Paul -- A Basic Stylometric Study

[Peter Kirby]

It is highly difficult to reach any certain conclusions about Philemon, as it is too short to be tested on its own.

Perhaps it may be possible to test it in conjunction with the text of Colossians, with which it has some associations content-wise and position-wise?

If so, we get this combined result.

testsize: 1916 ['Colossians' and 'Philemon']


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.728391310663206'; $VAR2 = '3.51189861103886e-81'; $VAR3 = '7.35972905727683e-06'; $VAR4 = '0.271601329607737';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.416994541158713'; $VAR3 = 25; $VAR4 = '0.583005458841287';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0585 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0585 Test, Z-Score-Based Method
0.0072992700729927
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.992753623188406

Author Z-Score-Based P-Values
$VAR1 = '0.0585220973985938'; $VAR2 = '2.82161071336877e-82'; $VAR3 = '5.91312354241368e-07'; $VAR4 = '0.0218216214721443';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Decent indicator. 12.1% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '0.00301641977679549'; $VAR2 = '0.00836716228971203'; $VAR3 = '0.00064591397764131'; $VAR4 = '0.0041949917108248'; $VAR5 = '0.00124585650321434'; $VAR6 = '0.00661672743608942'; $VAR7 = '0.000793240293616611'; $VAR8 = '0.00300088965172121'; $VAR9 = '0.00294999653544203'; $VAR10 = '0.00365266569947571'; $VAR11 = '2.58076278300936e-06'; $VAR12 = '0.00218422355940539'; $VAR13 = '1.52891136427212e-05'; $VAR14 = '7.77109155596503e-06'; $VAR15 = '0.000307378427157025'; $VAR16 = '0.00230617271034045'; $VAR17 = '0.000227544214360605'; $VAR18 = '0.00439116164339174'; $VAR19 = '0.00650766224234748'; $VAR20 = '3.6170288989139e-06'; $VAR21 = '0.0562514159498295'; $VAR22 = '0.00744473974658625'; $VAR23 = '0.0500012912239514'; $VAR24 = '0.0422444093847056'; $VAR25 = '0.08182050093849'; $VAR26 = '0.0606689238109903'; $VAR27 = '0.0161236183873266'; $VAR28 = '0.0396392531214076'; $VAR29 = '0.00249589053682064'; $VAR30 = '0.00458740516280054';

That's not exactly good for 'Philemon'. Apparently Colossians fares better on its own than it does with its junior partner.

[Peter Kirby]

Next we'd like to test "Ephesians."

We should start with letting "Paul" be represented by 1 Cor, 2 Cor, shorter Gal, 1 Thess, and Phil.

testsize: 2421


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.625148845819996'; $VAR2 = '1.04978178960668e-151'; $VAR3 = '1.83990356587963e-10'; $VAR4 = '0.374851153996013';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.359059296380126'; $VAR3 = 25; $VAR4 = '0.640940703619874';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0218 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0218 Test, Z-Score-Based Method
0.0279503105590062
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.972809667673716

Author Z-Score-Based P-Values
$VAR1 = '0.0218092710240656'; $VAR2 = '3.66232389594031e-153'; $VAR3 = '6.41878422950294e-12'; $VAR4 = '0.0130772542664772';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Poor indicator. 21.2% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '0.00106047500392377'; $VAR2 = '0.00266535581109288'; $VAR3 = '0.000211819784609032'; $VAR4 = '4.31063431307809e-05'; $VAR5 = '0.0010412867619995'; $VAR6 = '0.00220150998665368'; $VAR7 = '0.000118803078264993'; $VAR8 = '0.00101101768793208'; $VAR9 = '0.00107069988395932'; $VAR10 = '0.000585680338557976'; $VAR11 = '1.28102740354498e-08'; $VAR12 = '0.000391121969748497'; $VAR13 = '4.82876996557001e-08'; $VAR14 = '9.88852003322117e-10'; $VAR15 = '3.04219117360917e-07'; $VAR16 = '0.000376406090733584'; $VAR17 = '2.99695819486764e-06'; $VAR18 = '0.000480488652486857'; $VAR19 = '0.00144541082599439'; $VAR20 = '1.26560123748304e-09'; $VAR21 = '0.0372444806089384'; $VAR22 = '0.00139767547983313'; $VAR23 = '0.0329575175239211'; $VAR24 = '0.028923994523803'; $VAR25 = '0.0389307550494461'; $VAR26 = '0.0187830490860272'; $VAR27 = '0.00559125812406415'; $VAR28 = '0.0189629827139593'; $VAR29 = '0.000859371617090269'; $VAR30 = '0.00127576367353001';

But we should also try adding Colossians to the training set also.

testsize: 2421


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.820162912729533'; $VAR2 = '1.0594751187369e-150'; $VAR3 = '1.25225902502717e-10'; $VAR4 = '0.179837087145241';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.596293403133725'; $VAR3 = 25; $VAR4 = '0.403706596866275';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0575 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0575 Test, Z-Score-Based Method
0.0093167701863354
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.990769230769231

