Recalibrating Carrier - Correct Odds of Jesus's Historicity 46 - 18%
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Recalibrating Carrier - Correct Odds of Jesus's Historicity 46 - 18%
“Finally, from so little sleeping and so much reading, his brain dried up and he went completely out of his mind.”
― Miguel de Cervantes Saavedra, Don Quixote
― Miguel de Cervantes Saavedra, Don Quixote
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Re: Recalibrating Carrier - Correct Odds of Jesus's Historicity 46 - 18%
The video is from 2017. Dr Carrier responds to the video on his blog here: https://www.richardcarrier.info/archives/12183
I'm no expert on BT at all. But there have been lots of criticisms of Dr Carrier's approach to using Bayes Theorem, some of which I documented in my review of his book "On the Historicity of Jesus": http://members.optusnet.com.au/gakuseid ... l#Section2
One thing that the Youtuber states in his video that I think gets wrong is the idea that Carrier is being "fair" and even generous to the weight of odds for HJ side. That is demonstrably false. For example, he gives the following odds (page 594):
Made from sperm 2/1 (in favour of historicity)
Made from a woman 2/1 (in favour of historicity)
That suggests that, for every 3 examples of "made from sperm", you'd expect to find that 2 supports historicity and 1 supports celestial mythicism. So 1 in 3 references of "made from sperm" support a non-earthly origin! That is an absurdly low figure in support of historicity.
Then there is Carrier's constantly confusing the idea of "earthliness" with "historicity". To my mind, GA Wells' theory would score higher than Carrier's minimal mythicism, even based on Carrier's numbers. Wells' Paul's Jesus lived on earth, it's just that that Jesus never existed. So Wells' theory picks up many of the "pro-historicity" figures while keeping a lot of Carrier's "pro-mythicism" figures.
I still think that BT may be useful in questions about historicity. I think it should be addressed. But as more than one critic of Carrier has pointed out, it should be calibrated by examining cases that aren't controversial, to work out how to apply to questions of history generally and show that it can indeed be used for such purposes, before being applied to a controversial topic like the historicity of Jesus.
I'm no expert on BT at all. But there have been lots of criticisms of Dr Carrier's approach to using Bayes Theorem, some of which I documented in my review of his book "On the Historicity of Jesus": http://members.optusnet.com.au/gakuseid ... l#Section2
One thing that the Youtuber states in his video that I think gets wrong is the idea that Carrier is being "fair" and even generous to the weight of odds for HJ side. That is demonstrably false. For example, he gives the following odds (page 594):
Made from sperm 2/1 (in favour of historicity)
Made from a woman 2/1 (in favour of historicity)
That suggests that, for every 3 examples of "made from sperm", you'd expect to find that 2 supports historicity and 1 supports celestial mythicism. So 1 in 3 references of "made from sperm" support a non-earthly origin! That is an absurdly low figure in support of historicity.
Then there is Carrier's constantly confusing the idea of "earthliness" with "historicity". To my mind, GA Wells' theory would score higher than Carrier's minimal mythicism, even based on Carrier's numbers. Wells' Paul's Jesus lived on earth, it's just that that Jesus never existed. So Wells' theory picks up many of the "pro-historicity" figures while keeping a lot of Carrier's "pro-mythicism" figures.
I still think that BT may be useful in questions about historicity. I think it should be addressed. But as more than one critic of Carrier has pointed out, it should be calibrated by examining cases that aren't controversial, to work out how to apply to questions of history generally and show that it can indeed be used for such purposes, before being applied to a controversial topic like the historicity of Jesus.
It is really important, in life, to concentrate our minds on our enthusiasms, not on our dislikes. -- Roger Pearse
Re: Recalibrating Carrier - Correct Odds of Jesus's Historicity 46 - 18%
Carrier has addressed this: https://www.richardcarrier.info/archives/12183
(though both he and FoE get the meningitis example wrong; Carrier being more wrong that FoE, imho)
Here's extracts of Carrier's discussion in that post that pertain to Bayes' Theorem per se or to the NT and extra-biblical -
Carrier has another sub-section about Christianity below the heading 'Using Acts to Illustrate the Point' and a Conclusion
(though both he and FoE get the meningitis example wrong; Carrier being more wrong that FoE, imho)
Here's extracts of Carrier's discussion in that post that pertain to Bayes' Theorem per se or to the NT and extra-biblical -
.
The central gist of FoE’s argument isn’t well explained, and someone who doesn’t know math won’t know what he’s talking about. Even someone who knows math will be confused, because he confuses a variety of mathematical concepts, such as conflating odds with decimal probabilities. But to steelman his argument as best I can, he means to say this:
When you are going to multiply the probabilities of individual events, in order to determine the probability of the conjunction of all of those events, you can’t just multiply their individual probabilities if those events are in any way dependent on each other.
...He thinks dependent probabilities can’t be multiplied ... [But] that’s the only way they teach it in math class. What changes is not multiplying, but what probability you put into the multiplication.
Did He Just Say That?
