On dating the Gnostic literature after 325 CE

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Leucius Charinus
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Re: On dating the Gnostic literature after 325 CE

Post by Leucius Charinus »

Peter Kirby wrote:
Leucius Charinus wrote:
Peter Kirby wrote:The misrepresentation is the implication that Nongbri even discusses any of the papyri that I mentioned in that article.
Specifically which article did you mention? I thought you re-cited Nongbri's article. Sure Nongbri discusses the canonical papyri fragments, and not the non canonical fragments. I understand that.
There may be a purpose in citing Nongbri, but it was cited inaccurately above. You may have meant something different than what you said, of course, but that's also inaccuracy.
From reading Nongbri's article I get the impression he is saying that the current way of citing palaeographical dates (eg: mid 2nd century to late 2nd century) is not realistic because the error range stated is too small. I read him saying that any of these early (canonical) papyri could also be dated to the 4th century because there exists securely dated comparanda that is dated to the 4th century. The summary position (as I read Nongbri) is that the upper bound of palaeographical estimates, as a result of this comparanda, should be inclusive of the 4th century.

Yes, he is the only one I know so far who has made such a dramatic variation in the error bounds of palaeographical dating. However I did cite another article above, Early New Testament Manuscripts and Their Dates: A Critique of Theological Palaeography in which the authors also argue for a relaxation of the focus of "early" date ranges.

So I really don't understand your criticism, unless it is the fact that I am applying Nongbri's 4th century upper bound palaeographical estimates (for canonical papyri) to the non canonical papyri. But I do not see this application as irrational, since the point is being made on the actual estimation of palaeographical dates (with upper and lower bounds) - and should apply to both canonical and non canonical papyri across the board.



LC
That's an opinion, but it's your opinion, not Nongbri's in that article.

OK I accept that is the case. Rightly or wrongly I have generalised what Nongbri writes about P.66.

Peter Kirby wrote:
Leucius Charinus wrote:
Peter Kirby wrote:The misrepresentation is the implication that Nongbri even discusses any of the papyri that I mentioned in that article.
Specifically which article did you mention?
Rephrase: The misrepresentation is the implication that Nongbri even discusses, in that article, any of the papyri that I mentioned.
OK. I now understand that the papyri you mentioned are these:
  • 188 P.Oxy. 3.405 II/III Oxyrhynchus Irenaeus, Adversus Haereses 3.9, 2-3
    213 P.Oxy. 41.2949 II/III Oxyrhynchus Gospel of Peter
    214 P.Oxy. 4.654 III Oxyrhynchus Gospel of Thomas, Prologue and logoi 1-7
    215 P.Oxy. 50.3525 III Oxyrhynchus Gospel of Mary
    217 P.Oxy. 4.655 beg. III Oxyrhynchus Gospel of Thomas, logoi 24, 36-39
    224 P.Ryl. 3.463 beg. III Oxyrhynchus Gospel of Mary
    225 P.Oxy. 1.1 early III Oxyrhynchus Gospel of Thomas, logoi 26-33, 77a
    226 P.Schøyen 1.21 III unknown Acts of Paul and Thecla
And its quite true that Nongbri does not address these papyri. Most of the earliest of these papyri are dated via palaeography to the 3rd century.

I have a list of these (with the mainstream estimated chronology) here: http://www.mountainman.com.au/essenes/A ... papyri.htm

At this point I'd advise that if you really want to be taken seriously, you should become first hand familiar with the techniques of paleography. All of this is too fundamental to your whole endeavor for you to be citing someone here or there (who are exceptions in the world of paleography) for your conclusions, especially when you are extrapolating even more (inexpertly) from there.
I am no palaeographer, but I have read books and articles on the subject which are collated here: http://www.mountainman.com.au/essenes/article_071.htm In a number of these articles the authors express caution and have provided a number of specific and surprising counter-examples against treating palaeographical estimates as "certain" for the papyri fragments. Eric Turner admits that a "subjective factor" will always be present in such estimates. So we need error bounds that are as realistic as possible.

I have acknowledged that the early papyri (except the Irenaeus one) are estimated to be from the 3rd century. But I have argued that it is not unreasonable that all palaeographical estimates should be expressed as a date range, with a lower and upper bound, and that when an appropriate upper bound is evaluated then it will include the 4th century. This is obviously a defensive argument against the falsification of the hypothesis of the OP in the citing of palaeographical dates associated with these papyri. But I don't see it (100 years difference) as either unreasonable or ad hoc considering the issues involved in this form of dating.

However I am quite open to any criticism on this issue because, as you rightly say, I am no expert.




LC
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Re: On dating the Gnostic literature after 325 CE

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In the following I have attempted to sketch a test of the OP using Statistical_hypothesis_testing:
  • A statistical hypothesis is a scientific hypothesis that is testable on the basis of observing a process that is modeled via a set of random variables.[1] A statistical hypothesis test is a method of statistical inference used for testing a statistical hypothesis. A test result is called statistically significant if it has been predicted as unlikely to have occurred by sampling error alone, according to a threshold probability—the significance level. Hypothesis tests are used in determining what outcomes of a study would lead to a rejection of the null hypothesis for a pre-specified level of significance.
H0 - NULL (Mainstream) Hypothesis: Non canonical Christian manuscripts were being created in the 2nd and 3rd and 4th centuries.

H1 - ALTERNATE Hypothesis: Non canonical Christian manuscripts were only created in the 4th century.

If H0 were true then we would expect to be able to find physical evidence of non canonical Christian manuscripts in both the 2nd and 3rd centuries.

If H1 were true then we would not expect to be able to find physical evidence of non canonical Christian manuscripts in both the 2nd and 3rd centuries.