Author Z-Score-Based P-Values
$VAR1 = '0.0575025341835358'; $VAR2 = '7.42809791642759e-152'; $VAR3 = '8.77972732924739e-12'; $VAR4 = '0.0126085782355376';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Excellent indicator. 0% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '0.00106043840983581'; $VAR2 = '0.00266539114364134'; $VAR3 = '0.00021182392661418'; $VAR4 = '4.31118965067574e-05'; $VAR5 = '0.00104128648619663'; $VAR6 = '0.00220153705001724'; $VAR7 = '0.000118793729122006'; $VAR8 = '0.00101103055149232'; $VAR9 = '0.00107069783682719'; $VAR10 = '0.000585654735475838'; $VAR11 = '1.28103831929936e-08'; $VAR12 = '0.000391117350059785'; $VAR13 = '4.82938402499457e-08'; $VAR14 = '9.88851690411336e-10'; $VAR15 = '3.04220969562083e-07'; $VAR16 = '0.000376461717248696'; $VAR17 = '2.99701829243081e-06'; $VAR18 = '0.000480491943868935'; $VAR19 = '0.00144544742716841'; $VAR20 = '1.26560071546892e-09'; $VAR21 = '0.0372443042589439'; $VAR22 = '0.001397659115682'; $VAR23 = '0.0329575248123143'; $VAR24 = '0.0289239935231798'; $VAR25 = '0.0389307550015205'; $VAR26 = '0.0187829510183347'; $VAR27 = '0.00559123755502315'; $VAR28 = '0.0189627340729164'; $VAR29 = '0.000859369741037213'; $VAR30 = '0.00127576358457313';

It's an interesting situation and shows the possible "contradictions" that can emerge from interpreting stylometric results very strictly (especially single ones).

I am more intrigued by the match than by the non-match. This actually gives me some hope that Ephesians might actually be by "Paul," the author of the rest, since "Colossians" had already been (sort of) 'authenticated' before.

I will note by way of passing that there is an entire other branch of stylometry that deals with the questions of the impact of genre and of age on the style of an author, thus making inferences about the type of work or the date of a work within an author's oeuvre. Well, if we're willing to consider Colossians as possibly being a 'later' work of Paul, then we can understand the above as showing that inclusion of 'Colossians' sufficiently broadened the training data set, so that we'd better be able to identify 'later' works of Paul and not just earlier ones.

"Ephesians" will be added to the set of training data for "Paul," but only sometimes, since it is controversial and less secure than Colossians.

[Peter Kirby]

We actually see the same phenomenon with 2 Thessalonians.

If we add Colossians and/or Ephesians, then 2 Thessalonians ends up being a closer match.

If we don't allow either of the other two so-called deutero-Pauline epistles, then 2 Thessalonians is not a match anymore.

This does provide a few negative results that offer grist for the mill for those who believe all of them are 'deutero-Pauline' :

If compared against just 1 Cor, 2 Cor, shorter 'Gal', 1 Thess, and Phil., we get:

Colossians + Philemon (negative result)
Ephesians (negative result)
2 Thessalonians (negative result)

Unfortunately (for those who want to remove all ambiguity), we also get (from the same basis):

Colossians (positive result)

And adding Colossians to the mix, we also get:

2 Thessalonians (positive result)
Ephesians (positive result)

So this stylometric evidence is, unfortunately, ambiguous. You have several options:

(1) If you view Colossians as authentic, you can see it as the stylistic 'bridge' to the later period of Paul's life, thus making much more plausible the authorship of Ephesians and/or of 2 Thessalonians.

(2) If you view Colossians as inauthentic, you can see it as one of several shadows on the contours of the Pauline corpus (including Ephesians and 2 Thessalonians) that were written in the spirit of Paul's writing by people who had appreciated the letters written by "Paul."

(3) You can still do the same thing, while viewing Colossians as authentic and the others (Eph and/or 2 Thess) as inauthentic.

[i.e.: none of them, Colossians only, Collosians+Ephesians, Colossians+2 Thessalonians, or Colossians+Ephesians+2 Thessalonians as "Paul."]

Unfortunately that also very much resembles the current split (largely split between Anglo-American scholarship being more willing to treat more letters as Pauline and continental scholarship being less willing to treat more letters as Pauline), so it's disappointing not to get a firm read yet.

We still haven't circled back around to Romans, yet, though, so we may have some more surprises in wait.

