A bayesian approach to the Colwell Rule in John 1,1

REVISITING THE COLWELL CONSTRUCTION:

 

A BAYESIAN APPROACH TO JOHN 1,1

 

 

 

 

 

COLWELL'S RULE

 

The construction of the second part of John  1,1 is: "και θεος ην ο λογος"  (kai theos en ho logos) that is "and the Word was God". A famous scholar [1]of the Greek koiné has shown how, nearly always, in the New Testament, "definite predicate nouns which precede the verb usually lack the article, but definite predicate nouns which follow the verb usually take the article"

 

 

Subject + Copula + Article + Nominal Predicate = Nominal Predicate + Copula + Subject

 

 

 

Two equal cases to John 1,1 are John 1,49 and John 19,21 with: " basileus ei tou Israel " (You are King of Israel!) and "basileus eimi toon Ioudaioon" (I am King of the Jews): also the nominal predicate "king" does not have the article here, precedes the verb "to be" and refers to Jesus Christ.

 

Also admitting some exceptions, the so-called "Colwell's rule " is efficient in a very high number of cases. The table (developed from the same Colwell, analysing 367 verses of the New Testament) indicates as approximately in 90 per cent of the cases definite predicate nouns preceding the verb usually lack the article, but take the article when they follow the verb "to be".

 

 

 

After verb

Before verb

 

Total

 

Definite predicate nouns with the article

 

229

15

244

Definite predicate nouns without the article

 

26

97

123

Total

 

255

112

367

 

 

Later on, Colwell analysed the Septuagint and the Didaché, confirming the same percentages founded for the New Testament.

 

Colwell, in order to demonstrate the validity of its rule, pointed how in some authoritative manuscripts, three verses of the New Testament (Matthew 23,10; John 1,49; James 2,19) differs in the subject-copula-predicate order, also maintaining identical meaning. Codex Vaticanus and Codex Sinaiticus disagree: B each time has the predicate before the verb without the article, while א each time has the predicate after the verb with the article.

 

It is necessary to admit that "Colwell's Rule" cannot attest mathematically if a nominal predicate is determined or undetermined: logic and theology come into this; the rule only asserts that a determined nominal predicate is inclined to lose the article when  precede the verb and tend to conserve the article when follows the verb. From a grammatical point of view, Colwell's Rule is not a mathematical certainty but shows, if used correctly, a strong tendency, an empirical regularity, and a high probability. From a theological point of view, it is also necessary to admit that, if for the "monotheist" θεος always is determined (because only one God exists and all the others are "no gods"), for "non-trinitarian people" θεος can also be undetermined (because Jewish language uses "Elohim "also for angels, judges and vary powerful beings, while Greek language uses θεος also for the judges).

 

It is also necessary to remember that Colwell took into account only nominal determined predicates. Practically he was like a researcher sampling only snowy days and excluding from observations  serene days and rainy ones. If it is true that in snowy days they are some meteorological conditions, then the contrary is not necessarily true: high pressures, northern winds and low temperatures do not guarantee snowy precipitations. Saying this, it is not neither absurd, nor impossible nor unfair to estimate the inverse probability, that is the probability that, given some meteorological conditions, abundant snowfall would happen [2]. From a logical point of view, it is necessary to admit that, although it is not possible to use in a free and easy way the Colwell's rule and its converse (that is to employ the inverse of the Colwell's rule in order to assert with dogmatic certainty if nominal predicate is determined or undetermined), we cannot consider like an abuse every use of the Colwell's construction in order to support definiteness of  "θεος ".

 

Given the probability that θεος is determined and given the probability that θεος as anarthrous predicate nominative precede the verb, it is always possible to estimate, using Bayes's theorem, inverse probability, that is the probability that θεος is determined when precedes the verb "to be" without article.

 

 Therefore although it is not possible to use Colwell's statistics in a free and easy way, it seems however fair, possible and reasonable to employ, in a probabilistical way, Colwell's rule and  its converse. If we admit -also for a moment- that θεος in John 1.1 is determined, the loss of the article is reasonable and grammatically consistent with the Colwell 's rule.

 

 

BIBLICAL CONTEXT

 

According to Colwell a predicate nominative which precedes the verb cannot be translated as an “indefinite” or a “qualitative” noun solely because of the absence of the article; if the context suggests that the predicate is definite, it should be translated as a definite noun in spite of the absence of the article. In the case of a predicate noun which follows the verb the reverse is true; the absence of the article in this position is a much more reliable indication that the noun is indefinite. Loosely speaking, this study may be said to have increased the definiteness of a predicate noun before the verb without the article, and to have decreased the definiteness of a predicate noun after the verb without the article.