FoE correctly describes Bayes’ Theorem, but only in the short form, which is an incomplete formula to a lay observer, who won’t know what’s hidden in it (see Proving History, pp. 69 and 283-84). He says (and agrees) that the probability of historicity given the evidence equals the probability of that evidence given historicity, times the [prior/general] probability of historicity, all divided by the probability of the evidence “whether or not” Jesus existed. He makes an erroneous statement at this point, at timestamp 3:30, when he says, “which of course equals one because we have the evidence that we have.” That’s not how that works. The P(e) that completes the denominator of the short form is not simply “1” (100%) because e “is what we have.” That’s the Fallacy of Foregone Conclusions.
< . . snip . . >
... he is confusing two completely different probabilities, and to help anyone else from making that mistake even if he didn’t mean to, remember this:
The probability that the evidence exists given that we are observing it, and the probability that that evidence would exist given that a particular event happened in the past, are not the same probability.
< . . snip . . >
[previously Carrier had written under Relevance to OHJ] ... At no point in his video does he ever mention any ratio I assign to any item of evidence, nor does he ever explain how any particular one of those ratios should be changed to account for any dependence effect.
Getting to the Point
At timestamp 4:33 Fishers of Evidence says something about generating a prior probability from the Rank-Raglan data, but presses no criticism there I could discern, unless, when he says a prior must be generated “without reference to these bodies of evidence”, he means the RR data comes circularly from the evidence I put in e, or he means a prior can’t be based on evidence. Both would be incorrect. A prior is always based on evidence—everything you put in b. And you can put anything in b that you exclude from e (and vice versa). As I explicitly state in OHJ, I put the RR data into b, and then properly excluded that data when I examined the remaining content of the Gospels (see my discussion of this mistake when made by Tim Hendrix). But since FoE developed no clear criticism from this, I’ll move on to his central point.
At timestamp 4:55, FoE starts on about the difference between dependent and independent probabilities. He confusingly frames this in terms of summing vs. multiplying probabilities. But he never shows what he means. To understand what he means, see my better steelman summary above. Although he is confusing probability equations using odds ratios and probability equations using percentages. Though even using percentages, you can multiply dependent probabilities. You just have to make sure you are doing it correctly (see my previous discussion of this).
< . . snip . . >
FoE...commits two errors... First, he incorrectly claims you can’t derive a total probability from a series of dependent probabilities by multiplication. To the contrary, that is in fact how you usually do it. And second, he never identifies any examples of dependent probabilities in my series of estimates in OHJ.
He correctly notes that there are causal connections between groups of evidence, e.g. the Epistles had causal effects on the Gospels, and the Gospels had causal effects on Acts and the [e]xtra-biblical evidence. But he doesn’t identify a single probability I produce that is affected by these causal relations. For example, in Acts, I don’t just come up with “a probability of Acts given historicity/ahistoricity.” I actually divide Acts into three pieces of evidence, none of which reflect the dependency relations FoE alleges, except one, and for that I give a dependent probability, exactly as required by the math (see below). In other words, it does not appear FoE actually examined any of my estimates for any actual dependence relations. If he did, he would have discovered (a) many don’t have such relations to account for, and (b) the ones that do, I already accounted for!
For example, Acts is dependent on the Gospels only for the material it shares with the Gospels, which I don’t explicitly assign any probability to! I assume that content is 100% expected on either theory, because it’s 100% expected given “the Gospels exist,” and the Gospels exist, regardless of whether Jesus did. I assign it odds of 1/1. In other words, no effect. That’s a dependent probability, like the 2/3 chance of being rich given having won a lottery. FoE seems not to have noticed. His criticism is thus completely inapplicable here.
Meanwhile, for material pertaining to the history of the church not recorded in the Gospels, Acts is independent of the Gospels. And that’s the only material I assign a probability to. Although that material is causally dependent on the Epistles, I already account for that in my estimations of the likelihoods of those contents of Acts given what’s in the Epistles.
Indeed, the fact that Acts definitely used the Epistles as a source entails it deliberately contradicts the Epistles when indeed it frequently does so, which entails the probability that Acts is a reliable source is near zero. Although that isn’t a probability I use in OHJ. I only estimate how likely it is that Acts would lack the things it does, even given the fact that its author knew and was influenced by (and aiming even to contradict) the Epistles. So the probabilities I put in are already dependent probabilities as required. FoE’s criticism is again wholly inapplicable.
...you can derive total probabilities with dependent probabilities by multiplication ...
< . . snip . . >
For example, what is the probability Acts would have faked up the trial speeches for Paul to match the street sermons, and thus included references to a historical Jesus, instead of as we have it now, trial speeches that bizarrely omit any references to a historical Jesus, and street sermons that include such references? This would be, one might argue, a probability dependent on the existence of Luke’s Gospel. In other words, Luke certainly knows the material that evinces a historical Jesus, and it could have caused him to fake evidence everywhere in Acts. But in this case, he didn’t. He kept this bizarre incongruity between Paul’s trial speeches and street sermons (OHJ, pp. 375-80). That fact by itself is more likely if Jesus didn’t exist than if he did—though as I argue, the difference is extremely small: a likelihood ratio of only 9/10 against historicity on the a fortiori side. And that’s what that ratio would be even considering the fact that Acts was written by someone who knew the Gospel material. In other words, this 9/10 is the same figure as the 3/51 in the poker example above, and the 2/3 in the lottery example. It is thus not invalid. It’s perfectly correct. FoE’s argument has no relevance here.
