APPENDIX C

The Implications of Statistical Probability for the History of the Text[1]

Zane C. Hodges and David M. Hodges

Today, the whole question of the derivation of “text-types” through definite, historical recensions is open to debate. Indeed, E.C. Colwell, one of the leading contemporary [1975] critics, affirms dogmatically that the so-called “Syrian” recension (as Hort would have conceived it) never took place.[2] Instead he insists that all text-types are the result of “process” rather than definitive editorial activity.[3] Not all scholars, perhaps, would agree with this position, but it is probably fair to say that few would be prepared to deny it categorically. At least Colwell’s position, as far as it goes, would have greatly pleased Hort’s great antagonist, Dean Burgon. Burgon, who defended the Textus Receptus with somewhat more vehemence than scholars generally like, had heaped scorn on the idea of the “Syrian” revision, which was the keystone to Westcott and Hort’s theory. For that matter, the idea was criticized by others as well, and so well-known a textual scholar as Sir Frederic Kenyon formally abandoned it.[4] But the dissent tended to die away, and the form in which it exists today is quite independent of the question of the value of the TR. In a word, the modern skepticism of the classical concept of recensions thrives in a new context (largely created by the papyri). But this context is by no means discouraging to those who feel that the Textus Receptus was too hastily abandoned.

The very existence of the modern-day discussion about the origin of text-types serves to set in bold relief what defenders of the Received Text have always maintained. Their contention was this: Westcott and Hort failed, by their theory of recensions, to adequately explain the actual state of the Greek manuscript tradition; and in particular, they failed to explain the relative uniformity of this tradition. This contention now finds support by reason of the questions which modern study has been forced to raise. The suspicion is well advanced that the Majority text (as Aland designates the so-called Byzantine family[5]) cannot be successfully traced to a single even in textual history. But, if not, how can we explain it?

Here lies the crucial question upon which all textual theory logically hinges. Studies undertaken at the Institut für neutestamentliche Textforschung in Münster (where already photos or microfilms of over 4,500 [now over 5,000] manuscripts have been collected) tend to support the general view that as high as 90 [95] percent of the Greek cursive (minuscule) manuscripts extant exhibit substantially the same form of text.[6] If papyrus and uncial (majuscule) manuscripts are considered along with cursives, the percentage of extant texts reflecting the majority form can hardly be less than 80 [90] percent. But this is a fantastically high figure and it absolutely demands explanation. In fact, apart from a rational explanation of a text form which pervades all but 20 [10] percent of the tradition, no one ought to seriously claim to know how to handle our textual materials. If the claim is made that great progress toward the original is possible, while the origin of 80 percent of the Greek evidence is wrapped in obscurity, such a claim must be viewed as monstrously unscientific, if not dangerously obscurantist. No amount of appeal to subjective preferences for this reading or that reading, this text or that text, can conceal this fact. The Majority text must be explained as a whole, before its claims as a whole can be scientifically rejected.

It is the peculiar characteristic of New Testament textual criticism that, along with a constantly accumulating knowledge of our manuscript resources, there has been a corresponding diminution in the confidence with which the history of these sources is described. The carefully constructed scheme of Westcott and Hort is now regarded by all reputable scholars as quite inadequate. Hort’s confident assertion that “it would be an illusion to anticipate important changes of text from any acquisition of new evidence” is rightly regarded today as extremely naive.[7]

The formation of the Institut für neutestamentliche Textforschung is virtually an effort to start all over again by doing the thing that should have been done in the first place—namely, collect the evidence! It is in this context of re-evaluation that it is entirely possible for the basic question of the origin of the Majority text to push itself to the fore. Indeed, it may be confidently anticipated that if modern criticism continues its trend toward more genuinely scientific procedures, this question will once again become a central consideration. For it still remains the most determinative issue, logically, in the whole field.

Do the proponents of the Textus Receptus have an explanation to offer for the Majority text? The answer is yes. More than that, the position they maintain is so uncomplicated as to be free from difficulties encountered by more complex hypotheses. Long ago, in the process of attacking the authority of numbers in textual criticism, Hort was constrained to confess: “A theoretical presumption indeed remains that a majority of extant documents is more likely to represent a majority of ancestral documents at each stage of transmission than vice versa.”[8] In conceding this, he was merely affirming a truism of manuscript transmission. It was this: under normal circumstances the older a text is than its rivals, the greater are its chances to survive in a plurality or a majority of the texts extant at any subsequent period. But the oldest text of all is the autograph. Thus it ought to be taken for granted that, barring some radical dislocation in the history of transmission, a majority of texts will be far more likely to represent correctly the character of the original than a small minority of texts. This is especially true when the ratio is an overwhelming 8:2 [9:1]. Under any reasonably normal transmissional conditions, it would be for all practical purposes quite impossible for a later text-form to secure so one-sided a preponderance of extant witnesses. Even if we push the origination of the so-called Byzantine text back to a date coeval with P⁷⁵ and P⁶⁶ (c. 200)—a time when already there must have been hundreds of manuscripts in existence—such mathematical proportions as the surviving tradition reveals could not be accounted for apart from some prodigious upheaval in textual history.