 

At the beginning of the world the presence of a small god with YHWH is drastically denied.  It is written:

 

·         "I am YHWH your God, who brought you out of the land of Egypt, out of the house of bondage. You shall have no other gods before me”. (Exodus 20,2-3)

·         "'See now that I, even I, am he, and there is no god beside me; I kill and I make alive; I wound and I heal; and there is none that can deliver out of my hand. (Deuteronomy 32,39)

·         Thus says the YHWH, your Redeemer, who formed you from the womb: "I am YHWH, who made all things, who stretched out the heavens alone, who spread out the earth. Who was with me?” (Isaiah 44,24)

·         "You are my witnesses," says YHWH, "and my servant whom I have chosen, that you may know and believe me and understand that I am He. Before me no god was formed, nor shall there be any after me. (Isaiah 43,10)

·         Thus says the YHWH, the King of Israel and his Redeemer, YHWH of hosts: "I am the first and I am the last; besides me there is no god. (Isaiah 44,6)

 

 

In the New Testament we have instead “the Word” with God at the beginning:

 

·         All things were made through him, and without him was not anything made that was made. (John 1,3)

·         But in these last days he has spoken to us by a Son, whom he appointed the heir of all things, through whom also he created the world. (Hebrews 1,3)

·         For in him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or principalities or authorities--all things were created through him and for him. (Colossians 1,6)

·         "And to the angel of the church in Laodicea write: 'The words of the Amen, the faithful and true witness, the beginning of God's creation. (Revelation 3,14)

 

 

Also Christ on the throne of God denies the monotheism.  Now Christ is exalted to the right hand of God (Daniel 7,13-14; Psalm 110,1; Matthew 26,64; Acts 2,33; Acts 7,55-56; Hebrew 1,13; Revelation 3,21; Revelation 5,13). At the end Jesus Christ will not be on the "throne of God" but on the "throne of God and of the Lamb" (Revelation 22.1 and 22,3):  the Son will not be host but owner and holder of the same throne of the Father. 

 

If today YHWH has today close to him only a "Elohim" (a smaller god, an angel or an archangel) and if at the end of times YHWH will give his throne to a "Elohim" (the throne of God and the Lamb of Apocalypse 22.1 and 22,3), his power will be diminished because his power and his glory will be shared with an inferior being.  In fact it is written:  "I am YHWH;  this is my name;  and I will not give my glory to an other"  (Isaiah.42,8 and Isaiah 48,11) and “For who in the skies can be compared to the YHWH? Who among the heavenly beings is like the YHWH” (Psalm 89,6). 

 

In Old Testament, to the creation, the Wisdom of God (Proverb 8) already existed and the Spirit of God was moving over the face of the waters (Genesis 1): they were not little gods, angels, archangels, messengers or representatives of YHWH but parts of YHWH (and no Hebrew has never found nothing of strange). The unit of God (Deuteronomy 6,4):

 

 

"Hear, O Israel: YHWH our God is one YHWH”

 

שמע ישראכ יחךח אלחים יחךח אחד

 

 

 is a composed unit that Hebrews have rendered with אחד [echad], while the ideal Jewish word in order to indicate absolute unit is יחיד [yachid]. 

 

Specific examples of how “echad” demonstrates compound unity are:

There is another Hebrew word, “yachid”, that is used to express the idea of absolute oneness. Examples of it are:

 

 

 

AN ATTEMPT TO ESTIMATE THE INVERSE PROBABILITY

 

Applying Bayes theorem it is possible to estimate the so-called "inverse probability" or "probability of the causes": in our case the probability that θεος is determined when anarthrously precedes the verb "to be". Practically, the problem is like that one of the casual extraction of one little ball of a given colour, given several urns: the Bayes formula allows to estimate the probability that the little ball comes from a given urn rather than from an other one. Bayes theorem, for instance, is used from medical researchers in order to estimate probability that a given symptom is caused from a given disease P(Mi/Sj), when are known P(Mi) (that is probability of a given diseases) and P(Sj/Mi) (that is probability of a given symptom in a given disease).

 

Even it is necessary to be careful using statistics in theological studies and in textual critical analysis, we cannot deny that, from a logical-formal point of view, it is possible to estimate with reasonable exactness probability that θεος is determined when precedes - without article - the verb “to be” (like in John 1,1). From Colwell’s study in 86% of the cases (97 times on 112) anarthrous nominal determined predicates precedes the verb “to be”, while in remaining 14% of the cases (15 times on 112) nominal determined predicates precede the verb “to be“ preserving the article.

 

After Colwell, many scholars showed how also nominal undetermined and/or qualitative predicates are anarthrous when precede the verb “to be”. It seems reasonable to us, in first approximation, to suppose that this happens in 80% of cases, while we also assume that in 20% of the cases nominal undetermined predicates precede the verb “to be” preserving the article.