WHAT'S BEEN FOUND? EVALUATING and QUANTIFYING THE EVIDENCE

What physical evidence of the non canonical Christian manuscripts has been discovered and how is the actual evidence to be represented?

For example do we count codices or texts? The NHC has 12 codices and over 50 texts. How are papyri fragments to be counted and/or weighted in this survey compared to codices and more complete manuscripts? For example is it appropriate to count pages as an atomic unit of physical evidence?

The physical evidence is being dated by different dating methodologies including palaeography, cartonnage, C14. Are these dating methodologies to be weighted according to their accuracy and error bounds. I would be inclined to treat the cartonnage and C14 to be more certain than the palaeography, but I might be biased. Stated another way, how do we validly compare apples and oranges, or is it possible?


PHYSICAL EVIDENCE CITED FOR PRIOR TO 325 CE


(1) Via palaeographical dating a series of papyri fragments of codex leaves (See above post).
(2) Via C14 dating there is an argument that Codex Tchacos is prior to 325 CE, and PK has expressed this as a probability.

PHYSICAL EVIDENCE CITED FOR AFTER 325 CE

(3) Via palaeographical dating and cartonnage analysis, dozens of [Coptic] non canonical codices have been dated to the mid 4th century.

If the atomic unit of physical evidence is the text (within the codex) then there are probably well over 70 texts that are so dated. If the physical unit of physical evidence is as small as a page or a leaf (this would include one papyri fragment for example) then the number of leaves are probably in the thousands. IDK which of these "units" would be more appropriate as a measure of physical evidence. Any ideas?


Comparing the two hypotheses H0 and H1 in their ability to explain the pattern of evidence

According to H0 the probability p(H0 2nd century) > 0; and p(H0 3rd century) > 0

According to H1 the probability p(H1 2nd century) = 0; and p(H1 3rd century) = 0



Weak point in the Null (Mainstream) Hypothesis ?

After determining the "atomic unit of physical evidence" (i.e a codex, a text, a page or leaf) and a method whereby various dating methodologies can be validly compared together a set of data can be agreed upon which represents the physical evidence admitted to statistical testing.

IMO there is a weak point in the null hypothesis and that is an absence of the expected physical evidence for the 2nd and 3rd centuries. According to H0 the probability p(H0 2nd century) > 0; and p(H0 3rd century) > 0.

Starting with the codex as the unit of physical evidence, we have say 20 codices from the 4th century. (NHC=12, Quarara=4, Others=4, Manichaean codices=???) The C14 result on Codex Tchacos will provide some percentage of 3rd century (or pre-325) physical evidence. But that's about it. I see this as a problem for the null hypothesis, because it expects physical material from before Nicaea. The fact that codices have been preserved from the 4th century makes it more likely that codices would be also able to be preserved from the 3rd century, but we dont find any.

Whatever probability is assigned to p(H0 2nd century) + p(H0 3rd century) it must be greater than zero and probably reasonably similar to the probability p(H0 4th century). I am at a loss at the moment on how to arrive at an estimation of this probability, even a ball park. But whatever it is, after 20 "tests" - reflected in the number of physiocal codices discovered - it may only be said to have one hit. This seems very unusual. After 20 finds, with a probability roughly the same as that it would ascribe to the 4th century, it has been dwarfed. NOTE: The actual probability may not be capable of being estimated to any specific figure, but it must be represented by some figure comparable to p(H0 4th century).


The problem IMO probably becomes far more accute when the unit of physical evidence is not treated as a codex, but as a text (story) within a codex, or within a manuscript. Examining "leaves" or "pages" as units in this might be over the top, but then again it may be more appropriate - because the papyri fragments are neither codices or "Complete Texts / STories) IDK.


The problem (IMO) for the null hypothesis is explaining why so little physical evidence (units) have turned up in the 2nd and 3rd centuries.

Can this be quantified any better?
Thanks for any assistance.





LC
A "cobbler of fables" [Augustine]; "Leucius is the disciple of the devil" [Decretum Gelasianum]; and his books "should be utterly swept away and burned" [Pope Leo I]; they are the "source and mother of all heresy" [Photius]
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Re: On dating the Gnostic literature after 325 CE

Post by Leucius Charinus »

I understand that the ideas which I have explored here and earlier have been antithetical to mainstream consensus and at the edge of being unsupported by an evaluation of the evidence. I have above formulated a statistical hypothesis test. This test attempts to compare the null hypothesis (mainstream idea that the Gnostics wrote some stuff < 325 CE) to my alternate hypothesis (the Gnostics are > 325 CE).

It is my (long-considered) opinion that although this alternate hypothesis is new and antithetical to the prevailing paradigm of mainstream thinking, it does have some merit. In order to quantify and gauge this merit I have spent some time trying to devise this statistical hypothesis test. I trust that this is a responsible and objective way to approach the issue.




LC
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Re: On dating the Gnostic literature after 325 CE

Post by Peter Kirby »

Leucius Charinus wrote:I understand that the ideas which I have explored here and earlier have been antithetical to mainstream consensus and at the edge of being unsupported by an evaluation of the evidence. I have above formulated a statistical hypothesis test. This test attempts to compare the null hypothesis (mainstream idea that the Gnostics wrote some stuff < 325 CE) to my alternate hypothesis (the Gnostics are > 325 CE).

It is my (long-considered) opinion that although this alternate hypothesis is new and antithetical to the prevailing paradigm of mainstream thinking, it does have some merit. In order to quantify and gauge this merit I have spent some time trying to devise this statistical hypothesis test. I trust that this is a responsible and objective way to approach the issue.

