Paul’s Style and the Problem of the Pastoral Letters: Assessing Statistical Models of Description and Inference

2.1 The Debate on Paul and the Pastorals

In this section, we review the major trends in the history of the debate on the authenticity of the Pastoral Letters with a particular focus on the role of style and computational methodologies. Up until the introduction of historical-critical methods in Enlightenment-era biblical scholarship, New Testament interpreters have assumed the Pauline authorship of the letters to Timothy and Titus.^[4] In the nineteenth century, following initial challenges to the Pauline authorship of the Pastorals, some New Testament scholars defended their authenticity.^[5] In the twentieth century, the view that Paul did not write the Pastorals gained traction, but some critical scholars nevertheless produced commentaries on the Pastorals from the perspective of Pauline authorship.^[6] In the early twenty-first century, the majority of scholars think that the Pastoral Letters were not written by Paul, although there is the occasional critical argument to the contrary.^[7]

Scholars who adjudicate the debate operate, as far as we can tell, with the unstated yet reasonable premise that Paul’s literary output provides a standard of measurement against which the Pastorals can be compared. In other words, there is in the New Testament a group of “authentic” letters that can serve as a touchstone.^[8] In connection with this premise, debates on the Pauline and Pastoral Letters generally revolve around the following issues:

• The Pastorals envision a structured church with well-defined roles for local functionaries beyond anything seen in the authentic Pauline letters. In this connection, the Pastoral Letters lack the degree of eschatological urgency found in the authentic Paulines, which suggests that these letters were written in a context when Christians recognized that they must formally organize community life. Also in this connection, some scholars view the Pastorals as responding to an early form of Gnosticism.^[9]

• The Pastorals have a different Christology in comparison to the rest of the Pauline corpus. The Pastorals describe Jesus largely in terms of a “savior” and speak of his “appearance,” both of which are uncharacteristic of the authentic Paulines. Other theological differences include the understanding of faith, which in the Pastorals tends to denote a body of religious teachings, whereas in Paul’s authentic letters, faith is most often described in terms of a religious disposition. Furthermore, the emphasis in the Pastorals on the importance of good doctrine and sound teachings also figures heavily in the debate.^[10]

• The Pastorals use ethical terms and metaphors that differ from what is found in the authentic Paulines. Familiar Pauline concepts related to one’s relationship with God, such as love and one’s existence “in Christ,” take on different meanings in the Pastorals. Furthermore, in the Pastorals, there is an emphasis on “conscience,” which is not heavily thematized in the authentic Paulines.^[11]

• The Pastorals advance a highly restricted view of the role of women in the assembly of believers and in general society, whereas the authentic Pauline letters often take for granted that women are active in both spheres.^[12]

2.2 Style and the Origins of the Debate

In addition to the four issues listed above, style is also a key issue in discussions of the Pauline and Pastoral Letters. In fact, observed stylistic differences between both corpora were a major factor that set the earliest debates in motion. Friedrich Schleiermacher is among the earliest critics who disputed the authenticity of a Pauline letter. In 1807, Schleiermacher penned a public letter to J. Chr. Gass, wherein he questions the authorship of 1 Timothy to a large degree on linguistic grounds, in particular the large number of hapax legomena found in that letter.^[13] Johann Gottfried Eichhorn expanded Schleiermacher’s argument by claiming that all three Pastorals are inauthentic, a finding he says is supported by the presence of peculiar words and phrases found nowhere else in the Pauline corpus.^[14] Shortly thereafter, Wilhelm M.L. De Wette argued against the authenticity of the Pastorals, claiming that “one familiar with Paul’s style of writing will find much aside from the differences in vocabulary…that betrays an imitator, who writes not from the living fulness of the Apostle’s mind.”^[15] Toward the end of the nineteenth century, Heinrich Holzmann lodged what is seen as the watershed study in the history of criticism of the Pastorals.^[16] Holzmann advanced a set of primarily linguistic arguments and noted, for example, that the Pastorals lack 25 particles typical of Paul’s style and that they contain a suspicious abundance of compound words and idiosyncratic phrases found nowhere else in the Pauline corpus.^[17] From the inception of the debate, scholars have discussed the issue of the authorship of the Pastorals in no small measure from the perspective of style and have utilized letters deemed authentically Pauline as a touchstone to evaluate the authenticity of the disputed ones.^[18]

2.3 Statistical Approaches to the Style(s) of Paul and the Pastorals

The earliest debates on the authenticity of the Pastoral Letters eventually gave rise to statistical analyses of their style(s). These studies, like the ones strictly in the qualitative tradition, also utilize a selection of texts from the Pauline corpus as a standard of measurement against which the Pastorals can be compared. The first New Testament scholar to contribute a statistical analysis was Percival Neale Harrison, who found that “In vocabulary, grammar, and style…the Pastorals show a marked divergence from the other epistles bearing the name of Paul.”^[19] Harrison finds that the Pauline corpus consists of “two vocabularies, Pauline and Pastoral,” the latter of which is closer to the Apostolic Fathers than other New Testament authors.^[20] Nevertheless, Harrison also finds that the Pastoral Letters contain a number of “Pauline fragments,” which he defines as excerpts of text originally written by Paul. Harrison arrives at his fragment hypothesis first by finding great stylistic variation between the Pastorals and the other ten letters in the Pauline corpus and second by noting that five sections within the Pastorals represent an exception. Harrison concludes that these five sections are authentic Pauline fragments because they are stylistically similar to the texts that he uses as a standard of measurement.^[21] In the wake of Harrison’s study, many other scholars deployed statistical approaches to the Pauline and Pastoral Letters, and the operative premise that Paul’s letters can be used as a standard of measurement has manifested itself in three main ways.