Here is 2 Thessalonians with the minimal training corpus (1 Cor, 2 Cor, shorter 'Gal', 1 Thess, and Phil.):

testsize: 820


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.395458086785985'; $VAR2 = '0.191595378521612'; $VAR3 = '0.233620904159974'; $VAR4 = '0.179325630532429';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.489321218685862'; $VAR3 = 25; $VAR4 = '0.510678781314138';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.14 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.14 Test, Z-Score-Based Method
0.00712105798575788
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.992929292929293

Author Z-Score-Based P-Values
$VAR1 = '0.144531694367401'; $VAR2 = '0.0700241204213338'; $VAR3 = '0.0853835747608789'; $VAR4 = '0.0655397830778991';

Control Z-Score-Based P-Values
$VAR1 = '0.0687594660441467'; $VAR2 = '0.0620624156712501'; $VAR3 = '0.00780220666451607'; $VAR4 = '0.0218372928286713'; $VAR5 = '0.0246662080602326'; $VAR6 = '0.0280834120093621'; $VAR7 = '0.00579114442226901'; $VAR8 = '0.0139502661676028'; $VAR9 = '0.0236181497217051'; $VAR10 = '0.0269079694116585'; $VAR11 = '0.00315343346892556'; $VAR12 = '0.0112566526902021'; $VAR13 = '0.00038348363165939'; $VAR14 = '0.000574631066668256'; $VAR15 = '0.00178496944768786'; $VAR16 = '0.0251154707477614'; $VAR17 = '0.033534787194665'; $VAR18 = '0.0242637481559387'; $VAR19 = '0.0270553473111595'; $VAR20 = '0.000594006808045714'; $VAR21 = '0.112735232279553'; $VAR22 = '0.0486157858929896'; $VAR23 = '0.0946151920745979'; $VAR24 = '0.0644799670964745'; $VAR25 = '0.150840116312627'; $VAR26 = '0.121923545461723'; $VAR27 = '0.0979585370974728'; $VAR28 = '0.0738515198149417'; $VAR29 = '0.01783970053608'; $VAR30 = '0.0169579862037634';

Here is 2 Thessalonians after adding Colossians:

testsize: 820


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.458317043634509'; $VAR2 = '0.171380007403744'; $VAR3 = '0.209911037858309'; $VAR4 = '0.160391911103437';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.55389281903583'; $VAR3 = 25; $VAR4 = '0.44610718096417';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.18 Test, Z-Score-Based Method
0.857142857142857
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.18 Test, Z-Score-Based Method
0.0111902339776195
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.987112970711297

Author Z-Score-Based P-Values
$VAR1 = '0.1872847712905'; $VAR2 = '0.0700320137253515'; $VAR3 = '0.0857771738203037'; $VAR4 = '0.0655418837354179';

Control Z-Score-Based P-Values
$VAR1 = '0.0687588410932895'; $VAR2 = '0.0620620306349956'; $VAR3 = '0.00780216968312773'; $VAR4 = '0.0218373760159598'; $VAR5 = '0.0246659385310648'; $VAR6 = '0.0280830092209996'; $VAR7 = '0.00579117294324977'; $VAR8 = '0.0139502674871898'; $VAR9 = '0.0236181354428359'; $VAR10 = '0.0269079923937891'; $VAR11 = '0.00315344005260585'; $VAR12 = '0.0112565855911596'; $VAR13 = '0.00038348381489696'; $VAR14 = '0.000574631191484725'; $VAR15 = '0.00178494383887954'; $VAR16 = '0.025115307595773'; $VAR17 = '0.0335346618699215'; $VAR18 = '0.024263872940633'; $VAR19 = '0.0270553070359084'; $VAR20 = '0.000593989539111456'; $VAR21 = '0.112735140135436'; $VAR22 = '0.0486154227268272'; $VAR23 = '0.0946152929908425'; $VAR24 = '0.0644799446109303'; $VAR25 = '0.150839798759911'; $VAR26 = '0.121923428180118'; $VAR27 = '0.0979586520008796'; $VAR28 = '0.0738515048403131'; $VAR29 = '0.0178398710573289'; $VAR30 = '0.0169579948459948';

Here is 2 Thessalonians after adding Colossians and Ephesians:

testsize: 820


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.474803024618046'; $VAR2 = '0.166179330117736'; $VAR3 = '0.20353265421517'; $VAR4 = '0.155484991049048';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.570237682421521'; $VAR3 = 25; $VAR4 = '0.429762317578479';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.2 Test, Z-Score-Based Method
0.75
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.2 Test, Z-Score-Based Method
0.00712105798575788
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.990594558280148

Author Z-Score-Based P-Values
$VAR1 = '0.200144403748122'; $VAR2 = '0.0700498126953436'; $VAR3 = '0.0857954132746687'; $VAR4 = '0.0655418125238944';

Control Z-Score-Based P-Values
$VAR1 = '0.0687588823102705'; $VAR2 = '0.0620620744112862'; $VAR3 = '0.00780218400339275'; $VAR4 = '0.0218373766188926'; $VAR5 = '0.0246658002506511'; $VAR6 = '0.0280833490643281'; $VAR7 = '0.00579117222719189'; $VAR8 = '0.0139502669065006'; $VAR9 = '0.0236181341221141'; $VAR10 = '0.0269079905762001'; $VAR11 = '0.00315343953292311'; $VAR12 = '0.0112565030409107'; $VAR13 = '0.000383483717943397'; $VAR14 = '0.000574631104517267'; $VAR15 = '0.00178493075952909'; $VAR16 = '0.0251152656135057'; $VAR17 = '0.0335347554181776'; $VAR18 = '0.0242638627064597'; $VAR19 = '0.027055285152894'; $VAR20 = '0.000594019731176355'; $VAR21 = '0.112735165979223'; $VAR22 = '0.048615863684788'; $VAR23 = '0.0946152952892366'; $VAR24 = '0.0644799353027735'; $VAR25 = '0.150839773407983'; $VAR26 = '0.121923314411118'; $VAR27 = '0.0979586219047136'; $VAR28 = '0.0738514652184053'; $VAR29 = '0.0178397796468473'; $VAR30 = '0.0169579922570321';

[Peter Kirby]

That's not exactly good for 'Philemon'. Apparently Colossians fares better on its own than it does with its junior partner.