LC
Can this be quantified any better?
Thanks for any assistance.
Let's suppose that I took a very simple and very generous approach to your suggestion.

The phenomena to be explained are the presence or absence of non-canonical manuscripts pre-325, the possible explanations are that all of the texts were written after 325 or that some of them were written before, and the general approach is Bayesian reasoning under uncertainty.

Let h be the hypothesis that all the texts are written after 325, and let q be the real and current existence of 1 or more pre-325 manuscript(s) of the same.

[1] Be very generous. Assign equal prior probabilities to _all_ of them being after 325 and _some_ of them being before 325. P(h) = P(~h) = 0.5.

[2] Be very generous. Assign P(~q|~h) = 0.5, which is to say that there is a 50% chance of there being no extant pre-325 manuscripts of non-canonical texts given that there are some non-canonical texts written before 325. We could debate this assumption (and I'm sure that you would want to do so), but it seems amply justifiable when compared to literature of this period generally, for which we do not usually have manuscripts so very close to the time of the writing of the original literary texts (300 to 1000 years or more time until the first few manuscripts is not at all uncommon) or even all that much in these two particular centuries generally, compared to what must have been written then (since manuscripts wear out and only chance and the dry sands of Egypt have saved some goodly part of it).

[3] Be very generous. Assign P(q) = 0.8, which is to say that there is a 20% chance that none of the manuscripts we have of non-canonical texts are pre-325. Since we have several manuscripts that have been dated in their most probable dating range, as considered by the experts who have examined them, before 325, and what we have against such probable dates amounts to little more than gainsaying about the possibility of a later dating (not that this is any more likely), this is also a very generous assumption, even if I'm sure that you'd like to debate it too.

[4] Be logical. Assign P(q|h) = 0 and P(~q|h) = 1, which is something you've already acknowledged.

[5] Be logical. Assign P(~q) = 0.2, which follows from [3], and assign P(q|~h) = 0.5, which follows from [2].

At this point we want to use a modified form of Bayesian reasoning where we divide the total probability space into two parts, the part where q is true and the part where q is false. We then find out how much of each space each hypothesis claims for itself, and then we multiply these proportions back against the space claimed by the original statements q and not q. As follows:

Image

[6] P(h|q) = P(q|h) * P(h) / ( P(q|h) * P(h) + P(q|~h) * P(~h) ) = 0 * 0.5 / ( 0 * 0.5 + 0.5 * 0.5 ) = 0. This represents the probability of h under the portion of the probability space where q is true.

[7] P(h|~q) = P(~q|h) * P(h) / ( P(~q|h) * P(h) + P(~q|~h) * P(~h) ) = 1 * 0.5 / ( 1 * 0.5 + 0.5 * 0.5 ) = 2/3 = 66.67%. This represents the probability of h under the portion of the probability space where q is not true.

[8] To find out the probability of h, given the uncertainty regarding q, we multiply 0.8 * 0 and 0.2 * 0.6667, to arrive at a 13.333% chance.

This is your own argument (considered in isolation), and the premises are not strictly true (they have been manipulated in your favor), and the conclusion that you are supporting (even under those stipulations) still only comes out to a 13.333% chance. If we used more realistic numbers, and combined this evidence with all the other facts at our disposal, your conclusion would then vanish into right obscurity.
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Re: On dating the Gnostic literature after 325 CE

Post by Leucius Charinus »

Peter Kirby wrote:
Leucius Charinus wrote:I understand that the ideas which I have explored here and earlier have been antithetical to mainstream consensus and at the edge of being unsupported by an evaluation of the evidence. I have above formulated a statistical hypothesis test. This test attempts to compare the null hypothesis (mainstream idea that the Gnostics wrote some stuff < 325 CE) to my alternate hypothesis (the Gnostics are > 325 CE).

It is my (long-considered) opinion that although this alternate hypothesis is new and antithetical to the prevailing paradigm of mainstream thinking, it does have some merit. In order to quantify and gauge this merit I have spent some time trying to devise this statistical hypothesis test. I trust that this is a responsible and objective way to approach the issue.

LC
Can this be quantified any better?
Thanks for any assistance.
Let's suppose that I took a very simple and very generous approach to your suggestion.
Thanks very much for this example PK. I have spent some time examining it. It has been instructive in a number of ways. However I now understand that it does not quite address the problem that I had in mind, and that is because I did not state the problem in specific enough terms. Additionally what I wanted to achieve was a method of introducing the actual evidence itself, quantified in various appropriate forms.

Firstly, what I stated was this .... The problem (IMO) for the null hypothesis is explaining why so little physical evidence (units) have turned up in the 2nd and 3rd centuries.

What I should have said is this .... The problem (IMO) for the null hypothesis (i.e. the mainstream theory) is explaining why so little physical evidence (units) have turned up in the 2nd and 3rd centuries when compared to the 4th century.

Sorry about not stating the problem specifically. I will briefly state the problem for the null hypothesis, by which I mean the mainstream theory underpinning non canonical authorship (evidenced by codex manufacture). So its not my theory that I want to address here initially, its what I perceive as a problem or failure in the mainstream theory.

Consider two buckets in which we are to place all the known physical evidence.

DEFINING TWO STATISTICAL BUCKETS

To be generous to the mainstream theory consider two separate (unequal) time-spans:

a) ANTE-NICENE = 125-324 CE (two centuries)
b) POST-NICENE = 325-424 CE (one century)

Evidence is assembled in different categories (codex, text ms, papyri leaves) and after being dated by various means (C14, cartonnage, palaeography) is placed into one of the two buckets. By statistical considerations it is obviously possible to apportion a date range (eg C14) into both buckets. I would expect that it will also be reasonable to define a suitable date range for the palaeographically dated evidence, perhaps with some percentage probability being in the 4th century.