My taking this dependence into account is even explicit: I estimate that even if Jesus didn’t exist, the fact that Luke would add a reference to historicity in Stephen’s speech given that Luke wrote the Gospel under his name is just as likely as that such a reference would be there if Jesus did exist. So the ratio is 1/1. Which means it has no effect. Stephen’s speech argues neither for nor against historicity. As I wrote: “when Luke inserts into Stephen’s speech a brief reference to the historicity of Jesus…this could obviously be Luke importing his own narrative assumptions,” among other possibilities I enumerate (OHJ, p. 383). Thus, I’m fully taking into account the fact that this is a dependent probability. And my incorporation of it is mathematically correct. I don’t literally assign either outcome a 100% probability (see OHJ, p. 605; cf. pp. 288-89, n. 18 and p. 357, n. 122); it could be 50% likely Luke would fake evidence and 50% likely he’d include a reference if Jesus really existed. What I estimate is that whatever those two probabilities may be, they are going to be so nearly the same that there is no measurable difference between them, and therefore Stephen’s speech argues for neither theory. And this is so even given Acts’ reliance on the Gospels and Epistles. So their being dependent probabilities makes no difference to the math. Contrary to what FoE claims.
I similarly adduce that the Gospels, deriving material from the Epistles (as I explicitly admit they do in OHJ), have the same probability of including Epistle-connected material whether Jesus existed or not, because of their dependence on the Epistles for that material. In other words, the Gospels cannot corroborate that material, if they are not independent of it. Thus, again, I am doing exactly what Fishers of Evidence says I should: accounting for the interdependence of some of the evidence when I assign probabilities.
All my probabilities thus are just like the poker draw probabilities: they are already factoring in the causal relations among the different categories of evidence. This is indeed so explicit in my discussion of the extra-biblical evidence (in Ch. 8) ... My finding that no external sources corroborate the Gospels is derived from their dependence on those Gospels.
Thus, that Tacitus should mention a Gospel claim about Jesus (if in fact he ever did) is already 100% expected on the existence of the Gospels, regardless of whether Jesus existed or not. That reference in Tacitus thus has no effect on our final probability of historicity. That’s how dependent probability works. And ironically, here it’s Christian apologists who typically don’t grasp the point that Fishers of Evidence is making: that the probability the extra-biblical sources would mention Jesus, even if he didn’t exist, is dependent on the Gospels having already done so (and their Christian informants subsequently relying on the Gospels, as we know they did).
https://www.richardcarrier.info/archives/12183
The central gist of FoE’s argument isn’t well explained, and someone who doesn’t know math won’t know what he’s talking about. Even someone who knows math will be confused, because he confuses a variety of mathematical concepts, such as conflating odds with decimal probabilities. But to steelman his argument as best I can, he means to say this:
When you are going to multiply the probabilities of individual events, in order to determine the probability of the conjunction of all of those events, you can’t just multiply their individual probabilities if those events are in any way dependent on each other.
...He thinks dependent probabilities can’t be multiplied ... [But] that’s the only way they teach it in math class. What changes is not multiplying, but what probability you put into the multiplication.
Did He Just Say That?
FoE correctly describes Bayes’ Theorem, but only in the short form, which is an incomplete formula to a lay observer, who won’t know what’s hidden in it (see Proving History, pp. 69 and 283-84). He says (and agrees) that the probability of historicity given the evidence equals the probability of that evidence given historicity, times the [prior/general] probability of historicity, all divided by the probability of the evidence “whether or not” Jesus existed. He makes an erroneous statement at this point, at timestamp 3:30, when he says, “which of course equals one because we have the evidence that we have.” That’s not how that works. The P(e) that completes the denominator of the short form is not simply “1” (100%) because e “is what we have.” That’s the Fallacy of Foregone Conclusions.
< . . snip . . >
... he is confusing two completely different probabilities, and to help anyone else from making that mistake even if he didn’t mean to, remember this:
The probability that the evidence exists given that we are observing it, and the probability that that evidence would exist given that a particular event happened in the past, are not the same probability.
< . . snip . . >
[previously Carrier had written under Relevance to OHJ] ... At no point in his video does he ever mention any ratio I assign to any item of evidence, nor does he ever explain how any particular one of those ratios should be changed to account for any dependence effect.
