Science in Christian Perspective
Paul, Participles and Parameters
RAYMOND N. KIEFT
Director, Institutional Research Department of Mathematics
Central Michigan University Mount Pleasant, Michigan 48858
MAYNARD C. NIEBOER
Campus Pastor Christian Reformed Ministry
Central Michigan University Mount Pleasant, Michigan 48858
From: JASA 26
(June 1974): 52-55.
We all intuitively recognize differences in style among authors. We even try to express these stylistic differences subjectively by such terms as "eloquent", "verbose", "pleasing", "smooth", "flowing", etc. However, we do not normally try to pinpoint, refine or even analyze comparative differences in any detailed or quantitative way. On a more sophisticated level, literary critics have wrestled with the problem of style and its role as an accurate criterion of authorship. Scholars have long been engaged in distinguishing authentic and spurious pieces of literature for a given author. However, the application of style as a criterion for authorship has been mainly a matter of art and subjective judgment even among these scholars. Recent attempts have been made to turn this aspect of literary criticism into a science by combining insights from modern linguistics and statistics; the result is a hybrid known as literary statistics.8
Differences in style within the so-called Pauline Corpus of the Bible have long been noted and described even by the most conservative biblical scholars, and in recent years evangelical scholars have generally conceded that the book of Hebrews is non-Pauline. These scholars have usually attributed the differences in style to the occasional nature of the writing, Paul's use of a scribal secretary (amanuensis), and a certain progression in Pauline thought. Yet attempts to explain stylistic differences have never led evangelical scholars to question the authorship of the thirteen Pauline epistles. A "statistical" approach to Scripture had its beginning in 1921 when P. N. Harrison examined the Pauline authorship of the Pastoral Epistles (I, II Timothy, Titus). Harrison acknowledged that every so-called Pauline epistle has certain characteristics, which is lacking in others. Yet, for the most, the letters form a more or less clearly defined series within certain limits. However, in terms of comparative word usage, unique words, and certain grammatical features, Harrison concluded that the Pastorals form an exception to the Pauline series, and must have been written by a "Paulist" at some later date.2
Even more recently, a minister in Scotland, A. Q. Morton, has been talking a great deal about "scientific and conclusive" evidence showing that only Romans, I and II Corinthians, Galatians, and possibly Philemon are from Paul, and that the rest of the epistles are from four or five different authors.3 Morton feels that at first the church had no reason to question the authenticity of the Pauline epistles. But for the last 150 years, scholars have sought to obtain more accurate information about Paul and about Christianity itself. They have done the best they can with the tools available, but there has been little or no agreement concerning which are Paul's and which are spurious. Morton concludes that traditional literary criticism is non-uniform and too inconclusive to he of real value; there is widespread disagreement concerning the proper criteria for evaluations, and most of the findings are contradictory. Morton also dismisses theological analysis as an acceptable tool for determining authorship on the same grounds. He feels that statistics is the only truly objective, and thus valid approach.
Literary critics have wrestled with the problem of style and its role as an accurate criterion of authorship.
Morton posits that any Greek prose author has a pattern which is as distinctive
for him as a fingerprint. This distinctive pattern is unconscious, but may be
discerned in terms of sentence length and the frequency of Greek
particles (notably kai). He claims that this has been consistently proven in 400 samples
to late Hellenistic authors. In each ease, discrepancies in these
coincided with the scholarly opinion on the genuine and spurious
to the various authors. These tests were then applied to the thirteen letters
ascribed to Paul. Morton concluded that only the four major letters (Hauptbriefe)
are genuine Pauline writings. Morton has gone on to apply several other tests
in addition to sentence length and kai frequency.4,5 The point is
that his tests
have a cumulative value rather than completely independent confirmation.
Purpose and Method
It is our thesis that more basic work still needs to be done concerning parameters which adequately define style and the minimum sample size that can be used. In this paper, we want to investigate one major literary characteristic which has not been studied to date, namely the Pauline use of the participle. We use the statistical technique called discriminant analysis to study the usage of the participle by distinguishing among groups of similar participle usage. B. Van Elderen has provided us with a systematic tabular count of the usage of the participle.7 This count becomes the data for the discriminant analysis.
Discriminant analysis is a statistical method that is used to discriminate between two groups of individuals or objects on the basis of several properties of those individuals or objects. Mosteller and Wallace used discriminant analysis in their study of the disputed Federalist Papers.6 Wachal used discriminant analysis in his study of the authorship of Federalist 55 and concludes that discriminant analysis is to be preferred as a classifying procedure."