But wait... there's more!

You see, if we add Ephesians to the mix, or if we add Ephesians and 2 Thessalonians to the mix, then the picture changes.

The result was negative with just 1 Cor, 2 Cor, shorter Gal, 1 Thess, and Phil as the training corpus for "Paul."

When Ephesians is added to that list, the result for "Colossians and Philemon" is positive:

testsize: 1916


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.842141688679665'; $VAR2 = '8.08427277292974e-78'; $VAR3 = '3.80908180600917e-06'; $VAR4 = '0.157854502238529';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.591007576060597'; $VAR3 = 25; $VAR4 = '0.408992423939403';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.11 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.11 Test, Z-Score-Based Method
0.0048661800486618
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.995157384987894

Author Z-Score-Based P-Values
$VAR1 = '0.118233347174918'; $VAR2 = '1.13499977767058e-78'; $VAR3 = '5.3477995168917e-07'; $VAR4 = '0.0221621449420862';
Good compatibility. Z-Score-Based P-Value > 0.1.
Excellent indicator. 0% of the rest have P-Value > 0.1.

Control Z-Score-Based P-Values
$VAR1 = '0.00301644496809286'; $VAR2 = '0.0083671249031009'; $VAR3 = '0.000645887806989311'; $VAR4 = '0.00419501427800222'; $VAR5 = '0.0012459140057823'; $VAR6 = '0.00661656265838357'; $VAR7 = '0.000793250491030867'; $VAR8 = '0.00300086319430422'; $VAR9 = '0.00294990379061512'; $VAR10 = '0.00365276525732507'; $VAR11 = '2.58082846415942e-06'; $VAR12 = '0.00218435612466747'; $VAR13 = '1.52851857453455e-05'; $VAR14 = '7.7711801836459e-06'; $VAR15 = '0.000307378807867016'; $VAR16 = '0.00230612345328111'; $VAR17 = '0.000227544153680064'; $VAR18 = '0.00439116477640404'; $VAR19 = '0.00650771317129977'; $VAR20 = '3.61703767576989e-06'; $VAR21 = '0.056251614258799'; $VAR22 = '0.00744489317380135'; $VAR23 = '0.0500012868281179'; $VAR24 = '0.0422445221648404'; $VAR25 = '0.0818205133238103'; $VAR26 = '0.0606693009502639'; $VAR27 = '0.0161236070486016'; $VAR28 = '0.0396394588896905'; $VAR29 = '0.00249583699099621'; $VAR30 = '0.00458742746964474';

When 2 Thessalonians is also added to that list, the result for "Colossians and Philemon" is still more positive:

testsize: 1916


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.871940077724227'; $VAR2 = '1.3291526589289e-79'; $VAR3 = '3.44970201074403e-06'; $VAR4 = '0.128056472573762';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.644915558409697'; $VAR3 = 25; $VAR4 = '0.355084441590303';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.14 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.14 Test, Z-Score-Based Method
0.0024330900243309
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.99757281553398

Author Z-Score-Based P-Values
$VAR1 = '0.148604994891434'; $VAR2 = '2.26527864856941e-80'; $VAR3 = '5.87933692670246e-07'; $VAR4 = '0.0218247009614549';
Good compatibility. Z-Score-Based P-Value > 0.1.
Excellent indicator. 0% of the rest have P-Value > 0.1.

Control Z-Score-Based P-Values
$VAR1 = '0.00301643963063478'; $VAR2 = '0.0083671592049479'; $VAR3 = '0.000645919710919213'; $VAR4 = '0.00419502325562131'; $VAR5 = '0.00124587241292149'; $VAR6 = '0.00661673465127736'; $VAR7 = '0.00079326185757687'; $VAR8 = '0.00300085928213072'; $VAR9 = '0.00294998530278591'; $VAR10 = '0.00365270383229701'; $VAR11 = '2.58091933624513e-06'; $VAR12 = '0.0021842700700412'; $VAR13 = '1.52876265489382e-05'; $VAR14 = '7.77139036188806e-06'; $VAR15 = '0.000307378909146875'; $VAR16 = '0.00230615508110043'; $VAR17 = '0.000227541470975365'; $VAR18 = '0.00439116477633265'; $VAR19 = '0.00650764976336094'; $VAR20 = '3.61703612075705e-06'; $VAR21 = '0.0562513601906669'; $VAR22 = '0.00744477735269304'; $VAR23 = '0.0500012860081977'; $VAR24 = '0.0422444898544919'; $VAR25 = '0.0818205126864578'; $VAR26 = '0.0606692046731397'; $VAR27 = '0.0161236241963371'; $VAR28 = '0.0396390598759447'; $VAR29 = '0.00249585722838513'; $VAR30 = '0.00458741585759364';

For those who believe that "Philemon" was likely authentic, it's enough to make you wonder whether Colossians and Ephesians (at least) weren't also.