Getting to the Point
At timestamp 4:33 Fishers of Evidence says something about generating a prior probability from the Rank-Raglan data, but presses no criticism there I could discern, unless, when he says a prior must be generated “without reference to these bodies of evidence”, he means the RR data comes circularly from the evidence I put in e, or he means a prior can’t be based on evidence. Both would be incorrect. A prior is always based on evidence—everything you put in b. And you can put anything in b that you exclude from e (and vice versa). As I explicitly state in OHJ, I put the RR data into b, and then properly excluded that data when I examined the remaining content of the Gospels (see my discussion of this mistake when made by Tim Hendrix). But since FoE developed no clear criticism from this, I’ll move on to his central point.
At timestamp 4:55, FoE starts on about the difference between dependent and independent probabilities. He confusingly frames this in terms of summing vs. multiplying probabilities. But he never shows what he means. To understand what he means, see my better steelman summary above. Although he is confusing probability equations using odds ratios and probability equations using percentages. Though even using percentages, you can multiply dependent probabilities. You just have to make sure you are doing it correctly (see my previous discussion of this).
< . . snip . . >
FoE...commits two errors... First, he incorrectly claims you can’t derive a total probability from a series of dependent probabilities by multiplication. To the contrary, that is in fact how you usually do it. And second, he never identifies any examples of dependent probabilities in my series of estimates in OHJ.
He correctly notes that there are causal connections between groups of evidence, e.g. the Epistles had causal effects on the Gospels, and the Gospels had causal effects on Acts and the [e]xtra-biblical evidence. But he doesn’t identify a single probability I produce that is affected by these causal relations. For example, in Acts, I don’t just come up with “a probability of Acts given historicity/ahistoricity.” I actually divide Acts into three pieces of evidence, none of which reflect the dependency relations FoE alleges, except one, and for that I give a dependent probability, exactly as required by the math (see below). In other words, it does not appear FoE actually examined any of my estimates for any actual dependence relations. If he did, he would have discovered (a) many don’t have such relations to account for, and (b) the ones that do, I already accounted for!
For example, Acts is dependent on the Gospels only for the material it shares with the Gospels, which I don’t explicitly assign any probability to! I assume that content is 100% expected on either theory, because it’s 100% expected given “the Gospels exist,” and the Gospels exist, regardless of whether Jesus did. I assign it odds of 1/1. In other words, no effect. That’s a dependent probability, like the 2/3 chance of being rich given having won a lottery. FoE seems not to have noticed. His criticism is thus completely inapplicable here.
Meanwhile, for material pertaining to the history of the church not recorded in the Gospels, Acts is independent of the Gospels. And that’s the only material I assign a probability to. Although that material is causally dependent on the Epistles, I already account for that in my estimations of the likelihoods of those contents of Acts given what’s in the Epistles.
Indeed, the fact that Acts definitely used the Epistles as a source entails it deliberately contradicts the Epistles when indeed it frequently does so, which entails the probability that Acts is a reliable source is near zero. Although that isn’t a probability I use in OHJ. I only estimate how likely it is that Acts would lack the things it does, even given the fact that its author knew and was influenced by (and aiming even to contradict) the Epistles. So the probabilities I put in are already dependent probabilities as required. FoE’s criticism is again wholly inapplicable.
...you can derive total probabilities with dependent probabilities by multiplication ...
< . . snip . . >
For example, what is the probability Acts would have faked up the trial speeches for Paul to match the street sermons, and thus included references to a historical Jesus, instead of as we have it now, trial speeches that bizarrely omit any references to a historical Jesus, and street sermons that include such references? This would be, one might argue, a probability dependent on the existence of Luke’s Gospel. In other words, Luke certainly knows the material that evinces a historical Jesus, and it could have caused him to fake evidence everywhere in Acts. But in this case, he didn’t. He kept this bizarre incongruity between Paul’s trial speeches and street sermons (OHJ, pp. 375-80). That fact by itself is more likely if Jesus didn’t exist than if he did—though as I argue, the difference is extremely small: a likelihood ratio of only 9/10 against historicity on the a fortiori side. And that’s what that ratio would be even considering the fact that Acts was written by someone who knew the Gospel material. In other words, this 9/10 is the same figure as the 3/51 in the poker example above, and the 2/3 in the lottery example. It is thus not invalid. It’s perfectly correct. FoE’s argument has no relevance here.
My taking this dependence into account is even explicit: I estimate that even if Jesus didn’t exist, the fact that Luke would add a reference to historicity in Stephen’s speech given that Luke wrote the Gospel under his name is just as likely as that such a reference would be there if Jesus did exist. So the ratio is 1/1. Which means it has no effect. Stephen’s speech argues neither for nor against historicity. As I wrote: “when Luke inserts into Stephen’s speech a brief reference to the historicity of Jesus…this could obviously be Luke importing his own narrative assumptions,” among other possibilities I enumerate (OHJ, p. 383). Thus, I’m fully taking into account the fact that this is a dependent probability. And my incorporation of it is mathematically correct. I don’t literally assign either outcome a 100% probability (see OHJ, p. 605; cf. pp. 288-89, n. 18 and p. 357, n. 122); it could be 50% likely Luke would fake evidence and 50% likely he’d include a reference if Jesus really existed. What I estimate is that whatever those two probabilities may be, they are going to be so nearly the same that there is no measurable difference between them, and therefore Stephen’s speech argues for neither theory. And this is so even given Acts’ reliance on the Gospels and Epistles. So their being dependent probabilities makes no difference to the math. Contrary to what FoE claims.