First, many computational studies take as their point of departure alleged linguistic differences observed by scholars in the qualitative tradition. For example, since the qualitative tradition has observed that the Pastorals contain a suspiciously high number of hapax legomena in comparison to the other Paulines, a range of statistical studies has emerged to investigate this issue. Kenneth Grayston and Gustav Herdan analyzed the statistical significance of unique words in the Pastorals by measuring what they term a C-value, which calculates the frequency of unique words in a corpus in terms of percentage. Grayston and Herdan found that the C-value of the Pastorals is 46%, an unusually high result when compared to the C-values of each of the individual Pauline letters, all of which are between 30 and 34%.^[22] Another alleged stylistic difference observed by scholars in the qualitative tradition is that the Pastorals have a rich vocabulary in comparison to the authentic Paulines. Some scholars, such as Matthew Brook O’Donnell,^[23] Eta Linnemann,^[24] and Gerard Ledger,^[25] investigated this issue by computing Type-Token Ratios in the Pauline and Pastoral Letters. Jermo van Nes, in what is perhaps the most comprehensive study of the language of the Pauline and Pastoral Letters, uses linear regression analysis to re-examine the conclusions of previous scholars that the Pastorals are stylistically dissimilar from the authentic Paulines.^[26] Van Nes considers a range of lexical and grammatical features that have been viewed throughout the history of criticism as evidence that the Pastorals were not written by Paul and concludes that most linguistic differences do not rise to the level of statistical significance. In our opinion, studies that take previously observed stylistic differences as their points of departure are useful in that they either verify or challenge conclusions reached in previous scholarship. We also contend, however, that basing a statistical analysis solely on previously observed differences imposes severe limitations on the types of stylistic features to be considered. Instead of taking stylistic peculiarities in the Pastorals as our starting point, we propose to begin with the “authentic” corpus to determine the mathematical distribution of features that are rarely considered in Pauline stylometry.^[27] The advantage of this procedural order is that we would attain a firm standard of measurement: if we can determine whether stylistic features throughout Paul’s letters follow a certain distribution, we can investigate how well the same features follow the same theoretical distribution in the Pastorals.

Second, especially in the mid-twentieth century, some studies make claims about the extent of the authentic Pauline corpus based solely on the results of statistical analysis. Andrew Queen Morton produced a number of statistical studies, one of which focused on sentence length and common words and concluded that only Romans, 1 and 2 Corinthians, Galatians, and possibly Philemon were written by Paul. Regarding the other letters, Morton finds that “the odds against Pauline authorship are astronomical.”^[28] Elsewhere Morton claims that the part of speech of the last word in a Greek sentence is the most critical factor in authorship attribution. Accordingly, Morton finds that only Galatians, 1 Corinthians, and parts of Romans are Pauline.^[29] In both of his studies, Morton selects features based on what he thinks is most determinative of authorship and rejects the authenticity of any letter that emerges as an outlier. Anthony Kenny takes a similar approach in a stylometric study of the entire New Testament. Kenny’s method of determining the authenticity of any letter of disputed Pauline authorship is “to start with the corpus of Pauline writings handed on by tradition, and ask whether within that corpus there is any Epistle, or group of Epistles, which is marked out as different from the body as a whole.”^[30] Based on 99 linguistic features,^[31] Kenny provides “a rough measure of how well each Epistle is at home in the Pauline corpus,” which he lists in descending order: Romans, Philippians, 2 Timothy, 2 Corinthians, Galatians, 2 Thessalonians, 1 Thessalonians, Colossians, Ephesians, 1 Timothy, Philemon, 1 Corinthians, and Titus.^[32] Based on these results, Kenny finds that only the Pauline authorship of the letter of Titus is dubious: “I see no reason to reject the hypothesis that twelve of the Pauline Epistles are the work of a single, unusually versatile author.”^[33] We argue that, for both authors, there is an extreme over-reliance on statistical results to discriminate between authors. Methodologically, Morton and Kenny fail to consider that factors other than authorship, such as genre or topic, could account for stylistic variation within a given corpus.^[34] On the opposite extreme, Kenneth Neumann concludes that stylistic variation within the literary output of a single author is common. As a result, Neumann is pessimistic that stylometry is an effective enterprise in forensic authorship attribution.^[35] On the contrary, we argue that by fitting probability models to letters of undisputed Pauline authorship, we gain a statistical standard of comparison to be applied to the Pastorals and to be interpreted in light of scholarly core competencies.

Third, following the advent of multivariate statistical analysis in Pauline studies, scholars in recent decades have applied cluster analysis and related techniques to the Pauline corpus.^[36] These methods enable the analyst to place the letters of Paul into groups based on stylistic similarity. The first such study was by D.L. Mealand, who analyzes 19 stylistic variables and concluded that the four major letters of Paul are stylistically distinct from the three minor ones.^[37] James Libby applies correspondence analysis to the entire New Testament based on syntagmatic, paradigmatic, and semantic relationships within the Greek language. Libby concludes that 1 and 2 Thessalonians, Colossians and Ephesians, and 1 Timothy and Titus each form pairs, but that these clusters are more indicative of “epistolary subgenre” than authorship.^[38] Jacques Savoy performs cluster analysis on term frequencies and found that the following letters within the Pauline corpus group together: Romans/Galatians/1 Corinthians/2 Corinthians, Colossians/Ephesians, 1 Thessalonians/2 Thessalonians, 1 Timothy/2 Timothy/Titus.^[39] In our opinion, cluster analysis and related techniques are useful in so far as they respect the individuality of each letter and provide metrics of stylistic variation within the Pauline canon.^[40] We contend, however, that even with multivariate methods, a major question remains unanswered: is it possible to determine how certain features behave across the entirety of the undisputed Pauline corpus, as opposed to assessing which features tend to occur only in letters of a certain length, in letters addressed to particular communities, or in letters that are close in theme or topic?

2.4 Synthesis

The question of how stylistic features behave in the undisputed letters generally goes unanswered in Pauline stylometry. We argue this is a major oversight in previous research, particularly since all inferential methods, including multivariate ones, rely upon an accurate understanding of the statistical distribution of stylistic features. However, instead of first determining the best-fitting distribution for a given set of stylistic features, researchers typically assume that their data follow a normal distribution without verifying that assumption. In New Testament stylometry, Mealand’s study is a notable exception, as he applies a univariate normality test to 25 variables and discards 6 of them.^[41] This result, however, problematizes whether the remaining variables are normally distributed: 24% of his variables (6 out of 25) were shown to be non-normal, almost five times higher than the 5% expected by the level of significance with which he works. The assumption of normality is required for Mealand’s discriminant analysis, but without confidence in this assumption, we cannot be confident in his conclusions.

By not adequately investigating the statistical behavior of stylistic features in the undisputed letters, scholars fail to assess how to utilize Paul’s letters as a standard of measurement. This oversight is potentially detrimental when applying inferential methods to letters of disputed authorship, because many statistical tests only produce valid results if the data follow a certain distribution. We intend, therefore, to improve upon previous studies by fitting our stylometric data to various probability distributions, the pay-off of which is that we can measure how certain features behave throughout Paul’s letters before turning to the Pastorals. Equipped with the knowledge of which probability distributions are the best fits to our data, we apply the same models to the Pastorals to evaluate whether there are statistically significant stylistic differences between these corpora.