It's also enough to consider the idea that Paul's style might have matured a bit through his writing career (if "Paul" is seen as having one, anyway).

For those who aren't inclined to consider the deutero-Paulines as part of the same corpus and authorship as "Paul," might we wonder if they had a common author? They do seem to have some correlated effects thus far (adding them to the existing corpus has always improved the others to the point of flipping to "positive" results if not previously positive). It's a good question whether it's consistent/sound to believe that Colossians, Philemon, Ephesians, and possibly 2 Thessalonians might have been part of a single secondary author's corpus.

[Peter Kirby]

So far we have shown that it is possible to start with 1 Corinthians and with 'shorter' Romans and show that the samples match closest to the rest of their text. We've also shown that it is possible to start with 'shorter'/'longer' Romans and with 1 Corinthians and show that the samples of 2 Corinthians match closest to the other two. And, last but not least, we have shown that it is possible to start with 1 Corinthians and 2 Corinthians and show that the samples of Galatians, 1 Thessalonians, and Philippians match closest to them.

We have further shown that, starting with all of those (1 Cor, 2 Cor, shorter Gal, 1 Thess, and Phil), it looks like Colossians is a match for them. And we have finally shown that, starting with them and Colossians, both Ephesians and 2 Thessalonians can be matched. Or that, starting with them and Ephesians, Colossians and Philemon can be matched with the rest. On the other hand, there does seem to be a distinct group of "deutero-Paulines" here (Colossians, Philemon, Ephesians, 2 Thessalonians) that have slightly different style from the earlier group (1 Cor, 2 Cor, shorter Gal, 1 Thess, Phil), whether they are actually from the same "Paul" or otherwise. The epistle to the Colossians tends to provide the evidence of a 'bridge' between their styles and the plausibility of common authorship.

Now, the plausibility of the common authorship of 1 Corinthians and 'shorter' Romans was already seen from the start. Also, Romans is very generally considered to be one of the later epistles of Paul considered solidly authentic (for those who believe in those kinds of conclusions, anyway). So, for those who believe that Romans is by the same "Paul," we can perform a sort of 'reverse test': what do we need to have in the training set to get this conclusion for Romans?

We can start by seeing what happens if we throw the whole mess into the training set: 1 Cor, 2 Cor, shorter Gal, 1 Thess, Phil, Col + Phlm, Eph, and 2 Th. Then we'll pop them off that stack, from right to left (which roughly is in agreement with how strongly scholars feel about them as being "Paul").

For those who are willing to believe that Romans isn't by the same "Paul" as the author of 1 Corinthians, the exercise is fairly abstract. For those unwilling to believe that Romans isn't by "Paul," it's a good way of testing when we've gone too far and thrown out too many of the (apparently) later writings of Paul.

(Yes, if you are a total "Paul" skeptic, this approach may be less useful to you. But--and this everyone should find interesting--it does look like 'shorter' Romans is likely authored by the rest of the epistles canvassed here, while it seems unlikely that 'longer' Romans were. And the so-called 'additions' do seem to be the part that doesn't resemble the style of "Paul," defined as the author of 1 Corinthians and the rest that match 1 Corinthians.)

Here's the data using, again, the whole mess and the two 'shorter' Romans samples and the 'additions'.

testsize: 2087


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.968941167083357'; $VAR2 = '5.11487663202409e-118'; $VAR3 = '4.19228541900091e-09'; $VAR4 = '0.031058828724358';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.526721352705114'; $VAR3 = 26; $VAR4 = '0.473278647294886';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0471 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0471 Test, Z-Score-Based Method
0.113756613756614
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.897862232779097

Author Z-Score-Based P-Values
$VAR1 = '0.0471951288733428'; $VAR2 = '2.49135107497047e-119'; $VAR3 = '2.04197589435854e-10'; $VAR4 = '0.00151281158660385';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Decent indicator. 18.1% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '0.000166249007191013'; $VAR2 = '0.00437915991292018'; $VAR3 = '2.03065847277147e-13'; $VAR4 = '0.000633455761975589'; $VAR5 = '9.78641245052089e-07'; $VAR6 = '2.899586406812e-05'; $VAR7 = '8.71345310920554e-05'; $VAR8 = '0.000278064444805027'; $VAR9 = '0.000333581387105694'; $VAR10 = '0.00459259602498201'; $VAR11 = '4.34842572318091e-08'; $VAR12 = '1.45402284075578e-05'; $VAR13 = '5.67099704623462e-10'; $VAR14 = '1.26385505432249e-10'; $VAR15 = '6.90378330499368e-07'; $VAR16 = '0.000906110763728711'; $VAR17 = '0.0022602379310992'; $VAR18 = '0.00463329253859959'; $VAR19 = '0.00196701270864335'; $VAR20 = '1.32331712746363e-08'; $VAR21 = '0.0387289878586543'; $VAR22 = '0.00297043781906563'; $VAR23 = '0.03095831931012'; $VAR24 = '0.0269848263572378'; $VAR25 = '0.0393066687130911'; $VAR26 = '0.0424065715911627'; $VAR27 = '0.00577804244756196'; $VAR28 = '0.0225006262683589'; $VAR29 = '0.000965233625924518'; $VAR30 = '0.00116799854409532';