In consideration of the way scholarship have insisted that many of the texts in the Nag Hammadi codices are from the 2nd and 3rd century, I think that it may be fair to say that according to the mainstream theory, said theory predicts that there will a roughly equal amount of evidence in each of the two buckets. When we go through the exercise however an equal distribution is not found (see further below).

The phenomena to be explained are the presence or absence of non-canonical manuscripts pre-325, the possible explanations are that all of the texts were written after 325 or that some of them were written before, and the general approach is Bayesian reasoning under uncertainty.
I am going to try and paraphrase this and bring it into line with the specific test I had in mind.

The phenomena to be explained is the ratio of the amount of non-canonical manuscripts pre-325 compared to the amount of non-canonical manuscripts post-325. If this phenomena is considered outside of standard statistical bounds, then arguments need to made to adjust for such a finding.

The possible explanations are:

1) There is no significant anomoly
2) There is a significant anomoly but various explanations can account for it.
3) Alternatively all of the texts were written after 325 and material found in the ante-Nicene may be otherwise explained.



I am going to try and work this through .... but I am not sure whether this same approach is applicable or appropriate for the revised specification of the test.

Let h be the hypothesis that all the texts are written after 325, and let q be the real and current existence of pre-325 manuscripts of the same.

Let h be the hypothesis that texts were written continuously (equally) between 125 and 425 CE.
Let q be the real and current existence of manuscripts in two segments - two buckets as defined above.

[1] Be very generous. Assign equal prior probabilities to _all_ of them being after 325 and _some_ of them being before 325. P(h) = P(~h) = 0.5.

Agreed (with the original specification). However the revised scenario has it that equal prior probabilities are [most generously] assigned to each bucket.

[2] Be very generous. Assign P(~q|~h) = 0.5, which is to say that there is a 50% chance of there being no extant pre-325 manuscripts of non-canonical texts given that there are some non-canonical texts written before 325.
This is where I wanted to deviate from supplying a subjective input and instead go back to the evidence and try and marshall the evidence itself. The following figures have been derived from a rapid assessment and may require revision and may of course be challenged.


SUMMARY

Ratio of material in the two buckets [<325 to >325]

Codices .......... 0.8 to 20
Texts ............ 11 to 76
Pages (Leaves) ... 73 to 1,600
  • DETAIL

    EVIDENCE in <325 Bucket
    ======================================

    Category 1): CODICES

    Tchacos 220-340 CE C14 dating

    Category 2): Papyri Fragments

    p.oxy.654 3rd century [Palaeography] gThomas Prologue and logoi 1-7
    p.oxy.655 3rd century [Palaeography] gThomas logoi 24, 36-39
    p.oxy.1 3rd century [Palaeography] gThomas logoi 26-33, 77a
    p.Rylands.463 3rd century [Palaeography] gMary
    p.oxy.3525 3rd century [Palaeography] gMary
    P.Oxy. 405 c.200 CE [Palaeography] Irenaeus, Adversus Haereses 3.9, 2-3 (Matt 3)
    OTHER? early [Palaeography] To be specified.

    Total Codices = 0.8 ... some percentage of Codex Tchacos (via C14)
    Total PapyriF = 7
    Total Texts = 11 (+ %Tchacos - 4 texts)
    Total Pages = 73 (+ %Tchacos - 66 pages)


    EVIDENCE in >325 Bucket
    ======================================

    Category 1): CODICES

    NHC (12) 350 CE Cartonnage and [Palaeography]
    Qurara (4) 4th Only Tchacos has been recovered
    Manichaean (5) 4th
    Askew (1) 4th
    Akhmim (1) 4th
    Bruce (1) 4th

    Category 1) Papyri Fragments

    Total Codices = 20
    Total PapyriF = 250 ????
    Total Texts = 50 + 15 + 0 + 4 + 4 + 3 = 76
    Total Pages = 1600 (NHC = 1242)


    NOTE: Obviously the dating of Codex Tchacos is critical to the stats in the ante-Nicene bucket.

All of this data can be contested. There are three forms of data which can be each examined.

Codices .......... 0.8 to 20 (Ratio = 0.04)
Texts ............ 11 to 76 (Ratio = 0.13)
Pages (Leaves) ... 73 to 1,600 (Ratio = 0.04)

[3] Be very generous. Assign P(q) = 0.8, which is to say that there is a 20% chance that none of the manuscripts we have of non-canonical texts are pre-325. Since we have several manuscripts that have been dated in their most probable dating range, as considered by the experts who have examined them, before 325, and what we have against such probable dates amounts to little more than gainsaying about the possibility of a later dating (not that this is any more likely), this is also a very generous assumption, even if I'm sure that you'd like to debate it too.

Yes of course I would. However as outlined above I really wanted to try and plug in some statistical data representing the real evidence as it has been apportioned to the two separate buckets.

[4] Be logical. Assign P(q|h) = 0 and P(~q|h) = 1, which is something you've already acknowledged.
The h and q have been revised above, so I am not sure that the rest of the treatment will follow.

To summarise, what I am trying to get at is an acknowledgement that, given the data I have provided above is satisfactory, then whether the evidence is examined by the number of codices, or number of texts or number of physical papyrus leaves, even the best result (for texts - a ratio of 0.13) is far short of an expected 0.5 ratio (equally in each bucket).

It may be that such a divergence from an expected 50% is no big deal because of unknown factors. I'd like to discuss that possibility. In the above treatment I have made various allowances:
  • 1) I have allowed for 7 papryi fragments to be <325 CE, although I could argue each of these has a distinct probability of being in the >325 CE bucket when a 4th century upper bound is granted as possible.