I similarly adduce that the Gospels, deriving material from the Epistles (as I explicitly admit they do in OHJ), have the same probability of including Epistle-connected material whether Jesus existed or not, because of their dependence on the Epistles for that material. In other words, the Gospels cannot corroborate that material, if they are not independent of it. Thus, again, I am doing exactly what Fishers of Evidence says I should: accounting for the interdependence of some of the evidence when I assign probabilities.
All my probabilities thus are just like the poker draw probabilities: they are already factoring in the causal relations among the different categories of evidence. This is indeed so explicit in my discussion of the extra-biblical evidence (in Ch. 8) ... My finding that no external sources corroborate the Gospels is derived from their dependence on those Gospels.
Thus, that Tacitus should mention a Gospel claim about Jesus (if in fact he ever did) is already 100% expected on the existence of the Gospels, regardless of whether Jesus existed or not. That reference in Tacitus thus has no effect on our final probability of historicity. That’s how dependent probability works. And ironically, here it’s Christian apologists who typically don’t grasp the point that Fishers of Evidence is making: that the probability the extra-biblical sources would mention Jesus, even if he didn’t exist, is dependent on the Gospels having already done so (and their Christian informants subsequently relying on the Gospels, as we know they did).
https://www.richardcarrier.info/archives/12183
Carrier has another sub-section about Christianity below the heading 'Using Acts to Illustrate the Point' and a Conclusion
Last edited by MrMacSon on Mon Nov 05, 2018 5:25 pm, edited 1 time in total.
Re: Recalibrating Carrier - Correct Odds of Jesus's Historicity 46 - 18%
The headache-due-to-meningitis example in that video is inappropriate.
Formulas other than, and terminology not pertaining to, Bayes Theorem are used in determining diagnoses and tests to confirm them - https://www.medcalc.org/calc/diagnostic_test.php
e.g. Sensitivity (the ability of a test to correctly identify people who have a given disease or disorder); Specificity (the ability of a test to correctly exclude individuals who do not have a given disease or disorder); Likelihood Ratios, and Predictive Values (both Positive and Negative)
There is a reference on that webpage to Bayes' Theorem but in relation to a formula based on Bayes theorem for calculating the positive and negative predictive values of a test when the disease prevalence is known. That meningitis is a cause of 1 in 1,000 headaches is not the prevalence of meningitis, as prevalence refers to a rate per X head of a spatial population (eg. per 1,000; per 10k, per 100k, or even per million). (and, there are different types of meningitis, each with a different prevalence and a different test; each test, in turn, with a different sensitivity and specificity).
Another page from that site refers to a situation where there is conditional probability which is what Bayes' Theorem is about;
Formulas other than, and terminology not pertaining to, Bayes Theorem are used in determining diagnoses and tests to confirm them - https://www.medcalc.org/calc/diagnostic_test.php
e.g. Sensitivity (the ability of a test to correctly identify people who have a given disease or disorder); Specificity (the ability of a test to correctly exclude individuals who do not have a given disease or disorder); Likelihood Ratios, and Predictive Values (both Positive and Negative)
There is a reference on that webpage to Bayes' Theorem but in relation to a formula based on Bayes theorem for calculating the positive and negative predictive values of a test when the disease prevalence is known. That meningitis is a cause of 1 in 1,000 headaches is not the prevalence of meningitis, as prevalence refers to a rate per X head of a spatial population (eg. per 1,000; per 10k, per 100k, or even per million). (and, there are different types of meningitis, each with a different prevalence and a different test; each test, in turn, with a different sensitivity and specificity).
Another page from that site refers to a situation where there is conditional probability which is what Bayes' Theorem is about;
- (at the bottom) -
.
Presentation of results
The prevalence of a disease may be different in different clinical settings. For instance the pre-test probability for a positive test will be higher when a patient consults a specialist than when he consults a general practitioner. Since positive and negative predictive values are sensitive to the prevalence of the disease, it would be misleading to compare these values from different studies where the prevalence of the disease differs, or apply them in different settings.
< . . snip . . >
With these data, any reader can calculate the negative and positive predictive value applicable in [their] own clinical setting, when [they] know the prior probability of disease (pre-test probability or prevalence of disease) in this setting, by the following formulas based on Bayes' theorem:
https://www.medcalc.org/manual/roc-curves.php
Last edited by MrMacSon on Mon Nov 05, 2018 5:28 pm, edited 4 times in total.
