Fun with Bayes' theorem and the argument from silence

Discussion about the New Testament, apocrypha, gnostics, church fathers, Christian origins, historical Jesus or otherwise, etc.
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ApostateAbe
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Fun with Bayes' theorem and the argument from silence

Post by ApostateAbe »

The more sophisticated mythicists do not employ the argument from silence so much, but it remains the favorite argument among the legions of unsophisticated mythicists on the Internet. In short, the logic would seem to disprove the existence of almost everyone in ancient history. Sometimes that point isn't enough, so this is a full mathematical explanation of why that argument from silence fails. Note that it is NOT an argument for the existence of Jesus. It is a criticism of an argument. I will use Bayes' theorem to calculate the probability that Jesus never existed GIVEN that there are no extant unbiased first-hand written accounts of Jesus. Bayes' theorem has been abused by mythicists and Christians, but I think it is appropriate when we can all roughly agree on the input values. The estimates will assume that the hypothesized "Jesus" is a rural doomsday cult leader (not God, not a demigod, nor a genuine prophet) that we may expect in first-century Palestine.

H = the hypothesis that Jesus never existed.

H' = the hypothesis that Jesus existed.

D = the datum that there are no extant unbiased first-hand written accounts of Jesus.

P(H) = the prior probability that Jesus never existed = 0.5. This value is generous but largely irrelevant for calculating how much the probability increases or decreases.

P(D|H) = the probability of the datum that there are no extant unbiased first-hand written accounts of Jesus GIVEN that Jesus never existed = 0.999999999. Or there is only a one in a billion chance that there would be unbiased first-hand written accounts of Jesus of Nazareth GIVEN that Jesus never existed. This is a generously-high estimate.

P(D|H') = the probability of the datum that there are no extant unbiased first-hand written accounts of Jesus GIVEN that Jesus existed = 0.999. Or there is only a one in a thousand chance that there would be unbiased first-hand written accounts of Jesus GIVEN that Jesus existed. This is a generously-low estimate.

Calculate P(H|D), the probability that Jesus never existed GIVEN that there are no extant unbiased first-hand written accounts of Jesus.

P(H|D) = (P(D|H)*P(H))/(P(D|H)*P(H)+P(D|H')*(1-P(H)))
= (0.999999999*0.5)/(0.999999999*0.5+0.999*(1-0.5))
= 0.50025

P(H|D) = 0.50025. The probability that Jesus never existed increases by 0.00025 given that there are no extant unbiased first-hand written accounts of Jesus. It is 0.025%. It is a trivial increase in probability.

The high value of P(D|H') is what makes a big difference. The fallacy is to falsely imagine this value is low by intuitively assuming a modern environment where writing is common. For example, if Jesus the loud-mouthed doomsday cult leader were only recently killed, we may expect only a 0.1 chance that there would be no unbiased first-hand written accounts, and in that case P(H|D) recalculates to 0.91. The scarcity of writing in the ancient world makes a big difference.

Go to this page to easily calculate using Bayes' Theorem:

http://psych.fullerton.edu/mbirnbaum/ba ... esCalc.htm
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cienfuegos
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Re: Fun with Bayes' theorem and the argument from silence

Post by cienfuegos »

I do not disagree that the argument from silence is only minimally supportive of mythicism (more important would be the positive statements found in early Christian writings to support the view that Jesus was a character derived from scripture, which is what I think).

However, why do you limit your search to "unbiased, first-hand accounts." I would think that even "biased, first-hand accounts" that could stand scrutiny as authentic at least with equal standing with the consensus view of Paul's authentic body of work would count.
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ApostateAbe
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Re: Fun with Bayes' theorem and the argument from silence

Post by ApostateAbe »

cienfuegos wrote:I do not disagree that the argument from silence is only minimally supportive of mythicism (more important would be the positive statements found in early Christian writings to support the view that Jesus was a character derived from scripture, which is what I think).