testsize: 2134


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.989338082375587'; $VAR2 = '3.83465819192467e-146'; $VAR3 = '1.14236461342066e-13'; $VAR4 = '0.0106619176242987';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.650409092643671'; $VAR3 = 26; $VAR4 = '0.349590907356329';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0874 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0874 Test, Z-Score-Based Method
0.02710027100271
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.973614775725594

Author Z-Score-Based P-Values
$VAR1 = '0.0874965279574582'; $VAR2 = '3.39135108285115e-147'; $VAR3 = '1.01030112068229e-14'; $VAR4 = '0.000942934260909624';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Excellent indicator. 0% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '2.08738059043526e-07'; $VAR2 = '0.00195145052332708'; $VAR3 = '2.21104827989604e-10'; $VAR4 = '0.000878158155207376'; $VAR5 = '1.35552147610724e-08'; $VAR6 = '1.29702750362046e-05'; $VAR7 = '0.000229788879649306'; $VAR8 = '0.000653304017934407'; $VAR9 = '0.0007358247712623'; $VAR10 = '0.00710021227435882'; $VAR11 = '5.05498146773833e-09'; $VAR12 = '1.3183056826593e-05'; $VAR13 = '4.06301391527877e-07'; $VAR14 = '1.39190121332362e-08'; $VAR15 = '0.000359635587692213'; $VAR16 = '0.00253709944462034'; $VAR17 = '0.00496457194876365'; $VAR18 = '0.0176710531630924'; $VAR19 = '0.0051723186148855'; $VAR20 = '4.012300263437e-06'; $VAR21 = '0.0294539938649908'; $VAR22 = '0.00544033309892938'; $VAR23 = '0.0452648639294468'; $VAR24 = '0.0452192784919256'; $VAR25 = '0.041900531486103'; $VAR26 = '0.0470288483742554'; $VAR27 = '0.0180259244100213'; $VAR28 = '0.0388667576420962'; $VAR29 = '0.00193599193315093'; $VAR30 = '0.00111234298163141';

That's two positive results for 'shorter' Romans. And as for the additions?

testsize: 2881


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.857826237663214'; $VAR2 = '3.16169206765536e-120'; $VAR3 = '5.49713201430338e-65'; $VAR4 = '0.142173762336786';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.443362701119578'; $VAR3 = 26; $VAR4 = '0.556637298880422';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0705 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0705 Test, Z-Score-Based Method
0.00371747211895911
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.996296296296296

Author Z-Score-Based P-Values
$VAR1 = '0.0705209446433517'; $VAR2 = '2.59919202156632e-121'; $VAR3 = '4.51913132820359e-66'; $VAR4 = '0.0116879474924919';
Decent compatibility. Z-Score-Based P-Value > 0.05.
Decent indicator. 18.1% of the rest have P-Value > 0.05.

Control Z-Score-Based P-Values
$VAR1 = '1.13253177598248e-05'; $VAR2 = '0.00215145815284288'; $VAR3 = '1.49125425477807e-12'; $VAR4 = '0.000977880990475662'; $VAR5 = '9.50988549971095e-06'; $VAR6 = '0.000511448489487641'; $VAR7 = '0.000126376036230959'; $VAR8 = '0.00212917796065016'; $VAR9 = '0.00211280896104257'; $VAR10 = '0.00510018423656802'; $VAR11 = '4.521764504508e-08'; $VAR12 = '2.32658074740093e-05'; $VAR13 = '1.08423810573968e-11'; $VAR14 = '4.88036328552598e-12'; $VAR15 = '3.36807861804761e-06'; $VAR16 = '0.00583171334378478'; $VAR17 = '0.000456860696976353'; $VAR18 = '0.00752906079310731'; $VAR19 = '0.00700565444655475'; $VAR20 = '5.45273288660858e-10'; $VAR21 = '0.0656964890359312'; $VAR22 = '0.00585584575251539'; $VAR23 = '0.0714790668008604'; $VAR24 = '0.0539659182366047'; $VAR25 = '0.0672424364248775'; $VAR26 = '0.0885383187210957'; $VAR27 = '0.0173496140097876'; $VAR28 = '0.0501087606089695'; $VAR29 = '0.0035723712465378'; $VAR30 = '0.00486328535759934';

They're still a negative, even though the training set now includes all of 1 Cor, 2 Cor, shorter Gal, 1 Thess, Phil, Col + Phlm, Eph, and 2 Thess.

What about the full text of "Romans"? We should test that too.

