press: 2002)
Typical Problems:
1. The criterion is invalidly applied (e.g. the text actually fails to fulfill the criterion,
contrary to a scholar’s assertion or misapprehension)
2. The criterion itself is invalid (e.g. the criterion depends upon a rule of inference that is
inherently fallacious, contrary to a scholar’s intuition)
1. Scholars are obligated to establish with clear certainty that a particular item actually
fulfills any stated criterion (and what exactly that criterion is).
2. Scholars are obligated to establish the formal logical validity of any stated criterion
(especially if establishing its validity requires adopting for it a set of qualifications
or conditions previously overlooked)
You've cut and pasted 6 points from the paper without comment.
1(a), 2 and 3 are basically all saying that due weight must be given to alternative hypotheses, which we've agreed is common sense and disputed by nobody.
4 is an attempt to refute the idea that the more evidence there is for a hypothesis the less likely the hypothesis is to be true. It's pretty obvious that nobody thinks that, so arguing against it, yet alone using calculations to argue against it, is wholly unnecessary.
5 is word salad and extremely poor logic as I've already discussed
P1) Any argument that violates a valid form of argument is itself invalid.
P2) Bayes’ Theorem has been proven formally valid.
C1) Therefore any argument that violates Bayes’ Theorem is invalid.
P3) All valid historical arguments are described by Bayes’ Theorem.
Therefore any historical argument that cannot be described by a correct application of Bayes’ Theorem
is invalid.
Therefore Bayes’ Theorem is a good method of testing any historical argument for validity.
and 6 is a claim that you can get the benefits of mathematical rigour without having to do any maths.
A. Bayesian Reasoning without Mathematics
1. You don’t have to use scary math to think like a Bayesian, unless the problem is highly
complex, or you want clearer ideas of relative likelihood. For instance...
2. Easy Case of Rejection: If you estimate that the prior probability of h must be at least
somewhat low (any degree of “h is unlikely, given just b”), and you estimate the
evidence is no more likely on h than on ~h, then h is probably false (“h is unlikely
even given e”).
EXAMPLE: Talking donkeys are unlikely, given everything we know about the
world. That there would be a story about a talking donkey is just as likely if
there were a real talking donkey than if someone just made up a story about a
talking donkey. Therefore, e is no more likely on h (Balaam’s donkey actually23
spoke) than on ~h (Someone made up a story about Balaam’s donkey speaking),
and h (Balaam’s donkey actually spoke) is already initially unlikely, whereas ~h
(Someone made up a story about Balaam’s donkey speaking) is initially quite
likely (since on b we know people make up stories all the time, but we don’t
know of any talking donkeys). Therefore, we can be reasonably certain that
Balaam’s donkey didn’t talk. Note how this conclusion is worldview independent.
It follows from plain facts everyone can agree on.
3. Unexpected Case of Acceptance: If you estimate that the prior probability of h must be
at least somewhat high (any degree of “h is likely given just b”), even if you
estimate the evidence is no more likely on h than on ~h, then h is still probably
true (“h is likely even given e”).
EXAMPLE: That Julius Caesar regularly shaved (at least once a week) is likely,
given everything we know about Julius Caesar and Roman aristocratic customs
of the time and human male physiology. That we would have no report of his
shaving anytime during the week before he was assassinated is as likely on h
(Caesar shaved during the week before he was assassinated) as on ~h (Caesar
didn’t shave any time during the week before he was assassinated), since, either
way, we have no particular reason to expect any report about this to survive.
Nevertheless, h is probably true: Caesar shaved sometime during the week
before he was assassinated.
4. In the above examples, exact numbers and equations were unneeded, just the
innate logic of Bayesian reasoning sufficed. This is the case for most
historical problems. Only when the problem is complex does math become a
necessary tool.
For example, if you want some idea of how likely a hypothesis is, then
you may need to do some math, unless the relative degrees of likelihood are
so clear you can reason out the result without any equation. For instance, it is
very unlikely that any donkey spoke, therefore it is very unlikely that
Balaam’s story is true. But things are not always this clear.
Or, for example, when the prior probability of a hypothesis is low, but
the evidence is still much more likely on that hypothesis than any other (or
vice versa), then you need to evaluate how low and how high these
probabilities are, in order to determine if they balance each other out.