Statistical probability

This argument is not simply pulled out of thin air. What is involved can be variously stated in terms of mathematical probabilities. For this, however, I have had to seek the help of my brother, David M. Hodges, who received his B.S. from Wheaton College in 1957, with a major in mathematics. His subsequent experience in the statistical field includes service at Letterkenny Army Depot (Penna.) as a Statistical Officer for the U.S. Army Major Item Data Agency and as a Supervisory Survey Statistician for the Army Materiel Command Equipment Manuals Field Office (1963-67), and from 1967-70 as a Statistician at the Headquarters of U.S. Army Materiel Command, Washington, DC. In 1972 he received an M.S. in Operations Research from George Washington University.

Below is shown a diagram of a transmissional situation in which one of three copies of the autograph contains an error, while two retain the correct reading. Subsequently the textual phenomenon known as “mixture” comes into play with the result that erroneous readings are introduced into good manuscripts, as well as the reverse process in which good readings are introduced into bad ones. My brother’s statement about the probabilities of the situation follows the diagram in his own words. [Because of spacing the diagram comes on the next page.]

Provided that good manuscripts and bad manuscripts will be copied an equal number of times, and that the probability of introducing a bad reading into a copy made from a good manuscript is equal to the probability or reinserting a good reading into a copy made from a bad manuscript, the correct reading would predominate in any generation of manuscripts. The degree to which the good reading would predominate depends on the probability of introducing the error.

For purposes of demonstration, we shall call the autograph the first generation. The copies of the autograph will be called the second generation. The copies of the second generation manuscripts will be called the third generation and so on. The generation number will be identified as “n”. Hence, in the second generation, n=2.

Generation Numbers

Good Bad Diff.

1 o 1 0 1

2 o o · 2 1 1

3 o o · o o · · · o 5 4 1

4 o o · o o · · · o o o · o o · · · o · · o · · o o o · 14 13 1

5 o o · o o · · · o o o · o o · · · o · · o · · o o o · 41 40 1

o o · o o · · · o o o · o o · · · o · · o · · o o o · [9]

· · o · · o o o · · · o · · o o o · o o · o o · · · o

Assuming that each manuscript is copied an equal number of times, the number of manuscripts produced in any generation is k^n-1, where “k” is the number of copies made from each manuscript.

The probability that we shall reproduce a good reading from a good manuscript is expressed as “p” and the probability that we shall introduce an erroneous reading into a good manuscript is “q”. The sum of p and q is 1. Based on our original provisions, the probability of reinserting a good reading from a bad manuscript is q and the probability of perpetuating a bad reading is p.

The expected number of good manuscripts in any generation is the quantity pkG_n-1 + qkB_n-1 and the expected number of bad manuscripts is the quantity pkB_n-1 + qkG_n-1, where G_n-1 is the number of good manuscripts from which we are copying and B_n-1 is the number of bad manuscripts from which we are copying. The number of good manuscripts produced in a generation is G_n and the number of bad produced is B_n. We have, therefore, the formulas:

(1) G_n = pkG_n-1 + qkB_n-1 and

(2) B_n = pkB_n-1 + qkG_n-1 and

(3) k^n-1 = G_n + B_n = pkG_n-1 + qkB_n-1 + pkB_n-1 + qkG_n-1.

If G_n = B_n, then pkG_n-1 = qkB_n-1 = pkB_n-1 + qkG_n-1 and pkG_n-1 + qkB_n-1 – pkB_n-1 – qkG_n-1 = 0.

Collecting like terms, we have pkG_n-1 - qkG_n-1 + qkB_n-1 - pkB_n-1 = 0 and since k can be factored out, we have (p-q)G_n-1 + (q-p)B_n-1 = 0 and (p-q)G_n-1 – (p-q)B_n-1 = 0 and (p-q)(G_n-1 – B_n-1) = 0. Since the expression on the left equals zero, either (p-q) or (G_n-1 – B_n-1) must equal zero. But (G_n-1 – B_n-1) cannot equal zero, since the autograph was good. This means that (p-q) must equal zero. In other words, the expected number of bad copies can equal the expected number of good copies only if the probability of making a bad copy is equal to the probability of making a good copy.