    2) I have allowed the published C14 date on Tchacos, and your earlier analyses, to allocate 80% of the codex to the <325 CE basket. This percentage may be substantially less depending on further publications. Additionally there is the matter of the period of time the papyrus used for Tchacos may have sat on a shelf. Many people have noted its similarity to the NHC.

    3) The NHC and other 4th century codices, texts and papyrus fragments are certain to be dated in the >325 bucket because of their cartonnage analyses.

    4) The uncertainties in arriving at appropriate date ranges for codices, texts and papyrus fragments <325 CE have been momentarily ignored. The dating of Tchacos is pivotal because of its very dominant contribution to the <325 bucket.

    5) I have been very generous in allowing the <325 bucket to span two centuries in comparison to the >325 bucket. The 0.5 expectation of this bucket could be as high as 0.66, and yet the results (0.04 and/or 0.13) are not likely to change substantially.

Thanks very much for your application of Bayes here. I have learnt a great deal because of your sketch. I can also appreciate that when all the input figures are subjectively derived, the likelihood of GIGO increases. In the above I have tried to obtain and estimate the q (real evidence) figures from the actual physical evidence base.

I am not sure that I can reformulate the same type of test which you outlined and worked through given the revision of the exercise specified above. However it basically is intended to highlight the relatively low ratio of evidence in the <325 bucket when compared to the >325 bucket, as a deviation from an expected 50% ratio.

The fact that 20 codices have survived from the 4th century mitigates toward a prior probability that codices could also survive from the 3rd or 2nd century, but this is not found to be the case. I guess the real question is whether these results demonstrate a significant statistical anomoly (greater than some standard error bound) that require an explanation. Needless to say, I would be most appreciative of your opinion on this. (Or anyone else's for that matter, if anyone else has followed this)




LC
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Re: On dating the Gnostic literature after 325 CE

Post by Peter Kirby »

To do what you want to do, you'd need a control group. I can think of a few possibilities. One possibility is to use the NT manuscripts as a control group, but we could object that they might be different in more than one respect; e.g., one might say that the original NT texts had a much different total range of dating or that they had a much broader reception as important texts. Another possibility is to use a carefully-delimited set of church fathers, from the second to the fourth century, that do not make reference to the non-canonical texts. This would have the advantages of using coterminous ranges of proposed dating and roughly comparable reception history. A third possibility is to use a set of non-Christian texts with proposed dates ranging from the early second century to the late fourth century, which has much of the same advantages of the second possibility, without being part of the controversial history of the early church; on the other hand, this has the severe disadvantage of ignoring the effect that making Christianity licit could have to improve the quantity of Christian manuscripts. (I'd say the second one is the most appropriate.)

You'd also need to understand that, with what you've granted in the premises, you'd never arrive at the conclusion that all the non-canonical texts are to be dated post-325. Instead you'd be testing whether this broad category were sufficiently like the category used as a control group as to eliminate the need to consider them different in this respect at all, or whether there were some sufficiently detectable differences in this regard. You'd lastly need to allow that there are multiple possible explanations of the differences in the two groups, even if we do find that there is a statistical difference between them in this respect.
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Re: On dating the Gnostic literature after 325 CE

Post by Peter Kirby »

With reference to the texts and dates indicated here and here:

http://www.areopage.net/PDF/PapyriFromT ... nEgypt.pdf
http://en.wikipedia.org/wiki/Oxyrhynchus_Papyri

I have attempted to do a first pass at this.

Control Group

230-265 Julius Africanus
III Origen, homily on Luke
III/IV Origen, De principiis
III/IV Eusebius, H.E. 6.43.7-8,11-12
III/IV Melito, homily
III/IV Melito, homily
early IV Origen, Commentary on Genesis
early IV Aristides, apology
IV Melito, homily
IV Martyrdom of Dioscorus

Test Group

II/III Irenaeus, Adv. Haer.
III/IV Irenaeus, Adv. Haer.
II/III Gospel of Peter
III Gospel of Thomas
III Gospel of Mary
beg. III Gospel of Thomas
II Gospel of Peter
beg. III Gospel of Mary
early III Gospel of Thomas
III Acts of Paul and Thecla
III (IV?) Prot. James
III (IV?) 3 Corinthians
III/IV Acts of Paul
III/IV Acts of Paul
beg. IV Prot. James
early IV Acts of John
early IV Acts of Peter
early IV Sophia Jesu Christi
IV Acts of John (P. Oxy. 850)
III/IV Codex Tchacos
IV Askew Codex
IV Akhmim Codex
IV Bruce Codex
IV NHL Codex VII
III/IV Other NHL Codices

We get the following table.

II or II/III or IIIIII/IV or III (IV?) or early IVIV
Control262
Test9105

There are a few ways we could go with this, but one of them is to attempt to estimate the actual frequencies by splitting the middle group between the other two groups, and naming them appropriately.

Estimated pre-325Estimated post-325
Control55
Test1410

The Chi-square statistic is 0.1988. The P value is 0.655667. This result is not significant.

Suppose we were to take 10 of the codices from Nag Hammadi, assign them an assured date in the fourth century, and count them as separate data points. We'd then have arrived at this table instead:

Estimated pre-325Estimated post-325 (counting 10 more NHL codices separately as IV)
Control55
Test1420

The Chi-square statistic is 0.2452. The P value is 0.620474. This result is not significant.

Suppose we used different categories, to weigh the assigned III century dates against both the ambiguous and the definite IV.