1. Suppose an anthropologist has discovered a skull in an area that he knows possesses two types of skulls. He desires to classify his newly found skull as belonging to one of the two types that are found in the area by means of a series of measurements taken on the skull. He takes a set of skulls belonging to the first type and records the measurements taken on them. He records the same measurements on a set of skulls belonging to the second type. If the two types were somewhat similar with respect to all those measurements, it might not be possible to classify the skulls correctly by means of any single measurement because of a large amount of overlap in the distributions of this measurement for the two types. However, it might be possible that a linear combination of the various measurements exists such that the distribution of this linear combination for the two types would possess very little overlap. Using discriminant analysis, this linear combination could then be used to yield a type of discriminant index number by means of which skulls of the two types could be distinguished with a high percentage of
We investigate here one major literary characteristic which has not been studied to date, namely the Pauline use of the participle.
success. Once a discriminant index for each type of skull was determined the procedure for classifying a new skull would be to simply determine, on the basis of the same measurements, the index number for that skull. Whichever skull type index number it more closely approximated, that type of skull would be its classification type.
2, The first step in the discriminating process is to determine the relative importance of the participle types as discriminating agents. To accomplish this, a series of five multiple regression analyses were performed with each participle variable serving as the dependent variable in one of the analyses. In this manner, correlation coefficients were determined and could be used to determine the relative importance of the participle types. The multiple regression analyses suggested the attributive and circumstantial to be the most important discriminating agents of the five participle types listed by Van Elderen and hence were selected for use in the discriminant analysis.
3. The overall statistical feature of discriminant analysis is to attempt to maximize the variation between the different groups without noticeably increasing the variation within the group itself. This can best be accomplished by using methods of the calculus and maximizing the ratio of the Between-groups Mean Square to the Within-groups of Mean Square?
All the mathematical details and calculations for the application of discriminant analysis to the data can be found in the IBM 1130 Scientific Subroutine Computer Software Package, No. GH 200252-4, published by the IBM Corporation, White Plains, New York.
Presentation and Treatment of the Data
Table 46 in Van Elderen's work7 furnishes the data for this discussion and is reproduced below. Van Elderen has listed the distributions, according to percentage, of five types of participles as these participles occur in the 13 epistles. As
Distribution of Participles in Paul According to Typea,b
Letter Attributive Circumstantial Supplementary Indeprndent Substansive
Romans 1 61.0 29.9 1.2 7.9 34.3
Corinthians 56.4 37.0 5.5 1.1 38.6
Galatians 55.4 38.6 6.0 0.0 32.5
1 Thess. 57.9 38.6 0.0 3.5 19.3
II Thess. 65.4 27.0 3.8 3.8 30.8
I Timothy 51.3 43.7 3.7 1.3 18.8
II Timothy 59.3 40.7 0.0 0.0 14.8
II Corinthians 37.1 47.4 6.2 9.3 20.6
Ephesians 36.5 59.8 3.7 0.0 11.3
Philippians 26.8 67.9 5.3 0.0 14.3
Colossians 23.4 62.3 10.4 3.9 3.9 (!)
a) By percentage of the total
b) After Van Elderen.7
previously discussed, only the attributive and circumstantial types warranted
study based upon correlation obtained from regression analyses. In
and Philemon were not
The usage of the participle in the Pauline Corpus fails to furnish the sensitivity needed to distinguish differing styles.
used in the analysis. The data are furnished by the first two columns
of the Table
for the first eleven epistles.
Our study is an attempt to shed more light on the subject of the authorship of the Pauline Epistles. The paper specifically considers the attributive and circumstantial participles as parameters and by using discriminant analysis tests for significant differences in usage in the Pauline Epistles. The basic procedure involves arbitrarily grouping books and comparing similarities and differences among these groupings within the Pauline Corpus.
First Set of Groupings
Using Humans, I and H Corinthians, and Galatians as Group 1, and I and II Thessalonians and I and II Timothy as Group 2, the groups are distinguishable at the 5% level of significance. The discriminant analysis resulted in an index of 312.98 for Group 1 and an index of 346.93 for Group 2. Testing Ephesians, Philippians, and Colossians individually, the results were:
Ephesians 371.22 372.60
Philippians 369.40 370.19
Colossians 305.47 302.93
Comparing these values to the index values for each group we have:
(1) The numerical difference between the Group 1 value for Ephesians and the Group 1 index is 58.24 while the numerical difference between the Group 2 value for Ephesians and Group 2 index is 25.67. Since the difference between the Group values and the Group index is minimum for Group 2, Ephesians is determined to be more similar to Group 2.