To describe quantitatively Paul’s style, we consider the seven letters traditionally regarded as the undisputed Paulines: Romans, 1 and 2 Corinthians, Galatians, 1 Thessalonians, Philippians, and Philemon.^[42] To remain on secure ground when making claims about Paul’s style, we consider only these seven letters as “authentic,” since there are well-known problems with 2 Thessalonians, Colossians, and Ephesians. Previous studies have shown time and again that there is considerable stylistic variation even within the authentic letters (Section 2.3). We contend, however, that it is still possible to make statistically relevant claims about Paul’s style at the level of his seven-letter corpus. Indeed, this approach is consistent with one of the foundational premises of stylometry, namely, that each author has a unique stylistic fingerprint that will always be left behind when writing a text.

3.1 The Prominence of Vocabulary and Syntax

In this section, we explain how we select stylistic features to be analyzed. Statistical studies of the Pauline and Pastoral Letters almost exclusively revolve around lexical and syntactical features such as hapax legomena. In this way, previous contributions to the debate align with the way stylometry is typically practiced. Traditional stylometry operates with the premise that an author’s stylistic “fingerprint” is detectable through the rates at which he or she deploys quantifiable linguistic features such as common function words.^[43] Even studies that take more complex features as the basic unit of analysis nevertheless treat style primarily as a lexical and syntactical phenomenon. Donald Hardy, for example, analyzes the style Flannery O’Conner’s novels through so-called collocational analysis, which measures the statistical significance of word associations.^[44] Statistical studies of the Pauline and Pastoral Letters, then, have in common with other stylometric analyses their focus on vocabulary and grammar.

In recent years, however, a group of prominent voices in the digital humanities have called for a new definition of style, one that satisfies scholars who utilize traditional literary methods as well as those who engage in computational analysis. J. Berenike Hermann, Karina van Dalen-Oskam, and Christof Schöch define style as: “a property of texts constituted by an ensemble of formal features which can be observed quantitatively or qualitatively.”^[45] In explicating their definition, the authors note that in computational studies, “most style markers have so far been relatively simple in nature. Among such features are frequencies and frequency distributions of characters, words, lemmata, word classes or syntactical structures, taken by themselves or in sequences (n-grams).”^[46] As a way forward, the authors argue that “it seems both useful and possible to add the levels beyond the sentence among the style markers.”^[47] As examples, they mention “stylistically relevant phenomena such as metaphors or irony which, despite some recent advances, are currently analyzed in a qualitative rather than quantitative paradigm and remain a challenge to formal modeling, reliable automatic identification and computational assessment.”^[48] Additionally, these authors even suggest it would be valuable if elements of a text’s macro-structure such as paragraph length or point of view were given more prominence in the quantitative analysis of style.^[49] In comparison to traditional stylometry, this is a broader and more inclusive approach to style, which in our opinion has the potential to shed new and informative light on Pauline and the Pastoral Letters. Since vocabulary and syntax have been given more than enough attention in the debate, we take a broad approach to style and compare both corpora in terms of a fresh set of literary techniques.

In recent years – independently, as far as we can tell, from the authors discussed above – a few voices in New Testament studies have similarly called for the integration of non-linguistic features into stylometric analysis. Matthew Brook O’Donnell, for instance, criticizes computational stylometry in biblical studies because it fails to consider important non-linguistic elements in a text.^[50] James Libby argues that working solely with traditional stylistic criteria is no longer sufficient, because such an approach provides only a limited picture of an author’s style and because contemporary digital tools make possible different types of analysis.^[51] Paul Robertson theorizes that literary criteria in Paul’s letters are best classified according to “second-order criteria,” which he defines as terms and taxonomies the analyst develops for descriptive purposes and which may not have been shared by the cultural era in question.^[52] Although Robertson is not the only scholar who is dubious of traditional stylometry, he is to our knowledge the only one (within New Testament studies, at least) who engages in the quantitative analysis of style outside the parameters of vocabulary and syntax.^[53] The categories that Robertson uses to compute Paul’s style are as follows:^[54]

Universal Claims or AssertionsPathos

Appeals to AuthorityIrony or Satire

ConversationHyperbole

Prosopopoiia/EthopoiiaOppositions or Choices

Rhetorical QuestionsFigurations of Groupness

Metaphors or AnaloguesPlural Inclusive Addresses

Anecdotes or ExamplesSecond Person Addresses

ImperativesFirst Person Reflection

ExhortationAnalysis of Questions or Objections

Caustic InjunctionsSystematic Argument

According to Robertson, the features listed above are particularly characteristic of ethical-philosophical texts in the ancient Mediterranean world such as Paul’s letters or Epictetus’ Discourses.^[55] In this study, we adopt Robertson’s approach to feature selection but make no claims that certain literary features are characteristic of certain types of texts. Rather, we develop second-order categories specifically with an eye toward the debate about the Pauline and Pastoral Letters. Accordingly, we followed three general principles in developing categories to describe stylistic features in these corpora:

• First, we looked for literary techniques that describe in a general sense how Paul deploys letter-writing as a communicative tool. As a parallel to how traditional stylometry considers frequency rates of common function words such as “and,” “but,” or “the,” we consider the statistical distributions of common literary techniques found in Paul’s letters and find his stylistic fingerprint in the best fitting models.

• Second, in keeping with our goal to most effectively utilize Paul’s letters as a standard for measurement, we looked for literary techniques that recur throughout the “authentic” corpus, as opposed to literary techniques that we know occur only in one or two letters. During the process of feature selection, we relied upon general impressions of what is characteristic of Paul’s writing as we developed categories to describe various literary techniques. In subsequent stages of the research process, we tested our impressions mathematically.

• Third, we developed categories with an eye toward what is quantifiable. We specify, for example, that we only consider occurrences of self-fashioning when Paul explicitly uses the first-person (Section 3.2). Self-fashioning need not be understood strictly in terms of explicit claims that an author makes about himself. Theoretically, one could argue that Paul engages in self-fashioning with every word that he writes. In the interest of quantification, however, we limit ourselves to empirical text-features that can be counted and frame our categories accordingly.^[56]

3.2 Cataloging Stylistic Features

Following the three principles outlined above, we developed 18 categories to describe stylistic features in Paul’s letters. These 18 features do not encompass all aspects of Paul’s letter-writing but are representative of many of the major ways the apostle relates to his audiences from a distance. The features are listed below along with a brief description of each:

• Declarations of fact: The author lodges a claim with wide-ranging implications in a manner that is declarative as opposed to, say, analytical.