II or II/III or IIIIII/IV or III (IV?) or early IV or IV
Control28
Test915

The Chi-square statistic is 0.9877. The P value is 0.320294. This result is not significant.

Suppose we did this but then added the 10 other codices again as separate data points, from the NHL.

II/III or IIIIII/IV or III (IV?) or early IV or IV (counting 10 more NHL codices separately as IV)
Control28
Test925

The Chi-square statistic is 0.1725. The P value is 0.677856. This result is not significant.

Indeed, far from seeing these non-canonical texts as being substantially different from the texts typically considered their contemporaries, in respect of the range of the dating of their manuscripts, there actually seems to be more extensive evidence for pre-325 manuscripts of the non-canonical texts, compared to the control group of the patristic writings in the same period of the II to IV centuries.
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Re: On dating the Gnostic literature after 325 CE

Post by Leucius Charinus »

Peter Kirby wrote:To do what you want to do, you'd need a control group. I can think of a few possibilities.
Thanks again for the exercise. I have had a look at the stats behind control groups and as a result of that have done some brief cobweb brushing away in order to understand your examples and mathematics. Using control groups is going to get pretty ad hoc in antiquity. With modern data it would far more applicable. As a result of this research I have arrived at the following provisional way forward.

The test that I am proposing as being appropriate here is the [wiki]Pearson%27s_chi-squared_test[/wiki]

There may be reasons why this is not an appropriate test ...

Peter Kirby wrote:You'd also need to understand that, with what you've granted in the premises, you'd never arrive at the conclusion that all the non-canonical texts are to be dated post-325.
Yes I understand that. The test itself is on the mainstream theory which predicts (this obviously needs to be qualified) that there should be a more or less and equal amount of non canonical material on either side of 325 CE. The object of the test was to demonstrate that there is sufficient low p-value indicating that the observed deviation from the null hypothesis is significant. Additional explanations would be required to explain the statistical anomoly, and there are of course various explanations that could be put forward. At the same time, into this mix, the alternate hypothesis can be considered, as to whether it better explains the physical evidence. This is where the hypothesis that all the non canonical texts are to be dated post-325 fits in. [i.e. after demonstration of a statistical anomaly in the mainstream [null] hypothesis).


In the following I have attempted to apply the above chi-squared test to the data using the "codex view" of it. (I am happy to equally examine the "text view" (i.e. number of texts evidenced) and/or the "page or leaf view" (i.e. the number of pages of non canonical material evidenced).


Ante-Nicene Codices (two hunded years 125-324 CE)Post-Nicene Codices (one hunded years 325-424 CE)
Theoretical Evidence via mainstream (the null) hypothesis1111
Actual Evidence discovered121

The Chi-square statistic is 18.1818. The P value is off the scale. This result is significant at p < 0.001.


Suppose we allow that the 12 codices from the NHL are one item instead of 12 items.

Ante-Nicene Codices (two hunded years 125-324 CE)Post-Nicene Codices (one hunded years 325-424 CE) with NHL(x12) counting as one codex
Theoretical Evidence via mainstream (the null) hypothesis44
Actual Evidence discovered17

The Chi-square statistic is 4.5. The P value is << 0.05 which is still significant.

I have calculated these values for the "Text view" and the "Pages View" (based on the detailed evidence listed above) however the results are even worse.


DISCLAIMER

I have not worked with this stats stuff in a long time so I could have made some mistakes. I am not sure what you use to do the calculations, but I have attempted to use an excel spreadsheet, and my formulaes may not be correct. If you had the time to double check these calculations in the first instance I'd be appreciative of knowing there's something wrong with the formulaes I am using.


SUMMARY

Assuming the calculations are correct, there appears to be a significant statistical anomaly when the physical data is analysed using the assumptions made. Alternatively, for one reason or another the [wiki]Pearson%27s_chi-squared_test[/wiki] may not be appropriate. If it is appropriate, the first item to consider is obviously the HEADS/TAILS assumption that it is equally likely to find an ante-nicene codex as it is to find a post-nicene codex. There may be a range of valid explanations whereby this prior probability should be diminished for the 200 years prior to 325 to a much smaller amount. I have offered some possible reasons (and counter-reasons) above.

Thankyou PK for the exercise of brushing the cobwebs away from using this stuff. I think I may have mentioned somewhere that I last did this stuff formally in the very early 70's .... more than 40 years back down the track. I may yet be using an invalid formula to calculate the chi-square stat. I trust you will be able to check this pretty quickly.




LC
A "cobbler of fables" [Augustine]; "Leucius is the disciple of the devil" [Decretum Gelasianum]; and his books "should be utterly swept away and burned" [Pope Leo I]; they are the "source and mother of all heresy" [Photius]
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Re: On dating the Gnostic literature after 325 CE

Post by Peter Kirby »

You've indicated a count of "Ante-Nicene Codices" of 1 and a count of "Post-Nicene Codices" of 21.

However, several manuscripts have been classified incorrectly as non-codices.