Re: Recalibrating Carrier - Correct Odds of Jesus's Historicity 46 - 18%
Some of the rest of Carrier's blog-post is interesting, particularly as he elaborated on a point in the comments below the main article (a comment I have included below) -
[FoE] assumed an equal weighting for every item of evidence’s dependency. Which implausibly assumes the affect of every item of evidence on every other is exactly the same (such as the weirdness of the trial speeches in Acts on the omission of James from the entire public history). He just assumes that. Without argument. But even before attempting an argument, I can already tell you, it would be cosmically bizarre for that to actually be the case. And it’s clear FoE has no argument for it being the case, that he did not even consider the matter. Which renders his alternative result completely meaningless. It has no connection with any argument for dependence or causality among the items of evidence I demarcated. His own result is thus, in fact, far worse than even he thinks mine is.
Using Acts to Illustrate the Point
Let’s talk about how mathematicians actually combine dependent probabilities. And what I actually did in OHJ.
I’ve already discussed above how I make estimates of dependent probabilities in OHJ with respect to Acts. More specifically, I break that down into three things: (i) the missing family (and other personages who should have had a causal effect on the history of the church); (ii) the oddness of the trial speeches (which read as if there were no historical but only a cosmic Jesus); and (iii) the rest of the content of Acts (OHJ, p. 386). I find that the rest of the content of Acts is just as expected on either historicity or not, and thus assign a ratio of 1/1. This is actually already a dependent probability: because Luke is being caused by the Gospels to repeat Gospel-derived historicity material, the dependent probability that he would do so even if Jesus didn’t exist is 1 (at least, as near to one as makes all odds), once we grant the Gospels causally influenced him. That’s exactly like realizing the probability of drawing a second king is 3/51 and not 4/52. There is no other way to do this math. Any other method he uses, if it gets him a different result than multiplying 4/52 by 3/51 in the poker case, he’s doing it wrong. And likewise if he makes the same mistake with my assignment of 1/1 here.
But since 1/1 multiplied by anything has no effect, we can ignore that now and look at the other two ratios. For those other two items in Acts I assign on the a fortiori side a likelihood of 4/5 for the missing people and 9/10 for the weird trial speeches. (Which are already super weak evidence ratios, BTW…good evidence should weigh 1/4 or 4/1 or more or even a million or a billion to one, so I am not making anything like a strong claim of effect here. But moving back to the point at hand…) For FoE to claim that these should not be multiplied against each other (4/5 x 9/10), he needs to show two things: that those two things are dependent on each other; and that that dependence changes the ratios to something other than I assigned. For example, imagine Luke’s not thinking to ever mention James ever led the Church, in a supposedly researched history of that Church, is somehow caused by his trial speeches also not seeming to know about a historical Jesus, such that wherever there is the latter, there will always be the former. In that case, the dependent probability of the omission of James is 1/1, and it no longer has any effect. We are then left with simply the 9/10 oddness of the trial speeches. Just as if drawing a king from the deck, at odds of 4/52, causes the next draw always to be a king, such that the probability of drawing two kings right off the top is simply 4/52, not 4/52 x 3/51.
Unfortunately, Fishers of Evidence never does this. For anything in OHJ. He doesn’t explain how, for example, the trial speeches omitting a historical Jesus, affects the probability of James being omitted from the entire history of the church. In what way are they dependent on each other? And even if we can come up with any plausible dependence (and they have to be plausible; wildly implausible dependencies have too low a probability to show up in the math at the resolution I employ), does it change my estimates at all? Is it really credible to say the weirdness of the trial speeches would always cause an omission of James? Certainly not.*
If they have any effect on each other at all, it’s extremely small. There are too many ways either could happen independently of the other. So is that tiny effect large enough to make the conjunction of both together any different from 4/5 x 9/10? A difference, that is, that shows up at that resolution? (For example, a difference of a millionth would be so small it would disappear when rounding to the nearest whole percentage point.) Such causal dependencies thus have no visible effect. (And even if they do, the effect may be in entirely the other direction: see comment.)
[FoE] assumed an equal weighting for every item of evidence’s dependency. Which implausibly assumes the affect of every item of evidence on every other is exactly the same (such as the weirdness of the trial speeches in Acts on the omission of James from the entire public history). He just assumes that. Without argument. But even before attempting an argument, I can already tell you, it would be cosmically bizarre for that to actually be the case. And it’s clear FoE has no argument for it being the case, that he did not even consider the matter. Which renders his alternative result completely meaningless. It has no connection with any argument for dependence or causality among the items of evidence I demarcated. His own result is thus, in fact, far worse than even he thinks mine is.
Using Acts to Illustrate the Point
Let’s talk about how mathematicians actually combine dependent probabilities. And what I actually did in OHJ.
I’ve already discussed above how I make estimates of dependent probabilities in OHJ with respect to Acts. More specifically, I break that down into three things: (i) the missing family (and other personages who should have had a causal effect on the history of the church); (ii) the oddness of the trial speeches (which read as if there were no historical but only a cosmic Jesus); and (iii) the rest of the content of Acts (OHJ, p. 386). I find that the rest of the content of Acts is just as expected on either historicity or not, and thus assign a ratio of 1/1. This is actually already a dependent probability: because Luke is being caused by the Gospels to repeat Gospel-derived historicity material, the dependent probability that he would do so even if Jesus didn’t exist is 1 (at least, as near to one as makes all odds), once we grant the Gospels causally influenced him. That’s exactly like realizing the probability of drawing a second king is 3/51 and not 4/52. There is no other way to do this math. Any other method he uses, if it gets him a different result than multiplying 4/52 by 3/51 in the poker case, he’s doing it wrong. And likewise if he makes the same mistake with my assignment of 1/1 here.
