Science
in Christian PerspectiveScience
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.
Literary Statistics
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
Pauline Writings
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
from Isocrates
to late Hellenistic authors. In each ease, discrepancies in these
areas precisely
coincided with the scholarly opinion on the genuine and spurious
works attributed
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
addition, Titus
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:
Group 1
Group 2
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:
Group 1
Group 1
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
corresponding
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:
Group 1
Group 2
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
corresponding
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
and Galatians
the differences between classification into the group is very slight
(e.g. Romans
has difference of 23.97 for Group 1 and 22.46 for Group 2).
Conclusions
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.
BIBLIOGRAPHY
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.