• Appeals to authority: The author references a person, divine being, or text to bolster his own claims.

• Logical arguments: The author seeks to persuade his readers of the validity of an idea, or expounds upon an idea, with evidence and/or reasoning.

• Inferences: The author explicitly draws a conclusion based on what has proceeded.

• First-person self-fashioning: The author builds ethos by making claims about himself on topics such as his authority, past experiences, future plans, or exemplarity.^[57]

• First-person emphases: The author underscores his own voice by reinforcing that he is the one giving commands, offering opinions, and so forth, often with an emphatic pronoun or mention of his name.

• First-person figurations of groupness:^[58] The author constructs a depiction of a community, whether concrete or abstract, that includes at least himself and his audience and that includes a description of things such as the group’s ethical values, place in society, or eschatological destiny.

• Second-person claims about audience: The author depicts his readers in a specific way, also in terms of things such as their ethical values, place in society, or eschatological destiny.

• Second-person emphases: The author engages his readers by explicitly mentioning them, most often with an emphatic pronoun or the vocative case, even if doing so otherwise interrupts his flow of thought.

• Third-person contrasts: The author speaks disparagingly of others to construe them as outsiders or opponents and his focus is on the implied or explicit opposites with himself and/or his own group.

• General exhortations or advice: The author directs readers, usually with the hortatory subjunctive or imperative, to a general pattern of behavior, be it to adopt a new way of life, to maintain their current way of life, or to improve upon current performance.^[59]

• Specific commands: The author issues a particular directive to readers, as opposed to a general pattern of living, most often in the imperative mood.

• Expressions of affection or friendship: The author articulates warm feelings for and/or reinforces a sense of partnership with his audience, sometimes by deploying common tropes from ancient letter-writing (such as longing to see his readers), or even dismissing the fact of his physical absence by asserting, for example, his presence with his readers in spirit or through the letter.^[60]

• Expressions of confidence: The author articulates a sense of certainty in his audience, usually to perform a particular task or to live in accordance with a certain ethical framework.

• Second or third-person praise: The author positively evaluates a person, group, or virtue such as love, often to uphold the person or group as a moral exemplum because of, among other things, their past actions or present characteristics.

• Second-person blame: The author negatively evaluates his readers for something they have done or are doing, usually to prompt them to correct their behavior and/or to maintain a positive relationship with them.

• Satire: The author exposes what he considers to be flaws in his audience or others with ridicule, irony, or humor, usually as a form of public criticism on moral and/or social matters.^[61]

• Expressions of wish or desire: The author articulates his yearning for something specific, usually in the optative mood and/or in the form of a prayer.

In the process of feature selection, we conducted multiple close readings of the Pauline and Pastoral Letters. After we identified generalized ways to describe how Paul uses letter-writing as a communicative tool, we decided where in our judgment these features occur in Paul’s letters and catalogued text references accordingly.^[62] For example, we find that in Paul’s letter to the Romans inferences occur 25 times and first-person self-fashioning occurs 10 times. Therefore, we catalogue these features in this way:

This etic approach to feature selection contrasts with the way feature selection is conducted in traditional stylometry, which typically involves the use of corpus linguistics software to collect data for text properties such as word frequencies or clusters. The major advantage of engaging in feature selection through close readings is that we draw upon the expertise of scholars of the ancient world to identify and describe elements that are fundamental to the apostle’s style, even if these elements are not explicitly acknowledged by Paul or by contemporary literary theorists.^[63] In many of the features listed above, we describe stylistically relevant features of Paul’s letters using grammatical, rhetorical, or theoretical concepts already in use in biblical studies and related fields.

In this connection, some of our features, such as appeals to authority and first-person figurations of groupness, are similar or identical to the ones Robertson uses in his work. In other cases, we think we have improved upon Robertson’s categories. For example, Robertson includes as first-person reflection most instances where the apostle speaks about himself, which encompasses nearly every occurrence of the first-person singular.^[64] By contrast, we distinguish between direct claims Paul makes about himself (Rom 11:13: “I am the apostle to the Gentiles”) from those instances when he highlights that he is the one speaking (Phil 4:3: “Yes, I ask you also, true companion, help these women […]”). As a result, in our list of features, first-person self-fashioning is a separate literary technique from first-person emphases. Similarly, Robertson counts as second person address most instances where the author uses the second-person plural.^[65] By contrast, we distinguish between direct claims Paul makes about his audience (1 Cor 6:11: “But you were washed, you were made holy, you were made righteous in the name of the Lord Jesus and by the Spirit of our God”) from those instances when he simply draws his readers into the discussion (1 Thess 4:13: “But we do not want you to be uninformed, brothers, about those who are asleep […]”). As a result, in our list of features, second-person claims about audience is a separate literary technique from second-person emphases. In our approach to feature selection, stylistic features can be signaled by but are not defined by linguistic text-elements. For example, whereas in traditional stylometry the imperative mood might be considered a stylistic feature in its own right, in our study we judge whether Paul uses this mood to issue a general exhortation or advice or a specific imperative.

Unsurprisingly, the process of cataloging features revealed many instances where two or more features co-occur in the same verse. In these cases, we simply register these verses as containing a plurality of literary techniques. In the figure below, we provide two examples of such overlap.

Also unsurprisingly, the process of cataloging confronted us with instances where we had to judge whether a particular section of text contains one long occurrence of a given feature or multiple occurrences of that same feature. Does Romans 12:9–13, for example, contain a single occurrence of general exhortations or advice or does it contain many successive occurrences of this feature? In contrast to Robertson, who tends to log such passages as a single occurrence, we consider a text like Romans 12:9–13 to contain multiple general exhortations or advice, since Paul issues a variety of separate directives. Similarly, we consider Galatians 4:6–9 to include two occurrences of second-person claims about audience. Although both occurrences have in common that the Galatians are no longer enslaved, we find that Paul makes two substantial and separate claims about his readers.