However, why do you limit your search to "unbiased, first-hand accounts." I would think that even "biased, first-hand accounts" that could stand scrutiny as authentic at least with equal standing with the consensus view of Paul's authentic body of work would count.
I limited it to "unbiased" accounts because that is the typical demand made by the mythicists. The gospels and Paul are testimonies of Jesus that would count for something, even if they are not first-hand, except that they are biased. If there was a biased first-hand account of Jesus, then it would be dismissed as a lie.
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John T
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Re: Fun with Bayes' theorem and the argument from silence

Post by John T »

Absence of evidence is not evidence of absence.

Sincerely,

JT
"It is useless to attempt to reason a man out of a thing he was never reasoned into."...Jonathan Swift
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toejam
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Re: Fun with Bayes' theorem and the argument from silence

Post by toejam »

^Sure it is. Absence of evidence is not proof of absence, but it is evidence for it. If not, how else could one demonstrate that there is no marble inside an empty box other than by observing the inside of the box and finding no evidence for a proposed marble?
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Peter Kirby
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Re: Fun with Bayes' theorem and the argument from silence

Post by Peter Kirby »

toejam wrote:^Sure it is. Absence of evidence is not proof of absence, but it is evidence for it. If not, how else could one demonstrate that there is no marble inside an empty box other than by observing the inside of the box and finding no evidence for a proposed marble?
http://peterkirby.com/dharmakirti.html

"Non-apprehension as a reason may establish non-existence, if the object fulfills the conditon of apprehensibility by the knower. The specific nature of the object must be such that it is not remote from the senses due to any of the three kinds of remoteness: remoteness in space, remoteness in time, and remoteness by self-nature of the object."

Your marble example is specifically constructed so that it meets the criteria of a successful argument.

Other examples can be constructed which fail one or more criteria.

(1) Alien Life - go looking for it with a telescope - fails a criterion because of remoteness in space.
(2) Jesus - go looking for him in the Holy Land - fails a criterion because of remoteness in time.
(3) Atoms - go looking for them in that box (with a naked eye) - fails a criterion because of self-nature of the object.
"... almost every critical biblical position was earlier advanced by skeptics." - Raymond Brown
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ApostateAbe
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Re: Fun with Bayes' theorem and the argument from silence

Post by ApostateAbe »

Absence of evidence can be either a strong or a weak argument for the non-existence hypothesis, depending on the respective expectations of each hypothesis. Maybe we really do strongly expect to find strong evidence given the existence hypothesis. If we do NOT expect to find strong evidence given the existence hypothesis, then absence of evidence is a weak argument for non-existence. Don't depend on those proverbs. I think Carl Sagan popularized it mainly for use in defending the position that there exists extraterrestrial intelligent life in the Milky Way. And Christians of course abuse it to defend the existence of God.
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MrMacSon
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Re: Fun with Bayes' theorem and the argument from silence

Post by MrMacSon »

toejam wrote:^Sure it is. Absence of evidence is not proof of absence, but it is evidence for it.
Absence of evidence for something supports the proposition that something (or someone) does not exist, or never did.

The proposition something (or someone) never existed ought to be supported by other propositions or premises as part of an argument.
ApostateAbe wrote:Absence of evidence can be either a strong or a weak argument for the non-existence hypothesis, depending on the respective expectations of each hypothesis.
Expectations are a form of bias.
ApostateAbe wrote: Maybe we really do strongly expect to find strong evidence given the existence hypothesis.
"strong evidence" for what?
ApostateAbe wrote: If we do NOT expect to find strong evidence given the existence hypothesis, then absence of evidence is a weak argument for non-existence.
The double negatives - "do NOT expect" and "absence of evidence" makes this a non-sequitur. The proposition something (or someone) never existed ought to be supported by other propositions or premises as part of an argument.
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ApostateAbe
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Re: Fun with Bayes' theorem and the argument from silence

Post by ApostateAbe »

MrMacson, expectations of a theory are essential. Another way to express the principle is "predictive."
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MrMacSon
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Re: Fun with Bayes' theorem and the argument from silence

Post by MrMacSon »

Yes, absence of evidence is predictive.
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