But since 1/1 multiplied by anything has no effect, we can ignore that now and look at the other two ratios. For those other two items in Acts I assign on the a fortiori side a likelihood of 4/5 for the missing people and 9/10 for the weird trial speeches. (Which are already super weak evidence ratios, BTW…good evidence should weigh 1/4 or 4/1 or more or even a million or a billion to one, so I am not making anything like a strong claim of effect here. But moving back to the point at hand…) For FoE to claim that these should not be multiplied against each other (4/5 x 9/10), he needs to show two things: that those two things are dependent on each other; and that that dependence changes the ratios to something other than I assigned. For example, imagine Luke’s not thinking to ever mention James ever led the Church, in a supposedly researched history of that Church, is somehow caused by his trial speeches also not seeming to know about a historical Jesus, such that wherever there is the latter, there will always be the former. In that case, the dependent probability of the omission of James is 1/1, and it no longer has any effect. We are then left with simply the 9/10 oddness of the trial speeches. Just as if drawing a king from the deck, at odds of 4/52, causes the next draw always to be a king, such that the probability of drawing two kings right off the top is simply 4/52, not 4/52 x 3/51.
Unfortunately, Fishers of Evidence never does this. For anything in OHJ. He doesn’t explain how, for example, the trial speeches omitting a historical Jesus, affects the probability of James being omitted from the entire history of the church. In what way are they dependent on each other? And even if we can come up with any plausible dependence (and they have to be plausible; wildly implausible dependencies have too low a probability to show up in the math at the resolution I employ), does it change my estimates at all? Is it really credible to say the weirdness of the trial speeches would always cause an omission of James? Certainly not.*
If they have any effect on each other at all, it’s extremely small. There are too many ways either could happen independently of the other. So is that tiny effect large enough to make the conjunction of both together any different from 4/5 x 9/10? A difference, that is, that shows up at that resolution? (For example, a difference of a millionth would be so small it would disappear when rounding to the nearest whole percentage point.) Such causal dependencies thus have no visible effect. (And even if they do, the effect may be in entirely the other direction: see comment.)
- ... one could propose a scenario whereby Acts is using a source (let’s say, a pre-Acts history of the church) that omits any knowledge of a historical Jesus (hence simultaneously causing an omission of James from the events of the church and the omission of an earthly Jesus from the trial speeches of Paul). That would get one of those to be 100% expected on the occurrence of the other.
However, by positing that scenario, you just changed the probability substantially —in the other direction. Because the likelihood now that the preceding history of the church used by Acts lacked a historical Jesus, given that Jesus existed, is far less than 9/10. Indeed, it’s well below 1/4, even a fortiori. In other words, if Acts added a historical Jesus to an earlier history that lacked one, it is all but certain Jesus never existed, and a historical Jesus was later fabricated —by authors doing exactly what this scenario entails Luke did.
So you need to be careful in what you are proposing to create dependent probabilities among the evidence.
If you want to tie two pieces of evidence together by some hypothesis of how they both came to match the appearance of a “no Jesus” result, that hypothesis cannot be presumed without substantially reducing the probability Jesus existed.
It’s a Catch-22 for any historicity apologist. What you need is a scenario whereby that conjunction is expected even if Jesus existed. But then you have to compare the prior probability of that scenario, with the prior probability of the alternative (e.g. a pre-Acts that lacked a historical Jesus). The latter might actually be more likely. After all, how would some proposed lost evidence of a historical Jesus simultaneously cause Acts to omit both James (from history) and a historical Jesus (from Paul’s trial speeches)? Far more likely that would be caused by evidence against the historicity of Jesus, not by evidence for a historical Jesus. A pre-Acts that omits a historical Jesus would easily explain that conjunction. But you would have to come up with a pretty convoluted theory to get, say, a pre-Acts that includes a historical Jesus yet still causes him to disappear in our Acts at precisely those two points (the role and existence of James altogether, and the content of Paul’s trial speeches).
Richard Carrier March 19, 2017, 11:55 AM
Re: Recalibrating Carrier - Correct Odds of Jesus's Historicity 46 - 18%
This reminds me of the old Presbyterian joke about Mary. After heated debate it was decided by 51% vote that Mary was a virgin. Gotta love the Scots. A few more votes the other way and Mary would be a skilled and experienced teenager.
I do love the way Carrier pulls numbers out of his rear end, then tries to make it sound scientific. But there is an answer to that.
"There are three kinds of lies: lies, damned lies, and statistics." -Benjamin Disraeli:
I do love the way Carrier pulls numbers out of his rear end, then tries to make it sound scientific. But there is an answer to that.