That leaves 1(b) as the only interesting bit. This is the claim we've already discussed that if this is going to work, in the end you have to assign numbers to your probabilities. Now Bayesian probability is indeed a powerful tool for dealing with probabilities, but it requires probabilities as input and the end result will not be more reliable than that input. Carrier says nothing about the methodology he proposes to use in deciding the probability that, for example, we would have documentary evidence of the use of Brother of the Lord as a church title if it was used in this way. Is that 30% likely? 70% likely? Until there are specifics on how to make and justify this choice the whole process is no less vague than arguments that only talk about "more or less likely".
proudfootz wrote:So it would be a serious misunderstanding to imagine Carrier merely claims applying Bayesian methods can be helpful without maths, he actually puts forward arguments with examples.
The problem this example is put forward to address is the one of those scholars who simply say X is 'more likely' without justification (for example leaving out any consideration of competing theories).
It may be that the difficulty establishing the inputs is not solved here by Carrier. But perhaps making use of this powerful tool in dealing with probabilities shows up another area where scholars could tighten up their methodology.
Perhaps trying to prod scholars into examining their presumptions about what they mean by 'likely, and 'probable' and making explicit their reasons for doing so wouldn't be the worst thing that ever happened.
Byron wrote:If Carrier wants to show flaws in the current approach, he needs to do it justice.
Notably, Carrier misrepresents the criterion of embarrassment (or material against interest, as I prefer).
And there's the wider point that Carrier's criticisms relate to a small area of historiography, testing the reliability of material. Much historical study is more concerned with interpreting established events, such as how the Black Death affected feudalism, or the extent of religious motivation in the 17th Century British wars.
It does nothing to counter the impression that Carrier's fixated on a single-issue, atheism, and history is a means to this end.
logical bob wrote:Thanks for a much more thorough response.proudfootz wrote:So it would be a serious misunderstanding to imagine Carrier merely claims applying Bayesian methods can be helpful without maths, he actually puts forward arguments with examples.
He does, but look at his examples. Using the power of Bayesian probability he is able to conclude that Caesar probably shaved in the week before his death and that Balaam's donkey probably didn't really talk. Well sorry, but duh. Again you don't need Bayesian reasoning to figure this out. Now if he were to give an example where the method yielded something other than a statement of the glaringly obvious his claim that this approach is helpful would be more plausible.The problem this example is put forward to address is the one of those scholars who simply say X is 'more likely' without justification (for example leaving out any consideration of competing theories).
It may be that the difficulty establishing the inputs is not solved here by Carrier. But perhaps making use of this powerful tool in dealing with probabilities shows up another area where scholars could tighten up their methodology.
Perhaps trying to prod scholars into examining their presumptions about what they mean by 'likely, and 'probable' and making explicit their reasons for doing so wouldn't be the worst thing that ever happened.
It's a fair point, but Carrier actually treats probabilities just as loosely himself in the paper, when he announces without justification that Brother of the Lord is just as likely to be a title as a biological relationship or that the chance of a scribe including something embarrassing because it's true is low while the chance of him including it for a specific purpose is high.
These claims that Carrier's method supplies rigour would be more persuasive if he didn't at the same time make exactly the kind of non-rigourous argument he's trying to criticise. It doesn't make one confident that he'll be able to provide reliable probabilities to serve as inputs for a Bayesian argument.
ETA: Even in the examples you posted above, he's at it again. He declares that someone writing about a talking donkey is "no more likely" on the assumption that a donkey talked than on the assumption that no donkey talked. WTF?
Byron wrote:Exactly what I'd say to Carrier! He's claimed that Bayes' can establish historical probability objectively, but produced no means whereby probabilistic values can be assigned to non-statistical historical questions (ie, the tedious "Lord's brother" passage).
Again, you don't seem to understand what Carrier is saying.MusPonticus wrote:He claimed that Bayes' can establish historical probability objectively? Are you saying that Carrier claims that he can produce "objective" values for e.g. "the Lord's brother"-stuff?
Byron, are you sure you haven't just misunderstood Carrier?
RICHARD: That’s what the book is for, it addresses tons of them, and I’m sure your audience is listening now like: “Ah, what about this? No, it can’t work because…”
Well, what are the big ones? Let’s take one that even scientists debate even among scientists in applying Bayes’ theorem: is the problem of subjective probability estimates.
Obviously, I mean obviously, in history especially – but even in science this is often the case – we don’t have hard, scientifically verified statistical data. We don’t, we can’t poll – we can’t take a scientific phone poll of ancient Roman populations, right? Things like that, you don’t have that kind of data.
There are few cases where you do, very few, and it’s very limited what we can learn from them. Most history doesn’t have access to that data. So you have to give a sort of subjective probability estimate, because people would say “you’re just making shit up, or you’re guessing, or something”.
What I point out in the book and demonstrate in detail, is that: this is how we reason all the time anyway, so if this is a valid objection to Bayes’ theorem, it’s a valid objection to all of human reasoning.
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