If B_n is greater than G_n, then pkB_n-1 + qkG_n-1 > pkG_n-1 + qkB_n-1. We can subtract a like amount from both sides of the inequality without changing the inequality. Thus, we have pkB_n-1 + qkG_n-1 – pkG_n-1 – qkB_n-1 > 0 and we can also divide k into both sides obtaining pB_n-1 + qG_n-1 – pG_n-1 – qB_n-1 > 0. Then, (p-q)B_n-1 + (q-p)G_n-1 > 0. Also, (p-q)B_n-1 – (p-q)G_n-1 > 0. Also (p-q)(B_n-1 – G_n-1) > 0. However, G_n-1 is greater than B_n-1 since the autograph was good. Consequently, (B_n-1 – G_n-1) < 0. Therefore, (p-q) must also be less than zero. This means that q must be greater than p in order for the expected number of bad manuscripts to be greater than the expected number of good manuscripts. This also means that the probability of error must be greater than the probability of a correct copy.

The expected number is actually the mean of the binomial distribution. In the binomial distribution, one of two outcomes occurs; either a success, i.e., an accurate copy, or a failure, i.e., an inaccurate copy.

In the situation discussed, equilibrium sets in when an error is introduced. That is, the numerical difference between the number of good copies and bad copies is maintained, once an error has been introduced. In other words, bad copies are made good at the same rate as good copies are made bad. The critical element is how early a bad copy appears. For example, let us suppose that two copies are made from each manuscript and that q is 25% or ¼. From the autograph two copies are made. The probability of copy number 1 being good is ¾ as is the case for the second copy. The probability that both are good is 9/16 or 56%. The probability that both are bad is ¼ x ¼ or 1/16 or 6%. The probability that one is bad is ¾ x ¼ + ¼ x ¾ or 6/16 or 38%. The expected number of good copies is pkG_n-1 + qkB_n-1 which is ¾ x 2 x 1 + ¼ x 2 x 0 or 1.5. The expected number of bad copies is 2 – 1.5 or .5. Now, if an error is introduced into the second generation, the number of good and bad copies would, thereafter, be equal. But the probability of this happening is 44%. If the probability of an accurate copy were greater than ¾, the probability of an error in the second generation would decrease. The same holds true regardless of the number of copies and the number of generations so long as the number of copies made from bad manuscripts and the number from good manuscripts are equal. Obviously, if one type of manuscript is copied more frequently than the other, the type of manuscript copied most frequently will perpetuate its reading more frequently.

Another observation is that if the probability of introducing an incorrect reading differs from the probability of reintroducing a correct reading, the discussion does not apply.

This discussion, however, is by no means weighted in favor of the view we are presenting. The reverse is the case. A further statement from my brother will clarify this point.

Since the correct reading is the reading appearing in the majority of the texts in each generation, it is apparent that, if a scribe consults other texts at random, the majority reading will predominate in the sources consulted at random. The ratio of good texts consulted to bad will approximate the ratio of good texts to bad in the preceding generations. If a small number of texts are consulted, of course, a non-representative ratio may occur. But, in a large number of consultations of existing texts, the approximation will be representative of the ratio existing in all extant texts.

In practice, however, random comparisons probably did not occur. The scribe would consult those texts most readily available to him. As a result, there would be branches of texts which would be corrupt because the majority of texts available to the scribe would contain the error. On the other hand, when an error first occurs, if the scribe checked more than one manuscript he would find all readings correct except for the copy that introduced the error. Thus, when a scribe used more than one manuscript, the probability of reproducing an error would be less than the probability of introducing an error. This would apply to the generation immediately following the introduction of an error.

In short, therefore, our theoretical problem sets up conditions for reproducing an error which are somewhat too favorable to the error. Yet even so, in this idealized situation, the original majority for the correct reading is more likely to be retained than lost. But the majority in the fifth generation is a slender 41:40. What shall we say, then, when we meet the actual extant situation where (out of any given 100 manuscripts) we may expect to find a ratio of, say, 80:20? It at once appears that the probability that the 20 represent the original reading in any kind of normal transmissional situation is poor indeed.

