I'd like to ask you if any part of your review deals with the mechanics of Bayes Theorem as applied by Carrier. The reason I ask is because I believe (perhaps erroneously) that Carrier uses a cut-off date for his evidence that is directly used to argue his case, and AFAIU this cut-off date is c.150 CE. I notice your Part 2 introduces his treatment of Epiphanius who is a later 4th century "master heresiologist" who is obviously way past the 150 CE cut-off. I do understand that Bayes Theorem uses explicit terminology (see below) and that somehow this 4th century evidence is included even though this 150 CE cut-off date is also used.GakuseiDon wrote: ↑Sat Mar 18, 2023 2:27 amI'll be interested in people's feedback of my draft. If there is anything unclear or wrong, please don't hesitate to let me know.
Thank you!
I am happy to wait until a further more appropriate Part of your review is introduced in order to answer my question. The answer may relate to b and e (below) but atm I am not sure.
Thanks G'Don
7. Explanation of the Terms in Bayes’ Theorem
P = Probability (epistemic probability = the probability that something stated is true)
h = hypothesis being tested
~h = all other hypotheses that could explain the same evidence (if h is false)
e = all the evidence directly relevant to the truth of h (e includes both what is observed
and what is not observed)
b = total background knowledge (all available personal and human knowledge about
anything and everything, from physics to history)
P(h|e.b) = the probability that a hypothesis (h) is true given all the available evidence (e)
and all our background knowledge (b)
P(h|b) = the prior probability that h is true = the probability that our hypothesis would
be true given only our background knowledge (i.e. if we knew nothing about e)
P(e|h.b) = the posterior probability of the evidence (given h and b) = the probability
that all the evidence we have would exist (or something comparable to it would
exist) if the hypothesis (and background knowledge) is true. = [consequent probability]
P(~h|b) = 1 – P(h|b) = the prior probability that h is false = the sum of the prior
probabilities of all alternative explanations of the same evidence (e.g. if there is
only one viable alternative, this means the prior probability of all other theories is
vanishingly small, i.e. substantially less than 1%, so that P(~h|b) is the prior
probability of the one viable competing hypothesis; if there are many viable
competing hypotheses, they can be subsumed under one group category (~h), or
treated independently by expanding the equation, e.g. for three competing
hypotheses [ P(h|b) x P(e|h.b) ] + [ P(~h|b) x P(e|~h.b) ] becomes [ P(h1|b) x
P(e|h1.b) ] + [ P(h2|b) x P(e|h2.b) ] + [ P(h3|b) x P(e|h3.b) ])
P(e|~h.b) = the posterior probability of the evidence if b is true but h is false = the
probability that all the evidence we have would exist (or something comparable to
it would exist) if the hypothesis we are testing is false, but all our background
knowledge is still true. This also equals the posterior probability of the evidence if
some hypothesis other than h is true—and if there is more than one viable
contender, you can include each competing hypothesis independently (per above)
or subsume them all under one group category (~h). = [consequent probability]
EXTRACTED FROM: Richard C. Carrier, Ph.D.
“Bayes’ Theorem for Beginners: Formal Logic and Its
Relevance to Historical Method — Adjunct Materials
and Tutorial”
The Jesus Project Inaugural Conference
“Sources of the Jesus Tradition: An Inquiry”
5 December 2008 (Amherst, NY)
P = Probability (epistemic probability = the probability that something stated is true)
h = hypothesis being tested
~h = all other hypotheses that could explain the same evidence (if h is false)
e = all the evidence directly relevant to the truth of h (e includes both what is observed
and what is not observed)
b = total background knowledge (all available personal and human knowledge about
anything and everything, from physics to history)
P(h|e.b) = the probability that a hypothesis (h) is true given all the available evidence (e)
and all our background knowledge (b)
P(h|b) = the prior probability that h is true = the probability that our hypothesis would
be true given only our background knowledge (i.e. if we knew nothing about e)
P(e|h.b) = the posterior probability of the evidence (given h and b) = the probability
that all the evidence we have would exist (or something comparable to it would
exist) if the hypothesis (and background knowledge) is true. = [consequent probability]
P(~h|b) = 1 – P(h|b) = the prior probability that h is false = the sum of the prior
probabilities of all alternative explanations of the same evidence (e.g. if there is
only one viable alternative, this means the prior probability of all other theories is
vanishingly small, i.e. substantially less than 1%, so that P(~h|b) is the prior
probability of the one viable competing hypothesis; if there are many viable
competing hypotheses, they can be subsumed under one group category (~h), or
treated independently by expanding the equation, e.g. for three competing
hypotheses [ P(h|b) x P(e|h.b) ] + [ P(~h|b) x P(e|~h.b) ] becomes [ P(h1|b) x
P(e|h1.b) ] + [ P(h2|b) x P(e|h2.b) ] + [ P(h3|b) x P(e|h3.b) ])
P(e|~h.b) = the posterior probability of the evidence if b is true but h is false = the
probability that all the evidence we have would exist (or something comparable to
it would exist) if the hypothesis we are testing is false, but all our background
knowledge is still true. This also equals the posterior probability of the evidence if
some hypothesis other than h is true—and if there is more than one viable
contender, you can include each competing hypothesis independently (per above)
or subsume them all under one group category (~h). = [consequent probability]
EXTRACTED FROM: Richard C. Carrier, Ph.D.
“Bayes’ Theorem for Beginners: Formal Logic and Its
Relevance to Historical Method — Adjunct Materials
and Tutorial”
The Jesus Project Inaugural Conference
“Sources of the Jesus Tradition: An Inquiry”
5 December 2008 (Amherst, NY)