Fifty out of fifty-three occurrences is 94%. And this observation is the
apparent basis for the following conclusion in Dixon's thesis, available
on the Web:
"Third, this thesis demonstrates that the statistical probability
of QEOS being qualitative, rather than definite or indefinite, is
quite high, 94%."
This conclusion does not follow from the observation, because it does not
consider how likely the noun QEOS itself can be definite, indefinite, or
qualitative. Fortunately, the Rev. Thomas Bayes (d. 1761) realized, in a
theorem that now bears his name, that in considering how new information
affects prior probabilities, one must look at the relative probabilities.
The word QEOS is definite with some prior probability, P(D), which may be
estimated from examining the literature. We are interested in assessing the
probability that this word is definite given the new information that it is
(A)narthrous and (P)recedes the verb, or in a mathematical notation, P(D|AP).
According to Bayes Theorem, then,
P(D|AP) = P(D)P(AP|D) : P(D')P(AP|D'). (1)
In other words, we must consider the relative probability of QEOS being
definite when anarthrous and preceding the verb versus being non-definite
when anarathrous and preceding the verb.
We can estimate P(AP|D), the probability that QEOS will be anarthrous and
preceding the verb, when definite. Paul's thesis at the web site states:
"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."
Therefore, we estimate that a definite QEOS should precede the verb with
100%-86% = 14% probability. By Colwell's rule, all 14% is anarthrous.
For the estimate of P(AP|D'), the probability that QEOS will be anarthrous
and preceding the verb, when non-definite, we will use another observation
in his thesis:
"When he wished to express a qualitative predicate nominative with
the verb, he usually wrote it before the verb without the article,
50 of 63 occurrences or 80% probability."
Thus, P(AP|D') = 80%. Substituting these estimates back into equation
(1),
P(D|AP) = P(D)P(AP|D) : P(D')P(AP|D'), (1)
we find our odds calculation becomes:
P(D|AP) = P(D) 14% : P(D') 80%. (2)
If QEOS is just as likely to be definite as non-definite, or P(D) =
P(D') = 50%, then the odds become 50% 14% : 50% 80% = 7:40 = 7/47 = 15%.
In other words, for a noun that is just as likely to be or not to
be definite, an anarthrous noun preceding the verb is likely to be
definite only 15% of the time.
However, QEOS is not just as likely to be definite as non-definite.
In fact, it is overwhelmingly definite in the Fourth Gospel. Out of
the 80 other instances, I am able to discern no other example (outside
of Jn1:1) in which QEOS is not definite. This fact implies that the
prior probability that QEOS is definite, P(D), is at least something
like 79/80 or 98.75%. Plugging this value of P(D) = 98.75%, P(D') =
100% - 98.75% = 1.25% into equation (2), we find that the probability
that QEOS is definite, given the new information that QEOS is anarthrous
and appears before the verb, drops to 93%. Even if QEOS is ten times
more likely to be definite than it is observed to be, the odds would
only be about 50:50. It is nowhere near the 94% that was concluded.
In other words, although the fact that QEOS is anarthrous and precedes
the verb is indeed evidence for QEOS not being definite, it is extremely
weak evidence, since QEOS itself is so overwhelming definite.
Therefore, it is best to ignore the probabilistic argument in Jn1:1
and instead rely on a good, in-depth analysis of the context.
Stephen Carlson
-- Stephen C. Carlson : Poetry speaks of aspirations, scarlson@mindspring.com : and songs chant the words. http://www.mindspring.com/~scarlson/ : -- Shujing 2.35