 

We will see that results will not change considering different values.

 

Also admitting, as “anti-trinitarians” do, that θεος can also have undetermined value, it is necessary to remember that in Septuagint and in the New Testament, determined value is by far most frequent: in more than 9 cases on 10 the Greek text uses θεος to indicate the only true God, while in less than 1 case on 10 θεος is used for angels, judges, prophets, kings and men ..

 

In our case first difficulty comes from the estimate of the probability that " θεος" is determined: assigning to this variable value 98% we have used a subjective evaluation, even if data available allow us to have a “priori" distribution substantially founded. The P(D) value is higher in the New Testament where θεος is used 1343 times and it is referred to the only true God in 1320 cases (equal to 98.3%), while in Old Testament "elohim" it is used 2606 times and it is reported to the only true God in 2347 cases (equal to 90%): the reason of that seems imputable to the fact that, for the angels, the New Testament replaces θεος with αγγελoς, while in the Old Testament  "Elohim" is used for God and for the angels.

 

Applying Bayes theorem:

 

P(D/ANP) = [ P(D).P(ANP/D) ]/[ P(D).P(ANP/D) + P(ND).P(ANP/ND) ] = [ 0.98,0.86 ]/[ (0.98,0.86) + (0.02,0.80) ] = 0,985 = 98,5% where:

 

P(D) = 98% the probability that θεος is determined

P(ND) = 2% the probability that θεος is qualitative and/or undetermined

P (ANP/D) = 86% the probability that θεος  -as anarthrous nominal determined predicate- precedes the verb “to be”

P (ANP/ND) = 80% the probability that θεος –as anarthrous nominal undetermined and/or qualitative predicate- precedes the verb “to be”

P(D/ANP) =? the converse probability that θεος is determined when -without article- precedes the verb “to be”

 

 

It can easily be noted that there is little variation in results using studies, researches or different criteria of aggregation and using different values for P (ANP/ND) (that is probability that θεος –as anarthrous nominal undetermined and/or qualitative predicate- precedes the verb “to be”).

 

P (ANP/ND) 

P(D)

P(ANP/D)

P(D/ANP)     

100

98%

86%

97,7

90

98%

86%

97,9

80

98%

86%

98,1

70

98%

86%

98,4

60

98%

86%

98,6

50

98%

86%

98,8

40

98%

86%

99,1

30

98%

86%

99,3

20

98%

86%

99,5

10

98%

86%

99,8

0

98%

86%

100,0

 

 

In fact probability that θεος in New Testament  is determined is very high, as very high is probability that definite predicate nouns is without the article when, for emphasis, precedes the verb “to be”: all that make practically negligible probability and behaviour of anarthrous nominal undetermined and/or qualitative predicates.

 

Moreover valuation of the inverse probability comes out possible, legitimate and sufficiently careful. Evidently probability is not certainty but other is to say that probability is next to the 100% other is to assert that nothing can be supposed or, worse, that it is quite an "abuse" to try to suppose something.

 

 

HARNER AND DIXON  

 

Harner and Dixon [3] studied anarthrous nominal predicates preceding the verb “to be”: in 80%-90% of the cases they would be qualitative. Such statistics (using subjective criteria of splitting up anarthrous nominal predicates into determined and undetermined/qualitative) has pure grammatical value, since they leave theology and actual behaviour of "theos". They are very generic and they can be adapted to every possible anarthrous nominal predicate, since they use only grammatical informations. Moreover Dixon’s and Harner’s statistics do not examine what happens inside nominal qualitative predicates, because they estimate only the probability that whichever anarthrous nominal predicate preceding the verb “to be” is qualitative or determined.

 

Bayesian analysis instead uses three information: i) "a theological " information (in the New Testament "theos" is determined in 98% of the cases); ii) "a grammatical " information (determined nominal predicate precedes without article the verb "to be" in the 86-87% of the cases, like the sampling of Colwell testifies clearly); iii) the analysis of a "full range" of values (from 0% to 100%) for the probability that qualitative nominal predicate precedes without article the verb to be.

 

Obviously, it is not possible to get a mathematical certainty but it is however possible to reach two heuristic conclusions (valid for the search of true):

1.     the inverse probability is not an “abuse” but it exists, it is determined, it is very high and calculable;

2.        the behaviour of anarthrous nominal undetermined and/or qualitative predicates is negligible.

 

 

FINAL CONCLUSIONS

 

Bayesian approach is based on a subjective conception of probability, but initial hypotheses are integrated with a following sampling. It is therefore possible to pass from a degree of "a priori" confidence to a sound "a posteriori" probability, probability that integrate past experience and assumptions with observation and allows collecting all the information available on the parameter that we want to estimate.

