From: Stephen Carlson (scc@reston.icl.com)
Date: Mon Jan 22 1996 - 15:49:19 EST
Thanks to Wes Williams, for his answers about how often John uses
QEOS qualitatively rather than definitely. The reason I was asking
was that ever since a bunch of statistics were posted last fall on
the use of Colwell's rule in analyzing Jn1:1. Colwell's rule is
framed in terms of conditional probability (that is, when we are given
additional information about an event) and many of the statistics
that were posted were also conditional probabilities. I figured that
one of the most important theorems about conditional probability,
Bayes Theorem, ought to be relevant.
The following is my analysis of John 1:1c with a Bayesian approach.
My basic conclusion, if you don't want to read through it, is that
although the placement of QEOS before the verb, without the article,
is evidence for a qualitative meaning, it is very weak evidence for
it, due to the fact the QEOS is overwhelmingly definite in John.
This is not the kind of question that can be decided by the use of
statistics. Rather, good old-fashioned exegesis is called for.
A BAYESIAN APPROACH TO JOHN 1:1c
Consider a fair coin flipped twice. Now the probability that it came
up heads twice (HH) is 25%. If you were told that (at least) one of
the flips came up heads, what is the probability that both are heads?
In the mid-18th century, the Rev. Thomas Bayes was investigating this
kind of problem, and he figured out, in a theorem that now bears his
name, that we must look at the relative probabilities of the events
involved when new information is received. In this case, there is only
one chance that the coins are HH, but two chances, HT & TH, that there
are not two heads, given that one of them is heads. Therefore, the
odds are 1:2, or a probability of 33%. (If the information is that
the *first* coin was heads, the odds change to 1 {HH} : 1 {HT}, or 50%.)
Here we see how new information affects our understanding of the
probabilities. Before we're told anything about the flipped coins,
the prior probability for two heads was 25%. When we're told that
one of them is heads, that information changes the prior probability
to a posterior probability of 33%. Since the information that one of
the coins is heads increases the probability that both are head, it
constitutes evidence for that proposition. The strength of the evidence
is determined by looking at much the probability changes. In this case,
that information is good, but not strong, evidence.
Bayesian analysis is most practically used today in the context of
medical screening for diseases. Consider a disease, D, that affects
one person in a thousand [i.e, P(D) = 0.001], and there is a screening
test, which 90% of the time will give a positive result, P, when the
person has the disease [P(P|D) = .9], but will also give a positive
result in 2% of the cases when the person does not have the disease
[P(P|D') = .02]. What is the probability that a person who tests
positive for the disease will actually have it?
According to Bayesian analysis, we have to look at the relative
probabilities. Testing positive will happen for two reasons: (1)
one had the disease and the test workes, with probability: P(D)P(P|D) =
.001 * .9 = 0.0009; and (2) not having the disease and getting a
false positive, with probability P(D')P(P|D') = .999 * .02 = 0.01998.
Therefore the odds are 0.0009 to 0.01998, or only 4.3%, of actually
having the disease with a positive result. The answer may appear
counter-intuitive, but the reason the number worked out the way it did
is that the disease is so rare that most of the positive results are
false positives, even at the 2% rate. Because it produces answers
that are counter-intuitive, Bayes theorem can be a powerful tool in
analyzing probabilities.
Now, consider Jn1:1c: KAI QEOS HN hO LOGOS. What is the probability
that QEOS is definite (D), given that is is anarthrous and precedes
the verb (AP)? This is ripe for an application of Bayes Theorem.
We would need to calculate the odds P(D)P(AP|D) : P(D')P(AP|D'),
where P(D) is the (prior) probability that QEOS is definite in John,
P(AP|D) is the probability that a definite predicate nominative is
anarthrous and precedes the verb, and P(AP|D') is the probability
that a qualitative predicate nominative precedes the verb.
I must thank Dr. Paul Dixon for sharing with list back in May, some of
the results of his thesis on the abuse of Colwell's rule. He said,
"Our conclusions show that when John wished to express a
definite predicate nominative, he usually wrote it after
the verb with the article, 66 of 77 occurrences or 86%
probability. When he wished to express a qualitative
predicate nominative, he usually wrote it before the verb
without the article, 50 of 63 occurrences or 80% probability."
Therefore, P(AP|D') is 80%. Applying Colwell's rule, we'll assume
that all of the remaining 14% of the cases in which John does not
write a definite predicate nominative after the verb with the article,
he writes it before the verb without it. (My numbers do not have to
be exact to support my general conclusions, there is quite a bit of
tolerance in the exact values.) So, the odds that QEOS is definite
in Jn1:1 is P(D) * 14% : P(D') * 80%, where P(D) is the prior probability
that QEOS is definite.
What is that prior probability? John uses QEOS, in its various forms,
about 80 times, none of which (excluding Jn1:1c) is clearly qualitative.
Therefore, I may be justified in assuming a 1/80 or 98.75% prior
probability that QEOS is definite. The odds then become: 98.75 * 14 :
1.25 * 80, or about 93% probability. Therefore, although the fact that
QEOS is anarthrous and precedes the verb is evidence against it being
definite, it is not very strong evidence, because it is still 93%
probable (down from 98.75%) that it is definite. The fact that QEOS is
so overwhelmingly definite in John means that the normal indicator of a
qualitative meaning is not very probative. In fact, if the prior prob-
ability of it being qualitative improved to 1/8 (ten times more likely),
QEOS would still more likely than not statistically be definite in this
position.
CONCLUSIONS
1. The syntax of Jn1:1c is evidence in favor of QEOS being qualitative,
but its strength is very weak because the noun is overwhelmingly
definite.
2. What is more important, however, is evaluating the prior probability
of QEOS being qualitative before looking at the syntax. This article
assumed that it can be determined simply by counting the occurrences.
This may not be the best approach. The context itself may suggest
different populations (rather than the singular QEOS in John) for the
prior probability.
3. Due to the importance of the prior probability in how it affects the
Bayesian analysis and due to the strength of this kind of evidence,
statistics alone don't help much. We still have to examine the context
very carefully to determine its meaning. There is contextual evidence
for either position. Jn1:1c may be in contrast with v14 which calls for
the qualitative meaning, but the climactic structure of v1 and its
juxtaposition of QEON with KAI QEOS argues the other way.
4. Colwell's rule is not directly applicable to this situation, but it
helped to determine one of the relevant probabilities in the Bayesian
analysis.
Stephen Carlson
-- Stephen Carlson : Poetry speaks of aspirations, : ICL, Inc. scc@reston.icl.com : and songs chant the words. : 11490 Commerce Park Dr. (703) 648-3330 : Shujing 2:35 : Reston, VA 22091 USA
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