3.3 Mathematical Considerations for Feature Selection

Our departure from traditional stylometry in terms of feature selection is a crucial step toward achieving our stated goal of assessing how to utilize Paul’s authentic letters as a standard of measurement. After cataloging all features according to the process described above, we divide the authentic Pauline corpus into 20-verse text-blocks and count the number of occurrences of each feature in each of the 74 blocks. In this way, our stylistic features are discrete, since they take on whole-number values. We may, for instance, observe 0, 1, or 2 occurrences of a stylistic feature in a text-block, but it is impossible to observe 1.5 occurrences. Discrete data are not well-modeled by the normal distribution, which is an example of a continuous random variable, meaning that a variable that is normally distributed is not constrained to be a whole number. In stylometry, the normal distribution is most often used to model rates, such as word frequencies.^[66] Instead of rates, our stylometric data involve counts, since our method involves organizing Paul’s letters into text-blocks, which limits the occurrence of each literary technique to a small range of whole-number values. Since the normal distribution cannot model our stylometric data, we seek instead a model among the discrete probability distributions (Section 4).

With a dataset as small as Paul’s authentic letters, a discrete probability model gives us a sharper understanding of the behavior of stylistic features than we would gain with a continuous one, since continuous probability models are more appropriate for larger datasets. Previously, D.L. Mealand sought to overcome the problem of the size of the New Testament letters by computing word counts in text-blocks of 1,000 words,^[67] but this approach does not generate a good understanding of stylistic tendencies, since the small number of total text-blocks (35 blocks in 18 letters) results in small number of observations. By contrast, since our method renders 74 text-blocks across 7 letters, we have enough observations to fit the data to various distribution models. We argue, then, that considering epistolary modes of discourse enables us to make claims about Paul’s style in his authentic letters, even though this corpus of letters is quite small.

3.4 Synthesis

We contend that our approach to feature selection offers two advantages that push the debate on the Pauline and Pastoral Letters into uncharted territory.^[68] First, from the standpoint of how to define style, we argue that epistolary modes of discourse – such as whether Paul speaks of himself or about his readers, or whether he makes truth claims in a declarative or logical manner – are at least as stylistically relevant as word choice and other linguistic features. Since Pauline stylometry up until now has largely revolved around traditional features, we think a fresh perspective on style will enhance the discussion. Second, from a mathematical perspective, we argue that discrete probability models are critical to our pursuit of determining how to utilize Paul’s letters as a standard of measurement, since we will see how literary techniques behave across the corpus of authentic letters. For these reasons, we modify an approach to stylometry theorized by Hermann and practiced by Robertson to advance the centuries-old debate on the Pauline and Pastoral Letters.

4.1 Probability Distributions

In this section, we fit probability distributions to stylistic features in Paul’s letters. As indicated above, this marks a departure from most stylometric studies, which often use the normal distribution to model the rates of various features. Our approach, however, is in line with the approach taken by Mosteller and Wallace in their investigation of the authorship of the Federalist Papers.^[69] We begin with a general introduction to probability distributions and their applications to ancient texts.

In stylometry, aspects of an author’s style are observed and measured quantitatively. Nevertheless, these observations do not follow patterns that can be predicted with total accuracy in the way that, for example, the motion of a body under the influence of gravity can be predicted. Consequently, these patterns can only be described in terms of probability. In mathematical probability theory, a set of outcomes or observations, together with the probability of each outcome, makes up a distribution. A distribution is a mathematical description of a random variable. It can be used to describe the likelihood of different outcomes and make predictions based on that information. In our investigation of Paul’s letters, the outcomes are the number of times a given stylistic feature occurs in a text-block of 20 verses. To illustrate this concept, we provide a table which contains the distribution of declarations of fact.

In the table below, the first column lists the number of occurrences of declarations of fact in a text-block, and the second column lists the number of text-blocks that contain that number of occurrences. For example, our data show that 24 text-blocks contain 0 occurrences of declaration of fact, while 23 text-blocks contain 1 occurrence. Finally, the third column records the expected number of text-blocks which contain the given number of occurrences of declaration of fact based on the chosen distribution. For this example, the expected counts in the third column are based on the Poisson distribution (Section 4.3).

The strength of a probability model is assessed by its agreement between the observed values and the expected values. We visualize this distribution in the chart below, which shows general agreement between the observed and expected occurrences based on the Poisson model.

When studying a stylometric variable, it is necessary to determine its distribution, since this information is useful for both stylometric description and inference. Regarding description, determining the distribution provides insight into how Paul uses a stylistic feature beyond what measures of the central tendency, such as the mean and median, and beyond what measures of the spread, such as the standard deviation and the variance, can tell us. While these statistics provide a basic summary of stylometric data, determining the distribution offers a more nuanced description of Paul’s writing practices. Regarding inference, we compare the behavior of stylistic features in the authentic Paulines and the Pastorals and note quantitative differences. We ask whether the differences are significant – in other words, are the differences small enough that they could be explained in terms of the random variation found within the work of a single author? Or, conversely, are the observed differences so large that they are statistically unlikely to occur within the work of a single author? In short, determining the distributions of stylistic features in Paul’s letters helps us determine how these features behave in the authentic corpus, which in turn provides a standard of measurement in the quantitative comparison to the Pastorals.

In what follows, we describe three probability distributions and our method of fitting stylistic features to these models. Readers interested in the details of our statistical analysis are encouraged to read Section 4.2 on the binomial model, Section 4.3 on the Poisson model, and Section 4.4 on the negative binomial model. Alternatively, readers may safely skip to Section 4.5, where we display and discuss our results.

4.2 Assessing the Binomial Model

One of the simplest discrete probability models is the binomial distribution. This distribution models situations consisting of repeated trials, in which each trial results in exactly two outcomes, labeled “success” and “failure,” with a fixed probability of “success” and “failure.” The binomial distribution has the further requirement that all trials are independent. There is much to recommend this model, since the binomial setting has much in common with the occurrences of our stylistic features in Paul’s letters. For example, each verse may be considered a trial, which would be a “success” if a given feature occurs and a “failure” if it does not.

The binomial distribution is determined by two parameters: n, which represents the number of trials, and p, which represents the probability of “success” in a trial. Since we organize Paul’s letters into text-blocks of 20 verses, the value of the first parameter is n = 20. To determine the second parameter, we use the method of Maximum Likelihood Estimation, which states that the best-fitting binomial distribution arises when p = x ¯ / n , the average value of the observations divided by the number of trials.