 

In John 1,1 "a priori" is that -in New Testament- "θεος " is used 1343 times and it is referred to the only true God in very 1.320 cases, corresponding to a probability of 98,3%. Colwell’s sampling integrate the subjective degree of confidence and tell us that in 86% of the cases nominal predicate determined precedes the verb “to be” losing the article, while only in remaining 14% of the cases nominal predicate determined precedes the verb “to be” preserving the article.

 

Colwell did not sample anarthrous nominal undetermined and/or qualitative predicate preceding the verb “to be” but this does not weaken Colwell’s results: it is sufficient to test final results, assuming all possible probabilities for P (ANP/ND), that is probability that θεος –as anarthrous nominal undetermined and/or qualitative predicate- precedes the verb “to be”.

 

Colwell’s sampling is therefore scientific and rigorous, integrating our Biblical statistics " a priori " ed allows us to estimate between 97.7% and the 100% probability that θεος is determined when it precedes the verb "to be" without article. Bayes theorem allows us to formulate reasonable hypotheses on the structure of John 1.1 and on the logical value of the inverse of the Colwell’s rule, getting over the impasse in which Bruce Metzger seemed to have fallen [4] [5]

 

 

 

 

 

Domingo7

Enrico Domenico

 

 


[1] C. Colwell, A Definite Rule for Use of the Article in the New Testament, JBL, LII, pp. 12-21, 1933. Colwell’s study began, according to his article, in response to Torrey who claimed that certain nouns, three of which were precopulative nominal predicates, were anarthrous in John due to Semitic influence.

 

[2] A researcher could reasonably be interested only in snowy days, excluding from its observations serene days and rainy ones. Someone could observe that, if is true that in snowy days some particular conditions take place, is not always true the converse one: high pressure,  northern winds and low temperatures not always guarantee abundant snowfalls. However it is not neither absurd, nor impossible nor unfair to estimate the inverse probability, that is the probability that, given favourable conditions, snowy precipitations come true. P(N) is the probability of snowfall in a given town and P(CF/N) is the probability of favourable conditions (high pressure,  northern winds and low temperatures) when it snows. It is always possible to estimate the inverse probability P(N/CF), that is the probability that, given favourable conditions, snowy precipitations take place. Indicating with P(WN) = 1 - P (N) the probability that it does not snow in a given town, for the theorem of Bayes we have: P(N/CF) = [ P(N) * P(CF/N) ]/[ P(N) * P(CF/N) + P(WN) * P(CF/WN) ].  That is the ratio between the number of ways snow can occur and the total number of possible outcomes (snowy and not snowy days, given favourable conditions to the snow). Therefore, for our meteorologist, it is only necessary to estimate  P(CF/WN) that is the probability that, in snow absence, we can have favourable conditions to the snow. Taking in consideration only “snowy days”, does not change neither the probability of snowfall P(N) nor probability P(CF/N) that, in snowy days, some meteorological conditions occur. Not to have examined "not snowing days " does not give us absurd, impossible or undetermined results: it is possible to try to estimate the inverse probability P (N/CF), on condition of estimate a wide range of values for P(CF/WN), that is the probability that, in snow absence, are present favourable climatic conditions to it.

[3] Philip Harner, “Qualitative Anarthrous Predicate Nouns: Mark 15:39 and John 1:1,” JBL 92, 1973; Paul S. Dixon, “The Significance of the Anarthrous Predicate Nominative in John” (Th.M. thesis: Dallas Theological Seminary, 1975).

 

[4]  For P. Harner, D. Wallace and D. Hartley θεος -in John 1,1- has a qualitative value, neither determined nor undetermined. Qualitative value for “the Word was God” is “the Word was divine” that is “the Word had the same nature of God”. See Philip Harner, Qualitative Anarthrous Predicate Nouns: Mark 15:39 and John 1:1, JBL,  n.92,  pp. 75-87, 1973; D. Wallace, Greek Grammar Beyond the Basic, 1996, pp. 268-9; D. Hartley, Revisiting the Colwell Construction in Light of Mass/Count Nouns, PHD Thesis, Dallas, 1998.

 

[5] However “the Word was divine” is not convincing. θεος (Theos) is for God  and θειος (theios) is for divine. We have “the only true God” with or without article (for θεος= ο θεος see John 1,12; John 1,18; Romans 8,33 and 2 Corinthians 1,3). θειος without article is divine (2 Peter 1,3 and 1,4) but θειος with article (ο θειος) is Godhead (Acts 17,29). According to us, if it is possible to change un adjective into a noun adding an article, it is not possible to turn a noun into an adjective taking away the article.