"There are three kinds of lies: lies, damned lies, and statistics." -Benjamin Disraeli:
“’That was excellently observed’, say I, when I read a passage in an author, where his opinion agrees with mine. When we differ, there I pronounce him to be mistaken.” - Jonathan Swift
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Paul the Uncertain
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Re: Recalibrating Carrier - Correct Odds of Jesus's Historicity 46 - 18%
While Fishers of Evidence (the series) does a good job overall as an introduction to the highways and byways of Jesus mythistoricism, this particular episode is not their finest quarter-hour. Since the presenter doesn't show his work, it's hard to say what he's "adding" and why, and whether that "corrects" Carrier or not.
It is not a good sign that the Fishers' evidence probabilities apparently are one because they are what was observed. No, indeed, that is not how this works.
Anyway, accounting for conditional dependencies within the evidence just changes the terms within the "product of the likelihood ratios" style that Carrier prefers, but doesn't change the arithmetic operations. That is, it's still a chain of multiplications. For alternatve hypotheses G and H and observations a, b, ..., z, instead of
p(G | a, b, ... z) / p(H | a, b, ..., z)
= p(G) / p(H) * p(a | G) / p(a | H) * p(b | G) / p(b | H) * ... * p(z | G) / p(z | H)
you have the more general
= p(G) / p(H) * p(a | G) / p(a | H) * p(b | G, a) / p(b | H, a) * ... * p(z | G, a, b, ...) / p(z | H, a, b, ...)
I think Carrier is saying that he did the latter. If so, then he was right to do it that way.
A substantive question raised in the video concerns the Rank-Raglan index and the related issue of whether Carrier did or didn't use the Gospels as evidence. It seems clear that Carrier did use the Gospels as evidence, to wit, in order to arrive at a Rank-Raglan score. That score is a summary statistic of the contents of the Gospels. Where else are we going to find out whether Mary was said to be a royal virgin, or Jesus was said to have died on a hilltop, if not in the Gospels (or, if you prefer, Matthew alone)?
Now, that does raise a debatable point: given that the Gospels do contain some relevant information, is it really the case that they contain no other relevant information than how Jesus fares on the Proust questionnaire? Um, Rank-Raglan Index, I mean.
If that is what Carrier believes, then that is what his analysis should show. and apparently it does. This is subjective probability, a representation of a particular person's confidence, Richard Carrier's confidence in this case, and not a representation of the output of any objective process, such as one that generates worlds where Jesus really lived and other worlds where he didn't.
It should be clear, however, that just on that one point, other people will fall on either side of Carrier, some finding Rank-Raglan uninformative given the availability of the Gospels, and others finding all sorts of probative value besides how dull Mary's sex life may have been and whether the Romans understood the principle that if you're going to make an example of somebody, then you should kill him where people can see you do it. Like a hilltop, for example,
It is not a good sign that the Fishers' evidence probabilities apparently are one because they are what was observed. No, indeed, that is not how this works.
Anyway, accounting for conditional dependencies within the evidence just changes the terms within the "product of the likelihood ratios" style that Carrier prefers, but doesn't change the arithmetic operations. That is, it's still a chain of multiplications. For alternatve hypotheses G and H and observations a, b, ..., z, instead of
p(G | a, b, ... z) / p(H | a, b, ..., z)
= p(G) / p(H) * p(a | G) / p(a | H) * p(b | G) / p(b | H) * ... * p(z | G) / p(z | H)
you have the more general
= p(G) / p(H) * p(a | G) / p(a | H) * p(b | G, a) / p(b | H, a) * ... * p(z | G, a, b, ...) / p(z | H, a, b, ...)
I think Carrier is saying that he did the latter. If so, then he was right to do it that way.
A substantive question raised in the video concerns the Rank-Raglan index and the related issue of whether Carrier did or didn't use the Gospels as evidence. It seems clear that Carrier did use the Gospels as evidence, to wit, in order to arrive at a Rank-Raglan score. That score is a summary statistic of the contents of the Gospels. Where else are we going to find out whether Mary was said to be a royal virgin, or Jesus was said to have died on a hilltop, if not in the Gospels (or, if you prefer, Matthew alone)?
Now, that does raise a debatable point: given that the Gospels do contain some relevant information, is it really the case that they contain no other relevant information than how Jesus fares on the Proust questionnaire? Um, Rank-Raglan Index, I mean.
If that is what Carrier believes, then that is what his analysis should show. and apparently it does. This is subjective probability, a representation of a particular person's confidence, Richard Carrier's confidence in this case, and not a representation of the output of any objective process, such as one that generates worlds where Jesus really lived and other worlds where he didn't.
It should be clear, however, that just on that one point, other people will fall on either side of Carrier, some finding Rank-Raglan uninformative given the availability of the Gospels, and others finding all sorts of probative value besides how dull Mary's sex life may have been and whether the Romans understood the principle that if you're going to make an example of somebody, then you should kill him where people can see you do it. Like a hilltop, for example,