in my video on the basic credibility of
competing theories I made an obtuse
reference to a mathematical error made
by a prominent MIT assist and I've been
asked to explain this the methodist is
Richard carrier he makes his case for
mrs. ism in two books in proving history
he sets out a method by which evidence
will be sought and applied to a
mathematical decision-making model the
output of which is a probability that
Jesus was a historical figure carrier
employs Bayes theorem Bayes theorem is a
key result in basic probability theory
and it's widely used in probability and
statistics it's about conditional
probability when the probability of a
random event a occurring is conditional
on whether another random event B has
also occurred it is stated as this
formula in words it means the
probability of a given B is equal to the
probability of B given a time's the
probability of a without reference to be
all divided by the probability of B
without reference to a as an example an
exam has a pass rate of forty percent a
college offers an optional preparatory
course 1,000 people take the exam of
which 200 took the course as expected
400 parts of which 100 took the course
what is the probability of passing the
exam given that you have taken the
course the obvious answer is 50% we can
also use Bayes theorem so the
probability of passing the exam given
that you took the course is equal to the
probability of taking the course given
that you passed the exam which is point
two five times the probability of
passing the exam which is point for all
divided by the probability of taking the
course which is point two so in this
case Bayes theorem gets the right result
but
rather a roundabout way of doing in it
here's a more realistic example we have
a test to see if someone with a headache
has meningitis this test will be
positive in 99 and a half percent of
people with meningitis and it will be
positive in half a percent of people who
do not have meningitis we also know that
one in a thousand people with headache
have meningitis that being so if
somebody test positive what is the
probability that they have meningitis so
the probability of having meningitis
given that the test is positive is equal
to the probability of testing positive
given that they have meningitis times
the probability of having meningitis all
over the probability of testing positive
the probability of testing positive is
equal to the probability of having
meningitis and testing positive plus the
probability of not having meningitis and
testing positive this is what it comes
out that surprising perhaps carriers
formulation of the historicity question
then is the probability that Jesus
existed given the evidence we have is
equal to the probability of finding the
evidence we have given that he existed
times the probability that he existed
divided by the probability of finding
the evidence we have whether or not he
existed which of course equals 1 as we
have the evidence that we have carrier
actually used the odds form of Bayes
theorem which is exactly equivalent but
it's rather more confusing this is a
perfectly correct application of Bayes
theorem but it is rather a roundabout
way of calculating the probabilities and
it is rather obscure especially to his
audience who are primarily scholars of
the new testament in ancient history and
so are not generally familiar with
probability theory the complexity of
Bayes theorem does therefore rather
obscure the message it is not however in
correct the error he makes is a much
more fundamental one carrier does not
classify the issue into specific
arguments as I have done but rather in
two bodies of evidence calculating
probabilities set
Lee for evidence from the Acts of the
Apostles the epistles the Gospels and
the extra biblical record he also bases
his argument for the prior probability
that is the probability that Jesus
existed without reference to these
bodies of evidence on the rank raglan
hero class which if you follow the
mythos ISM versus historicity debate you
will certainly come across again not an
incorrect approach but rather a
convoluted one his era however is in
using what are called geometric
probability combinations in other words
multiplying probabilities together
rather than adding them up basic
probability theory concerned with things
like rolling dice and chlorine cards
uses these geometric combinations so
that for example the chance of rolling
two sixes is 1 over 6 times 1 over 6 or
1 over 36 the chance of drawing two
hearts from a deck of cards is 13 over
52 x 12 over 51 etc the problem is that
basic probability courses often gloss
over a hard assumption that must be met
if geometric probability combinations
are to be reasonable and that assumption
is that the probabilities being combined
are strictly independent of each other
and in the case of Jesus they clearly
aren't independent of each other ax was
written by the same author as one of the
Gospels the epistles may be independent
of the Gospels as they were written
before them but the Gospels cannot be
said to be independent of the epistles
neither can the biblical and extra
biblical records be said to be
independent of each other all groups of
evidence were derived ultimately from a
similar time and from the same or
similar religious groups the alternative
to geometric probability combinations is
arithmetic in which probabilities are
added up and weighed though strictly
independence is also an assumption for
models that use arithmetic probability
combinations it's a much softer one the
reason being that the individual
probabilities have a far lower overall
impact on the final result
than they do with geometric combinations
in the UK the best known illustration of
this error concerns the case of Roy
meadow meadow was a pediatrician who
gave evidence in several trials of cot
death cases including that of Sally
Clark a lawyer who had two children die
from cot death meadow calculated that
the odds of this happening by natural
causes was 73 million to one or one in a
hundred years in England and Wales he
arrived at this figure by squaring the
cot death rate in her socio-economic
group which was one in 8,500 live births
he probably did not realize that he was
making the assumption in this
calculation that cot death does not run
in families this was a foolish
assumption given that very few diseases
do not run in families even though at
the time the evidence of cot death
running in families was limited in fact
cot death does run in families and his
error put his calculation out by a
factor of at least 100 this means that
at least one family a year will be
affected by a second cot death from
natural causes as any such cases are
liable to end up in court natural causes
was the most probable explanation Sally
Clark was innocent and ultimately died
as a consequence of the stresses she had
endured this case in which an innocent
mother already grieving two children
were sent to prison left a lasting stain
on the British legal system anyway
returning to Jesus using geometric
combinations of probabilities from his
evidence groups carry a calculated upper
and lower bounds of probability they
were that the probability that Jesus
existed is between thirty two percent
and point zero eight percent I have
recalculated carriers probabilities
arithmetic Lee there are different ways
of doing this by using different
weightings for example but I have simply
waited his groups
equally my arithmetic calculation gives
an upper bound probability of
historicity of forty six percent and a
lower bound of eighteen percent this
seems not an unreasonable result but
caution is necessary carriers assessment
of the probabilities of the various
evidence groups was essentially
arbitrary he estimated these
probabilities in the knowledge that the
results would be used in his geometric
model he knew what the results of his
model would be but did not know the
error he had made and was therefore
minded to be generous towards
historicity in the light of what his
model produced had he been using an
arithmetic model he would no doubt have
been more circumspect his argument is
based on the idea of being very
reasonable towards the historicist
viewpoint and then demonstrating that
even being reasonable it still does not
hold up and this argument is utterly
fallacious it should be obvious that
when we examine an issue like
historicity versus mythos ism we weigh
evidence for one side or the other as
happens in court and as we do for
countless decisions in our lives
weighing is an inherently arithmetic
process in which weights are added or
subtracted but not multiplied or divided
I have no desire to dismiss carriers
work within the field of his expertise
that being New Testament and ancient
historical scholarship he makes a fair
argument but he really ought to fix his
mathematics to make it both fairer and
more accessible