Using this method, we found the best-fitting binomial distribution for each stylistic feature. We assessed how well the binomial distribution models our observed data with χ 2 -Goodness-of-Fit tests. To conduct the χ 2 -Goodness-of-Fit test, we combined all text-blocks beyond a certain cut-off into a single category to meet the requirement that at most one category would have an expected value below 5.^[70] A high p-value indicates that the binomial model is consistent with the observed data, while a low p-value suggests the binomial model is not consistent with the observed data. As the benchmark for statistical significance, we use the standard threshold of 5%, meaning we reject the binomial model for those features with a p-value below 5%. We record the p-value for each Goodness-of-Fit test in Section 4.5.

We see that the binomial distribution serves as a good model for some stylistic features, while for others it is rather poor. As a result, we consider in the following sections two additional discrete probability distributions, the Poisson distribution and the negative binomial distribution. The Poisson distribution improves upon the binomial in those cases when “successes” are rare, and the negative binomial improves upon Poisson when the data are “over-dispersed,” which occurs when large observations are common.

4.3 Assessing the Poisson Model

We begin by outlining some fundamental aspects of Poisson distributions, which can be found in many introductory textbooks on probability.^[71] A Poisson distribution describes the number of “successes” that occur in a fixed interval, provided that:

1. The probability of two or more successes in any sufficiently small interval is 0.

2. The probability of success is the same for any two intervals of equal length.

3. The number of successes in any interval is independent of the number of successes in any other non-overlapping interval.

We claim that many stylistic features in Paul’s letters meet these conditions:

1. If we take a small enough section of the text, there can be at most a single instance of any given stylistic feature.

2. As long as two text-blocks are of the same length, in many cases we have no reason to suspect that one text-block will contain more instances of a given feature than another text-block. There are some exceptions to this, which will occupy our attention when we turn to the negative binomial distribution (Section 4.4). For now, we simply note that this requirement will be true in many cases.

3. In most cases, we have no reason to suspect that the occurrence of one stylistic feature in one text-block should influence its occurrence in another block. Once again, there are exceptions, and these will become an important distinction between the Poisson and negative binomial models (Section 4.4).

A Poisson distribution is determined by a single parameter, λ , which represents both the mean and variance of the distribution. In our context, λ represents the average number of occurrences of a given stylistic feature in a text-block. To find the best-fitting Poisson distribution for a given set of observations, we determine the value of λ using the method of Maximum Likelihood Estimation. In the case of the Poisson distribution, this method states that the best-fitting Poisson distribution arises when λ takes the value of the mean of the data set.

To assess the strength of the Poisson model, we calculate the expected frequencies based on the value of λ . For any integer k , the probability of having exactly k occurrences of a given feature in a text-block is as follows:

Multiplying this probability by 74, the total number of 20-verse text-blocks in Paul’s letters, yields the expected number of text-blocks with exactly k occurrences of the given feature. Having obtained the observed and expected frequencies of each feature, we conduct χ 2 -Goodness-of-Fit tests. The results for each feature are recorded in Section 4.5.

In the table in Section 4.5, note that two stylistic features, appeals to authority and satire, have two sets of χ 2 -statistics and p-values because we analyzed the data in two different ways. For appeals to authority, one text-block stands out as an outlier. The text-block consisting of Romans 10:5–11:3 contains 12 instances of this feature while most text-blocks contain 0–2 occurrences. For this reason, we employed the method of Maximum Likelihood Estimation twice, once using the value of λ obtained by using all text-blocks and another time omitting the outlier. The first value of λ yielded the p-value of p = 26.4%, while the second value yielded p = 66.04%. Both p-values are well above the cut-off from a 5% level of significance, meaning we may safely conclude that the Poisson distribution is a good model for Paul’s use of appeals to authority, regardless of whether we retain or discard the outlier.

For satire, the first set of values results from organizing the text-blocks into three categories, those with no occurrences of satire, those with exactly 1 occurrence, and those with 2 or more occurrences. This is the standard way of organizing the data according to our method, since it results in exactly one category whose expected value is less than 5. The second χ 2 -statistic and p-value, recorded in parentheses, results from organizing the data into two categories, those with no occurrences of satire and those with 1 or more occurrences. This is not our standard way of organizing the data, but we have done so in this case because this alternative categorization yields a significantly higher p-value. Since such an increase in the p-value is caused by a small change in the way the data are categorized, we prefer the first p-value (0.04%), meaning we are not confident that the Poisson distribution is a good model for satire in Paul’s letters.

4.4 Assessing the Negative Binomial Model

Next, we consider the negative binomial distribution, another discrete probability distribution that improves the binomial distribution when the outcome of “success” is rare. When we find that a stylistic feature is better modeled by the negative binomial distribution, we must ask what aspects of this stylistic feature make it differ from the Poisson distribution, since there are multiple settings that give rise to the negative binomial. Among these settings, we consider the presence of non-homogeneous and contagious populations to be the possibilities most relevant to Paul’s letters. Our treatment of these two settings, which we defer to Section 4.5, follows the landmark study of accident statistics by A.G. Arbous and J.E. Kerrich.^[72] Before we can consider why the negative binomial may arise, we must first determine how well the model works for our stylistic features.

We conduct χ 2 -Goodness of Fit Tests to assess the negative binomial distribution. As with the Poisson distribution, we first determine the parameters of the negative binomial distribution that best fit our observed data. The negative binomial distribution depends on two parameters, r and p, where r is a positive integer and 0 < p < 1 . For any integer k ≥ 0 , the probability of exactly k occurrences of a given stylistic feature in a text block is as follows:

For a given value of r, the method of Maximum Likelihood Estimation can be used to determine p, according to the equation:

where x ¯ is the mean of the observations. Unfortunately, the value of r cannot be determined by the method of Maximum Likelihood Estimation because it must take integer values, so we checked all values of r within a reasonable range to find the value that minimized the χ 2 -statistic. Once we determined the values of the parameters r and p, we calculated the expected frequencies and compared them with the observed frequencies in the same manner as the Poisson distribution. The results of the χ 2 -Goodness-of-Fit-Tests are recorded in the table contained in Section 4.5.

As in Section 4.3, appeals to authority and satire have two sets of χ 2 -statistics and p-values because we analyzed the data in two different ways, for the same reasons described above. Interestingly, the results are similar. Regardless of whether we include the outlier among appeals to authority, the resulting distribution yields a high p-value, which indicates that the negative binomial serves as a good model. For satire, the standard way of organizing the text-blocks into categories results in a small p-value, p = 2.14%, below the conventional 5% cut-off. If an additional category is included, the p-value jumps to p = 44.92%. As a result, we conclude that the negative binomial distribution is not a good model for Paul’s use of satire.