Hence, approaching the matter from this end (i.e., beginning with extant manuscripts) we may hypothesize a problem involving (for mathematical convenience) 500 extant manuscripts in which we have proportions of 75% to 25%. My brother’s statement about this problem is as follows:

Given about 500 manuscripts of which 75% show one reading and 25% another, given a one-third probability of introducing and error, given the same probability of correcting an error, and given that each manuscript is copied twice, the probability that the majority reading originated from an error is less than one in ten. If the probability of introducing an error is less than one-third, the probability that the erroneous reading occurs 75% of the time is even less. The same applies if three, rather than two copies are made from each manuscript. Consequently, the conclusion is that, given the conditions described, it is highly unlikely that the erroneous reading would predominate to the extent that the majority text predominates.

This discussion applies to an individual reading and should not be construed as a statement of probability that copied manuscripts will be error free. It should also be noted that a one-third probability of error is rather high, if careful workmanship is involved.

It will not suffice to argue in rebuttal to this demonstration that, of course, an error might easily be copied more often than the original reading in any particular instance. Naturally this is true, and freely conceded. But the problem is more acute than this. If, for example, in a certain book of the New Testament we find (let us say) 100 readings where the manuscripts divide 80 percent to 20 percent, are we to suppose that in every one of these cases, or even in most of them, that this reversal of probabilities has occurred? Yet this is what, in effect, contemporary textual criticism is saying. For the Majority text is repeatedly rejected in favor of minority readings. It is evident, therefore, that what modern textual critics are really affirming—either implicitly or explicitly—constitutes nothing less than a wholesale rejection of probabilities on a sweeping scale!

Surely, therefore, it is plain that those who repeatedly and consistently prefer minority readings to majority readings—especially when the majorities rejected are very large—are confronted with a problem. How can this preference be justified against the probabilities latent in any reasonable view of the transmissional history of the New Testament? Why should we reject these probabilities? What kind of textual phenomenon would be required to produce a Majority text diffused throughout 80 percent of the tradition, which nonetheless is more often wrong than the 20 percent which oppose it? And if we could conceptualize such a textual phenomenon, what proof is there that it ever occurred? Can anyone, logically, proceed to do textual criticism without furnishing a convincing answer to these questions?

I have been insisting for quite some time that the real crux of the textual problem is how we explain the overwhelming preponderance of the Majority text in the extant tradition. Current explanations of its origin are seriously inadequate (see below under “Objections”). On the other hand, the proposition that the Majority text is the natural outcome of the normal processes of manuscript transmission gives a perfectly natural explanation for it. The minority text-forms are thereby explained, mutatis mutandis, as existing in their minority form due to their comparative remoteness from the original text. The theory is simple but, I believe, wholly adequate on every level. Its adequacy can be exhibited also by the simplicity of the answers it offers to objections lodged against it. Some of these objections follow.

Objections

1. Since all manuscripts are not copied an even number of times, mathematical demonstrations like those above are invalid.

But this is to misunderstand the purpose of such demonstrations. Of course the diagram given above is an “idealized” situation which does not represent what actually took place. Instead, it simply shows that all things being equal statistical probability favors the perpetuation in every generation of the original majority status of the authentic reading. And it must then be kept in mind that the larger the original majority, the more compelling this argument from probabilities becomes. Let us elaborate this point.

If we imagine a stem as follows

o A

¹o ·² (Error)

in which A = autograph and (1) and (2) are copies made from it, it is apparent that, in the abstract, the error in (2) has an even chance of perpetuation in equal numbers with the authentic reading in (1). But, of course, in actuality (2) may be copied more frequently than (1) and thus the error be perpetuated in a larger number of later manuscripts than the true reading in (1).

So far, so good. But suppose—

o A

True Reading (a) ¹o ·² Error (a)

³o o⁴

True Reading (b) ⁵o ⁶o ⁷o ·⁸ Error (b)

Now we have conceded that the error designated (a) is being perpetuated in larger numbers than the true reading (a), so that “error (a)” is found in copies 5-6-7-8, while “true reading (a)” is found only in copies 3 and 4. But when “error (b)” is introduced in copy 8, its rival (“true reading (b)”) is found in copies 3-4-5-6-7.[10] Will anyone suppose that at this point it is at all likely that “error (b)” will have the same good fortune as “error (a)” and that manuscript 8 will be copied more often than 3-4-5-6-7 combined?

But even conceding this far less probable situation, suppose again—

o A

¹o ·² Error (a)

³o ⁴o ⁵o ⁶o ⁷o ·⁸ Error (b)