This time, however, we find that there are 2 out of 3 negative results. Not looking so good for proponents of the 'longer' text of Romans.

testsize: 2355


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.896819632638724'; $VAR2 = '1.96071863032295e-142'; $VAR3 = '1.82885803932653e-05'; $VAR4 = '0.103162078780883';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.475926149613419'; $VAR3 = 26; $VAR4 = '0.524073850386581';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.047 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.047 Test, Z-Score-Based Method
0.0785498489425982
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.927170868347339

Author Z-Score-Based P-Values
$VAR1 = '0.0470881960043508'; $VAR2 = '1.02949020978026e-143'; $VAR3 = '9.60255804910912e-07'; $VAR4 = '0.00541660330467742';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Decent indicator. 18.1% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '3.40312381243325e-06'; $VAR2 = '0.000902308518946955'; $VAR3 = '8.75502951031939e-08'; $VAR4 = '0.00195774957425522'; $VAR5 = '1.36526877126884e-05'; $VAR6 = '0.000220385249829694'; $VAR7 = '0.000348304858028166'; $VAR8 = '0.000742915057071322'; $VAR9 = '0.000413337124641822'; $VAR10 = '0.00477579407996434'; $VAR11 = '5.33169018452946e-09'; $VAR12 = '4.35848127182072e-05'; $VAR13 = '6.96842770492551e-10'; $VAR14 = '1.04127728971179e-10'; $VAR15 = '7.47808840030724e-07'; $VAR16 = '0.000749774477426306'; $VAR17 = '0.000412948655187668'; $VAR18 = '0.00294879674589886'; $VAR19 = '0.0024977800635664'; $VAR20 = '2.90622081893838e-09'; $VAR21 = '0.0406049580618087'; $VAR22 = '0.00304063316295342'; $VAR23 = '0.0399563686544561'; $VAR24 = '0.0472554384197717'; $VAR25 = '0.0468324941665972'; $VAR26 = '0.0518519358682079'; $VAR27 = '0.00394786211005147'; $VAR28 = '0.0287464994655036'; $VAR29 = '0.00207705110744432'; $VAR30 = '0.00175354477679905';

testsize: 2442


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.990938605555455'; $VAR2 = '1.62204977499255e-174'; $VAR3 = '2.60993079675841e-07'; $VAR4 = '0.00906113345146492';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.548559817003035'; $VAR3 = 28; $VAR4 = '0.451440182996965';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.0466 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.0466 Test, Z-Score-Based Method
0.034375
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.966767371601208

Author Z-Score-Based P-Values
$VAR1 = '0.0466912633354727'; $VAR2 = '7.64280983330635e-176'; $VAR3 = '1.22975293762523e-08'; $VAR4 = '0.000426944480443429';
Poor compatibility. Z-Score-Based P-Value < 0.05.
Poor indicator. 21.2% of the rest have P-Value > 0.01.

Control Z-Score-Based P-Values
$VAR1 = '2.47986011813499e-05'; $VAR2 = '0.00407230922706681'; $VAR3 = '2.32963243303817e-08'; $VAR4 = '0.000285015363544604'; $VAR5 = '1.00424336022396e-08'; $VAR6 = '2.09117062444596e-06'; $VAR7 = '2.31527352151418e-05'; $VAR8 = '1.7776645685016e-05'; $VAR9 = '0.000386469743832394'; $VAR10 = '0.00266559016924608'; $VAR11 = '1.31196078099161e-10'; $VAR12 = '6.93781659734895e-06'; $VAR13 = '3.22005544688151e-10'; $VAR14 = '6.89059355774787e-13'; $VAR15 = '8.27048498379732e-07'; $VAR16 = '0.00104975636295906'; $VAR17 = '0.00306325866547393'; $VAR18 = '0.0097672344086596'; $VAR19 = '0.00162052799590588'; $VAR20 = '4.66673036495181e-09'; $VAR21 = '0.0230618354925736'; $VAR22 = '0.00347108914225437'; $VAR23 = '0.0339590483103935'; $VAR24 = '0.022561366789131'; $VAR25 = '0.0316623398062272'; $VAR26 = '0.0382394131013473'; $VAR27 = '0.0139460408983563'; $VAR28 = '0.0384248204319506'; $VAR29 = '0.000694948414748313'; $VAR30 = '0.000874892871455634';

testsize: 2305


Bayesian Author Test: Posterior Probabilities from Equal Priors, Z-Score-Based Method
$VAR1 = '0.932169909784165'; $VAR2 = '1.08960715735061e-104'; $VAR3 = '0.00274113142079994'; $VAR4 = '0.0650889587950354';

Bayesian Comparison of Best Author to Best Control: from Equal Priors, Z-Score-Based Method
$VAR1 = 1; $VAR2 = '0.471442547198216'; $VAR3 = 26; $VAR4 = '0.528557452801784';

Percentage of Samples in the Best Author Candidate that Meet the P-Value>0.1 Test, Z-Score-Based Method
1
Percentage of Samples outside the Best Author Candidate that Meet the P-Value>0.1 Test, Z-Score-Based Method
0.00588235294117647
Posterior Probability of a Sample Meeting the Test Being by the Best Author Candidate (with Prior = 0.5), Not Any Other, Z-Score-Based Method
0.994152046783626

Author Z-Score-Based P-Values
$VAR1 = '0.104613684386926'; $VAR2 = '1.22282234245476e-105'; $VAR3 = '0.000307626168050251'; $VAR4 = '0.00730467237891648';
Good compatibility. Z-Score-Based P-Value > 0.1.
Great indicator. 3% of the rest have P-Value > 0.1.

