Colwell's rule and other statistical arguments are occasionally used in analyzing Jn1:1, whether the QeoV of the last clause should be rendered definitely ("and the Word was God") or qualitatively ("and the Word was divine.") 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 are also conditional probabilities. Therefore, one of the most important theorems about conditional probability, Bayes Theorem, ought to be relevant.
Although the placement of QeoV before the verb, without the article, is evidence for a qualitative meaning, it is very weak evidence for it, due to the fact the QeoV 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.
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 and 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%. Similarly, when we're told that the first one is heads, that information changes the priority to a posterior probability of 50%. Evidence is information, which if accepted, causes us to consider a conclusion to be more likely than before or less likely than before. Irrelevant information, which does not make the conclusion either more or less likely, is not evidence. Since the information that one of the coins is heads increases the probability that both are heads, it constitutes evidence for that proposition. The strength of the evidence is determined by looking at how much the probability changes. In this case, knowing that one of the coin flips was head is good, but not strong, evidence that both were heads.
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]. There is a screening test that 90% of the time gives a positive result, P, only when the person actually has the disease [P(P|D) = .9], but will also give a false 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 consider at the relative probabilities. Testing positive will happen for two reasons: (1) one had the disease and the test worked, 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 of actually having the disease with a positive test result are 0.0009 to 0.01998, or only 4.3%. 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 QeoV hn o logoV. What is the probability that QeoV 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 QeoV 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 the B-GREEK mailing 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 very precise 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 QeoV 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 that QeoV is qualitative, or 98.75% prior probability that QeoV is definite. The odds then become: 98.75 * 14 : 1.25 * 80, or about 93% probability. Therefore, although the fact that QeoV 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 QeoV is so overwhelmingly definite in John means that the normal indicator of a qualitative meaning is not very probative. In fact, if the prior probability of it being qualitative improved to 1/8 (ten times more likely), QeoV would still more likely than not statistically be definite in this position.
Stephen Carlson