II - P. Oxy 4009 (codex, Gospel of Peter)
beg. III - P. Ryl. 3.463 (codex, Gospel of Mary)
early III - P. Oxy. 1 (codex, Gospel of Thomas)
III - P. Schoyen 21 (codex, Acts of Paul and Thecla)
III (IV?) - P. Bodmer 5 (codex, Protevangelium of James)
III (IV?) - P. Bodmer 10 (codex, 3 Corinthians)
III/IV - P. Berl. 13893 (codex, Acts of Paul)
III/IV - Hamburg, Pap.bil. 1 (codex, Acts of Paul)
beg. IV - P. Cair. VH 602 (codex, Protevangelium of James)
early IV - P. Kell. 97 A (codex, Acts of John)
early IV - P. Oxy 849 (codex, Acts of Peter)
early IV - P. Oxy. 1081 (codex, Sophia Jesu Christi)

If these were added to the left-hand column, there would then show 13 "Ante-Nicene Codices" and 21 "Post-Nicene Codices."
Leucius Charinus wrote:
Theoretical Evidence via mainstream (the null) hypothesis1111


Theoretical Evidence via mainstream (the null) hypothesis44

The reason that we use the Chi-square statistic is, basically and at least, (1) to remove the suspicion that we're seeing things that aren't there and can't be justified on the basis of our sample sizes and (2) to see whether our test group differs significant from our control group in at least one significant aspect. Using entirely "theoretical" figures destroys both of those purposes. We have no samples and thus no sample sizes for one of our groups, and we know nothing about the fictional control group to be able to speculate about what is going on here. This is not really a valid exercise.

Information that you've collected from the book The Birth of the Codex is relevant, given the current focus specifically on the codex.

http://www.mountainman.com.au/essenes/C ... to%208.jpg

According to this chart, non-Christian Greek manuscripts of the third century were 11.8% codices, and non-Christian Greek manuscripts of the fourth century were 52.2% codices. If we were somehow to take a random sample of 40 manuscripts from each century, discarding non-codices, we'd predict that we'd draw approximately the following:

Sampling of Greek Writings5 (i.e. 11.8% of 40)21 (i.e. 52.2% of 40)

We could then compare the non-canonical codices against the non-Christian Greek codices (side note: some of your post-Nicene codices are sometimes placed in the fifth century).

Ante-Nicene CodicesPost-Nicene Codices
Non-Christian521
Non-Canonical1321

Chi-square value 2.5339, degress of freedom 1, p-value 0.1114. The groups are not significantly different.

Suppose instead that I were to compare the non-canonical codices to the New Testament codices, the data being drawn from sources including the attached PDF and the lists of New Testament papyri online. My informal count found 51 codices with datings up to "III/IV" and 96 codices with datings up to "V/VI."

Ante-Nicene CodicesPost-Nicene Codices
Non-Christian521
New Testament5196

Chi-square value 2.413, degress of freedom 1, p-value 0.1203. The groups are not significantly different.

Ante-Nicene CodicesPost-Nicene Codices
Non-Canonical1321
New Testament5196

Chi-square value 0.1515, degress of freedom 1, p-value 0.6971. The groups are not significantly different.
Attachments
PapyriFromTheRiseOfChristianityInEgypt.pdf
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Re: On dating the Gnostic literature after 325 CE

Post by Leucius Charinus »

EDITING ...

Leucius Charinus wrote:The test that I am proposing as being appropriate here is the [wiki]Pearson%27s_chi-squared_test[/wiki]
WIKI wrote: Pearson's chi-squared test (χ2) is a statistical test applied to sets of categorical data to evaluate how likely it is
that any observed difference between the sets arose by chance. It is suitable for unpaired data from large samples.

It tests a null hypothesis ...
The null hypothesis being tested is the mainstream theory for the authorship of the non canonical literature.
WIKI wrote: ... stating that the frequency distribution of certain events observed in a sample is consistent with a
particular theoretical distribution.
The null hypothesis predicts a theoretical distribution (of the physical evidence of non canonical literature) which
spans the three century epoch between 125-425 CE. This is consistent with a theory of continuous authorship throughout
this span. Biblical scholars confidently conjecture/hypothesise/theorise that the authorship of many of the texts in
NHL (and many other non canoncial texts) span a period from the 2nd century to the 4th century. Any standard list of
non canonical texts sorted by date of proposed authorship will reveal texts being authored throughout these three
centuries.

It is therefore reasonable IMO - as a first approximation - to divide the epoch into equal segments, and to expect a
physical distribution of the evidence to be more of less divided equally between the segments.

WIKI wrote:The events considered must be mutually exclusive and have total probability 1.
We are not interested in the events after 425 CE since they do not relate to earliest authorship dates of the non
canonical literature. It is generally accepted most of the texts were authored by this date anyway, with only a few
exceptions. These exceptions can be treated as irrelevant for the study. Similarly some may supposed that some non
canonical texts were authored prior to 125 CE (e..g. gThomas). These may be included in the first epoch (125-224 CE).

As a result of this arrangement, the total probability examined is 1.


Peter Kirby wrote:You've indicated a count of "Ante-Nicene Codices" of 1 and a count of "Post-Nicene Codices" of 21.
The reason that I indicated a count of "Ante-Nicene Codices" of 1 (i.e. C14 gJudas) is because I wanted to count actual
codices (and not papyri fragments of codex pages/leaves) in the "count of codices". The object is to total the
discovered evidence as it has been found. The question is ... how is the evidence to be actually totalled? This is
question that needs to be addressed, discussed and agreed upon to a certain extent. Obviously there are many ways to
introduce methods of measurement to this exercise.

I have approached this question by identifying at least three separate levels at which to collect sub-totals:

1) SUMMARY LEVEL: This is a count of the number of complete or almost complete physical codices that have been
discovered. This register on its own is itself a rough gauge. Here the (7 or so) papyri fragments are momentarily set
aside. This is a count only of physical books discovered. The counting of papyri fragments occurs at the following two
levels.

2) INTERMEDIATE LEVEL: This is a count of the number of identifiable (non canonical) texts (stories, e.g gThomas) which
have been discovered. At this register, a small papyri fragment of an identifiable non canonical text will count as a
discovered text. Also at this register, if a codex contains five separate non canonical texts, then this will
contribute a count of 5 towards the discovered texts.