(2) The numerical difference between the Group 1 value for Philippians and the Group 1 index is 56.42 while the numerical difference between the Group 2 value for Philippians and the Group 2 index is 23.26. Since the difference between the Group value and the Group index is minimum for Group 2, Philippians is determined to be more similar to Group 2.
(3) The numerical difference between the Group 1 value for Colossians and the Group 1 index is 7,51 while the numerical difference between the Group 2 value for Colossians and the Group 2 index is 44.00. Since the difference between the Group value and the Group index is minimum for Group 1, Colossians is determined to be more similar to Group 1.
Thus, Ephesians arid Philippians are more similar to Group 2 while Colnssians is more similar to Group 1.
Second Set of Groupings
With Romans, I and II Corinthians, and Galatians as Group 1 and Ephesians, Philippians, and Colossians as Group 2, Hotelling's T2 showed that the groups were distinguishable at the 1% level of significance. The analysis resulted in an index of 273.03 for Group 1 and 348.05 for Group 2. Testing I and II Thessalonians, I and II Timothy, the results were:
I Thessalonians 297.39 290.10
II Thessalonians 248.66 230.51
I Timothy 302.74 298.76
II Timothy 319.65 315.53
Looking at the numerical difference between each Group value and the
Group index, we determine that I Thessalonians, TI Thessalonians, and I Timothy
are more similar to Group 1 while II Timothy is more similar to Group 2.
Third Set of Groupings
With I and II Thessalonians, and I and II Timothy as Group 1 and Ephesians, Phihppians, and Colossians as Group 2, Hotelling's T2 test showed that the groups were distinguishable at the 5% level of significance. The analysis resulted in an index of 242.88 for Group 1 and 226.80 for Group 2. Testing I and II Corinthians, Romans, and Galatians, the results were:
I Corinthians 229.56 219.27
II Corinthians 179.92 183.61
Romans 218.91 204.34
Galatians 232.50 222.80
Looking at the numerical difference between each Group value and the
Group index, we determine that all these epistles are more similar to Group 2
than Group 1. However, it should be noted that in the cases of Romans
the differences between classification into the group is very slight
has difference of 23.97 for Group 1 and 22.46 for Group 2).
These tests indicate that the usage of the participle in the Pauline Corpus offers no real additional assistance in determining differing literary styles. As a parameter for authorship in the Pauline Corpus, it fails to furnish the sensitivity needed to distinguish differing styles. For example, based upon the suggested groupings in this paper, inconsistencies in classifying elements of the Pauline Corpus have been noted. The separation of II Timothy from I Timothy in test two and the slight difference in the classification of Romans and Galatians in test three illustrate the point.
One must be careful not to "read into" these conclusions any support for the hypothesis that Paul wrote all the Pauline Epistles or for the hypothesis that Paul wrote only a portion of them. Such support or proof was not the intent of the investigation. Such support will have to wait until more sensitive parameters can be found and tested.
1Bruce, F. F., The Letters of Paul: An Expanded Paraphrase (Grand Rapids: Wm. B. Eerdmsns Publishing House, 1965), pp. 10f, 220f, 281, 321.
2Harrison, P. M., The Problem of the Pastoral Epistles, London: Oxford, 1921. cf. also A Comprehensive Critique of Harrison written by K. Grayston and C. Herdon, "The Authorship of the Pastorals in the Light of Statistical Linguistics," New Testament Studies VI (October, 1959) pp. 1-15.
3Morton, A. Q. and McLemon, James, Paul, the Man and the Myth, New York: Harper and Row, 1966.
4Morton, A. Q. and Michaelson, Sidney. "Last Words: A Test of Authorship for Greek Writers," New Testament Studies 18, no. 2 (January, 1972), pp. 192-208.
5The Authorship and Integrity of the New Testament, Edinburgh, Scotland, 1971.
6Mosteller, Frederick and Wallace, David, "Inference in an Authorship Problem: A Comparative Study of Discrimination Methods Applied to the Authorship of the Distributed Federalist Papers." Journal of the American Statistical Association, LVIII, (1963), pp. 281-289.
7Van Elderen, Bastian, The Pauline Use of the Participle, Unpublished Ph.D. dissertation, Pacific School of Religion, Berkeley, 1960.
8Wachal, R. S., Linguistic Evidence, Statistical Inference and Disputed Authorship, Ph.D. dissertation-University of Wisconsin, University Microfilms- 1970, Ann Arbor, Michigan. cf. also M. G. Niehoer, "Literary Statistics and Pauline
Authorship" Part 1 Journal ASA 23, no. 3 (September, 1971), pp. 96-99.
9Wachal, R. S., op. cit. pp. 242.