4.5 Results

Now that we have fitted our stylistic features to three distributions, we consider which distributions are most suitable for using Paul’s letters as a standard of measurement. We summarize our findings in the table below, which compares the p-values from our χ 2 -Goodness-of-Fit tests for each stylistic feature, based on the procedures described above.

Although the binomial distribution often provides a good fit, it is rarely a better model than the Poisson distribution. Moreover, in those few cases where it does offer some improvement, the improvement is very slight. For this reason, we will not pursue the binomial any further as a potential model. Next, we make conclusions as to which of the other two distributions, the Poisson or the negative binomial, is the stronger model for each literary feature. Our strategy is to generally prefer the Poisson distribution as long as the p-value for that model is above 5%. This preference comes from the fact that the Poisson distribution depends on a single parameter, unlike the negative binomial, which depends on two parameters, thereby making the Poisson distribution the simpler model. Thus, our rule-of-thumb is that the simpler model is the better one. Only when the p-value of the negative binomial model is approximately 10 times greater than the p-value of the Poisson model do we conclude that the negative binomial distribution serves as a better model. We summarize our results in the table below.

Eight stylistic features cannot be modeled by Poisson distribution but are a good fit for the negative binomial. To describe what this means in terms of Paul’s style, we consider two possible settings that could give rise to this distribution.^[73]

The first setting that creates a negative binomial distribution occurs when the population under study is not homogeneous. In other words, a population could consist of two or more sub-populations, each of which is homogeneous in the sense that it follows its own Poisson distribution. Under this scenario, the aggregate of these sub-populations, each with its own distinct Poisson distribution, would generate a negative binomial distribution. Theoretically, sub-populations within Paul’s authentic letters could reflect the work of editors and interpolators, who supply their own styles governed by distinct Poisson distributions, so that the resulting mix would generate a negative binomial distribution. In our opinion, an alternative theory better explains why expressions of affection or friendship are a better fit for the negative binomial. This stylistic feature tends to occur somewhat formulaically in letter-openings as Paul offers greetings and gives thanks, although the letter to the Galatians is a notable exception. However, expressions of affection or friendship are also found throughout the main bodies of Paul’s letters. Regarding Paul’s style, this suggests that the letter-openings and main bodies of Paul’s letters contain distinct Poisson distributions for expressions of affection or friendship, with the result that a negative binomial occurs in the aggregate.

The second setting that creates a negative binomial distribution is when the occurrence of one stylistic feature increases the probability that it will occur in a nearby text-block. This property has been called “contagious” because of the analogy with contagious disease, where the presence of disease in one individual increases the chances that it will occur in a nearby individual.^[74] If a stylistic feature is contagious, its occurrences do not occur independently, which is a requirement for the Poisson distribution (Section 4.3). We think that seven of Paul’s stylistic features fit the negative binomial model because they are contagious. Regarding first-person self-fashioning, for example, this means when Paul makes a claim about himself in a text-block, he is statistically more likely to make subsequent claims about himself in nearby text-blocks. Similarly, when Paul lodges a logical argument, he is more likely to put forth other logical arguments in the same context. Similarly, occurrences in one text-block of declarations of fact, second-person emphases, second or third-person praise, second-person blame, and specific imperatives in Paul’s letters tend to heighten the probability of subsequent occurrences in nearby text-blocks. In other words, these features in Paul’s letters have a cascading effect and, as a result, tend to cluster together in certain letter-parts. In some cases, contagious aspects of Paul’s style can be observed at the macro-level of epistolary structure, such as Galatians 1–2 where first-person self-fashioning is a defining feature and Galatians 3–4 where logical arguments characterize the unit.

There remain two stylistic features that are not well-modeled by either distribution: general exhortations or advice and satire. Paul’s use of satire seems to be a bad fit for these models because he uses this stylistic feature extremely rarely. Out of 74 text-blocks, 68 of them (roughly 92%) have no occurrences of satire. On the other hand, Paul uses general exhortation or advice very frequently, and many occurrences are highly concentrated in clusters, beyond what can be modeled by the Poisson or negative binomial. For example, the text-block corresponding to Romans 12:8–13:6 contains 23 occurrences of general exhortations or advice and the text-block corresponding to 1 Thessalonians 5:4–23 contains 13 occurrences. Aside from these clusters, the distribution of general exhortations or advice in Paul’s letters significantly departs from the shapes of both theoretical Poisson and negative binomial distributions, in no small measure because the frequencies do not decrease steadily. To illustrate this point, we display a sample of the distribution of general exhortations or advice in the chart below.

4.6 Synthesis

In this section, we fit stylistic features in Paul’s letters to various probability models to determine how to most accurately use the authentic letters as a standard of measurement. Most features are well-modeled either by the Poisson distribution or the negative binomial distribution, two distributions that improve upon the binomial when successes are rare. This result indicates that most stylistic features in Paul’s letters occur only occasionally and that no feature occurs throughout his letters at a significantly higher rate than the others. Our finding may come as a surprise, for instance, to those who label Galatians as an “angry” letter or to those who see Philippians as a letter of friendship.^[75] Statistically speaking, however, second-person blame and expressions of affection or friendship, like all of the stylistic features in our analysis, occur in a generally balanced manner throughout the authentic letters. This finding indicates that Paul in his letter-writing varied his style, consistently alternating between various epistolary modes of discourse, with the result that no stylistic feature dominates.

5.1 Significance Tests

In this section, we compare the Pastoral Letters to the authentic Paulines in terms of the Poisson and negative binomial distributions that we observed in the previous section. We treat each of the Pastorals as individual letters instead of a collection because it is debated whether the Pastorals are the work of a single author or multiple authors. After controlling the lengths of each of the Pastorals, we conduct significance tests at the 5% benchmark to compare the observed number of occurrences of each feature in the Pastorals with the number we would expect based on the best-fitting distribution determined by the authentic Paulines. Since the Poisson distribution is simpler than the negative binomial and since the negative binomial is the more conservative of the two, we only conduct negative binomial significance tests if there are statistically significant differences between Paul and the Pastorals based on the Poisson model. In running significance tests, our null hypothesis is that the Pastorals are stylistically similar to the authentic Paulines, in the sense that the stylistic features follow the same distributions as determined in Section 4.