3) DETAIL LEVEL: This is a count of the number of actual surviving physical leaves or pages. A fragment of a leaf
(whether codex or roll) will count as a full page. A five page manuscript will count as five pages, and a 100 page
codex will count as 100 pages.


You may also have other valid ideas about how to actually measure and tally the evidence that has been discovered. If so
I am interested. But in the meantime I am working with the assumption that how I have proposed to tally the evidence
under the above three levels is fair and objective.


However, several manuscripts have been classified incorrectly as non-codices.

II - P. Oxy 4009 (codex, Gospel of Peter)
beg. III - P. Ryl. 3.463 (codex, Gospel of Mary)
early III - P. Oxy. 1 (codex, Gospel of Thomas)
III - P. Schoyen 21 (codex, Acts of Paul and Thecla)

III (IV?) - P. Bodmer 5 (codex, Protevangelium of James)
III (IV?) - P. Bodmer 10 (codex, 3 Corinthians)
III/IV - P. Berl. 13893 (codex, Acts of Paul)
III/IV - Hamburg, Pap.bil. 1 (codex, Acts of Paul)
beg. IV - P. Cair. VH 602 (codex, Protevangelium of James)
early IV - P. Kell. 97 A (codex, Acts of John)
early IV - P. Oxy 849 (codex, Acts of Peter)
early IV - P. Oxy. 1081 (codex, Sophia Jesu Christi)

If these were added to the left-hand column, there would then show 13 "Ante-Nicene Codices" and 21 "Post-Nicene Codices."
You have indicated here that you are happy to treat both a 100 page codex and a small papyri fragment as equivalent
units of the discovered evidence, but I dont think that is fair or objective enough. You may disagree.

There is only one codex AFAIK that may be dated prior to 325 CE and that is Codex Tchacos via the [provisional] C14
analysis (220-340 CE). The rest of the codices discovered (which I listed above) are accepted to manufactured in the
4th century after 325 CE.

There is of course no argument that almost all Christian texts found in Egypt are in codex, not roll form. This survey
however is simply trying to tally the discovered evidence. If a papyri fragment in codex form is counted as one codex in
the tally, then how are we going to count a 100 page codex? This is a problem which I think I have addressed above. We
create separate tallies for codices and pages (or their fragments), with an intermediate tally for identified texts.

Peter Kirby wrote:
Leucius Charinus wrote:
Theoretical Evidence via mainstream (the null) hypothesis1111


Theoretical Evidence via mainstream (the null) hypothesis44

The reason that we use the Chi-square statistic is, basically and at least, (1) to remove the suspicion that we're
seeing things that aren't there and can't be justified on the basis of our sample sizes
Agreed.
... and (2) to see whether our test group differs significant from our control group in at least one significant
aspect. Using entirely "theoretical" figures destroys both of those purposes. We have no samples and thus no
sample sizes for one of our groups, and we know nothing about the fictional control group to be able to speculate
about what is going on here. This is not really a valid exercise.
The WIKI page [wiki]Pearson's_chi-squared_test[/wiki] does not mention "control groups". One of the key uses of this
test is to test a null hypothesis stating that the frequency distribution of certain events observed in a sample is
consistent with a particular theoretical distribution.

In this case the null hypothesis is the mainstream theory of non canonical text authorship and codex manufacturing. The
frequency distribution of the discovered evidence (at various tally levels) is supposed to be consistent with what the
mainstream theory expects.



Ante-Nicene "Pages" (two hunded years 125-324 CE)Post-Nicene "pages" (one hunded years 325-424 CE)
Theoretical Evidence via mainstream (the null) hypothesis800800
Actual Evidence discovered701530

The Chi-square statistic is 1332.25. The P value is off the scale.


Supposing I were to consider a number of valid reasons why would not expect to find the physical evidence of the
authorship and manufacture on non canonical books in the two centuries leading up to 325 CE. Instead of assuming that it
was just as likely to find as many such pages in the century after 325 CE as it was in the two centuries immediately
prior to it, it will be assumed that it is 15 times less likely. That is, supposing there is a reason that for every 15 pages
discovered in the century after 325 CE, we could only expect to find only one page in the two centuries immediately prior.



Ante-Nicene "Pages" (two hunded years 125-324 CE)Post-Nicene "pages" (one hunded years 325-424 CE)
Theoretical Evidence via mainstream (the null) hypothesis1001500
Actual Evidence discovered701530

The Chi-square statistic is 9.6. The P value is 0.001945774.


SUMMARY

Using these tallies of the count of physical leaves before and after 325 CE, unless there is a good reason (and there may be a good and valid reason [1]) to assume post Nicene "pages" have at least more than 17 times the likelihood of survival that ante Nicene pages (of NC texts) then this test will return a significant result < 0.05.

I maintain that this is a valid statistical test on the null (mainstream) hypothesis.




[1] Perhaps one good and valid reason is that only the Coptic (used from the mid 3rd century onwards) survived in any bulk, and that all of the Greek originals (fragments excepted) were destroyed. Not left to perish, but purposefully destroyed. If the Greek was left to perish, or buried as "Burial Goods" like many of the Coptic codices, then more of it should have been discovered. Orthodox Christians were unlikely to have destroyed too many, certainly not all, of the Greek non canonical codices prior to Nicaea. OTOH immediately after Nicaea there is literary evidence to suggest (officially) prohibited [Greek] books were to be destroyed.




LC
A "cobbler of fables" [Augustine]; "Leucius is the disciple of the devil" [Decretum Gelasianum]; and his books "should be utterly swept away and burned" [Pope Leo I]; they are the "source and mother of all heresy" [Photius]
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