Control Z-Score-Based P-Values
$VAR1 = '0.000223250076516164'; $VAR2 = '0.00343854058631449'; $VAR3 = '2.8499470774381e-08'; $VAR4 = '0.0177150331612473'; $VAR5 = '4.40623962047404e-06'; $VAR6 = '0.00135643729169241'; $VAR7 = '0.000586576841779988'; $VAR8 = '0.00449892878768938'; $VAR9 = '0.00248330934771445'; $VAR10 = '0.0102961342891083'; $VAR11 = '1.85832242405467e-06'; $VAR12 = '2.9177368303911e-05'; $VAR13 = '2.29859444778386e-07'; $VAR14 = '5.13968570625708e-09'; $VAR15 = '0.000287273354499491'; $VAR16 = '0.0064891926849733'; $VAR17 = '0.00363574930599767'; $VAR18 = '0.00473034153760149'; $VAR19 = '0.0127098388374609'; $VAR20 = '2.49707979922336e-06'; $VAR21 = '0.0693012316918001'; $VAR22 = '0.00826702972999107'; $VAR23 = '0.0656840723678538'; $VAR24 = '0.0722572521847812'; $VAR25 = '0.0637857281838222'; $VAR26 = '0.117287552590189'; $VAR27 = '0.0292074702630094'; $VAR28 = '0.0531460831003873'; $VAR29 = '0.00478236805921806'; $VAR30 = '0.00978202910297771';

[Tenorikuma]

Isn't one of the (many) signs of forgery in the deutero-paulines that they copy the contents of other epistles in a way that an authentic epistle would not? E.g. 2 Thessalonians copying from 1 Thessalonians to appear Pauline, Ephesians copying about 50% of Colossians, etc. Naturally, if you build an "accretive" Pauline corpus in this manner, more and more things will look Pauline that aren't.

[Peter Kirby]

Isn't one of the (many) signs of forgery in the deutero-paulines that they copy the contents of other epistles in a way that an authentic epistle would not? E.g. 2 Thessalonians copying from 1 Thessalonians to appear Pauline, Ephesians copying about 50% of Colossians, etc. Naturally, if you build an "accretive" Pauline corpus in this manner, more and more things will look Pauline that aren't.

Yes, it's not difficult to explain some of the similarity of the style in this way for the so-called deutero-Paulines.

I'm definitely not willing to make any claims regarding so-called "adversarial" stylometry: if someone is deliberately trying to mask their style or deliberately trying to copy someone else's style, then, essentially, all bets are off.

[Peter Kirby]

Isn't one of the (many) signs of forgery in the deutero-paulines that they copy the contents of other epistles in a way that an authentic epistle would not?

As a non-stylometric question, I'm not really so sure about this.

Consider that "Ephesians" is called "Laodiceans" in the older, Marcionite canon.

Consider that "Colossians" has this statement:

And when this letter has been read among you, have it also read in the church of the Laodiceans; and see that you also read the letter from Laodicea.

So, if A, then B. If there was an actual letter sent to the Colossians, then there was also an actual letter sent to the Laodiceans.

So, if Colossians could be authentic correspondence, then Laodiceans ("Ephesians") is either authentic also or pretending to be the lost letter to the Laodiceans.

And if someone wrote two letters on similar topics to two different churches at the same time, could that writer not plagiarize himself? Could that writer not use the one letter as the basis for writing another letter? Could that writer not want both letters read in both churches, seen as perhaps needing instruction on similar topics, for the benefit of both?

I would consider that, in general terms, self-'plagiarism' is an extremely common phenomenon, and it's prematurely discounted as an explanation.

[Tenorikuma]

Bart Ehrman summarizes the arguments regarding the evidential value of self-copying in Forgery and Counterforgery, which I assume you have read or otherwise have access to. The type of "self-plagiarism" you're suggesting would pretty much require Paul to have written written Ephesians after writing Colossians, with the latter still unsent sitting on his desk for comparison. Possible, I suppose.

Changing topics slightly, it has also been argued that Colossians is a non-Pauline expansion of a Pauline letter, and Ephesians being an adaptation of this expanded semi-Pauline letter would obviously put it in the non-Pauline category.

[Peter Kirby]

The type of "self-plagiarism" you're suggesting would pretty much require Paul to have written written Ephesians after writing Colossians, with the latter still unsent sitting on his desk for comparison. Possible, I suppose.

Yes. Unless it were Colossians that were written with reference to Laodiceans (Ephesians).

There is not a universal consensus of the direction of dependence, especially among those considering Laodiceans (Eph) as possibly "Paul."