In most cases, we fail to reject the null hypothesis that the Pastorals are stylistically similar to the authentic Paulines. This indicates that, for the most part, stylistic variation between the Pauline and Pastoral Letters is not statistically significant. This result challenges previous computational scholarship and the prevailing opinion in the qualitative tradition, which generally finds that the Pastoral Letters are stylistically distinct from the authentic Paulines (Section 2.3). However, two features in the Pastorals, namely third-person contrasts and declarations of fact, have p-values below 5%. In what follows, we explore the differences in the behavior of these features based on the Poisson distribution of third-person contrasts and both the Poisson and negative binomial distributions of declarations of fact. Although we determined above that declarations of fact are a better fit to the negative binomial (Section 4.5), we consider both distributions to demonstrate the consequences for statistical inference that arise based on one’s selection of probability distribution.

5.2 Poisson

5.2.1 Third-Person Contrasts

In the authentic Pauline letters, third-person contrasts occur at a mean rate of λ = 0.30 occurrences per text-block. Based on this information, we would expect Paul to deploy 1.70 occurrences of this stylistic feature in a text as long as 1 Timothy. By contrast, we observe 8 occurrences of this feature in 1 Timothy. We compute a p-value of 0.04%, meaning there is a 0.04% chance that the variation is due to random chance alone. Similarly, we would expect Paul to deploy 1.25 occurrences of third-person contrasts in a text as long as 2 Timothy. By contrast, we observe 7 occurrences of this feature in 2 Timothy. We compute a p-value of 0.03%, meaning there is a 0.03% chance that the variation is due to random chance alone. The single occurrence of third-person contrasts in the letter to Titus does not significantly differ from the 0.69 occurrences expected by the Poisson distribution we observed in Paul’s authentic letters. We visualize these results in the charts below, placing in a box the portion of the right-tail that contributes to the p-value.

5.2.2 Declarations of Fact

In the authentic Pauline letters, declarations of fact occur at a mean rate of λ = 1.35 occurrences per text-block. Based on this information, we would expect Paul to deploy 7.63 occurrences of this stylistic feature in a text as long as 1 Timothy. By contrast, we observe 15 occurrences of this feature in 1 Timothy. We compute a p-value of 1.18%, meaning there is a 1.18% chance that the variation is due to random chance alone. Occurrences of declarations of fact in 2 Timothy or Titus do not significantly differ from the Poisson distribution we observed in Paul’s authentic letters. We visualize these results in the charts below.

5.3 Negative Binomial

In Section 4.5, we found that the negative binomial distribution is the best-fitting model for declarations of fact in Paul’s letters. For this reason, we compute p-values for the Pastoral Letters using the negative binomial distribution. To highlight the importance of selecting the right distribution when making statistical inference, we compare the results with those obtained with the Poisson distribution (Section 5.2.3).

The procedure for conducting a significance test with a negative binomial distribution involves a few considerations not relevant to the Poisson distribution. Recall that the Poisson distribution depends on a single parameter, λ , which represents the average number of occurrences of a stylistic feature within a 20-verse text block. Therefore, when comparing the Pastorals with the authentic Pauline letters, we scaled the average rate for a 20-verse text-block to determine the expected number of occurrences of declaration of fact based on the length of each Pastoral Letter. This average value allowed us to determine λ and consequently the Poisson distribution for each Pastoral letter.

The negative binomial distribution relies on two parameters, r and p, neither of which can be determined directly from the average number of occurrences of a stylistic feature. For this reason, the average rate of occurrence cannot be scaled to determine the two parameters, meaning we must seek another way to find r and p. Our method is based on the following property of negative binomial random variables: suppose X 1 and X 2 are two random variables that follow a negative binomial distribution with two values of the first parameter, r 1 and r 2 , and the same value of the second parameter, p. Under this scenario, their sum, X 1 + X 2 , follows a negative binomial distribution, in which the value of the first parameter is r 1 + r 2 and the second parameter is p. This result can be extended to the sum of any number of negative binomial random variables.^[76]

Applying this property to the Pastoral Letters allows us to extend the negative binomial distribution of features from Paul’s authentic letters. To illustrate, we consider 1 Timothy, which contains 113 verses. Starting from the beginning of the letter, we divide 1 Timothy into 5 text-blocks of 20 verses, discarding the last 13 verses. If we consider the number of declarations of fact in a 20-verse text-block of the authentic Paulines to be a random variable X, then X follows a negative binomial distribution with r = 2 and p = 0.597. If we sum five negative binomial random variables, each with this same distribution, the result would be a negative binomial random variable with r = 10 and p = 0.597. If 1 Timothy is stylistically similar to Paul’s authentic letters, the occurrences of declarations of fact would be governed by this negative binomial distribution, which we have determined to be the most accurate standard of measurement.

To test whether 1 Timothy deviates from Paul’s style, we calculate the probability that we would observe as many as 14 instances of declarations of fact under the negative binomial distribution observed in Paul’s letters.^[77] This probability is the p-value, which we calculate as p = 3.73%. Following this method, we have 4 text-blocks in 2 Timothy and a total of 8 occurrences of declarations of fact, and 2 text-blocks in Titus and a total of 4 occurrences. For 2 Timothy, we find p-value = 22.02%, and for Titus we find p-value = 29.56%. We visualize these results in the charts below.

On the surface, our results are similar to those produced by significance tests using the Poisson distribution, with 1 Timothy containing a sufficiently high number of declarations of fact to render the difference statistically significant, while 2 Timothy and Titus have large p-values, suggesting that declarations of fact in these letters do not depart from Paul’s style as observed in the authentic letters. Although the conclusions for both the Poisson and negative binomial significance tests are similar, it is instructive to compare the p-values for 1 Timothy, both of which were below the 5% significance threshold. The p-value calculated under the negative binomial distribution is more than three times larger than the one found under the Poisson distribution, which reflects the fact that the negative binomial distribution has a larger right tail than the Poisson distribution, precisely the reason the negative binomial distribution is often considered an “over-dispersed” Poisson distribution. Thus, it is not unusual in a negative binomial distribution to find a large observation, such as the high number of declarations of fact we observe in 1 Timothy. These results show that researchers may reach vastly different conclusions depending on how they understand the underlying distribution of their data, and which tests they employ as a result. Our exercise reveals a broader lesson for Pauline stylometry, that determining how to use Paul’s letters as a standard of measurement is an essential (and generally overlooked) first step in making statistical inferences.