After the discussion in the last post about the authorship of the Gospels, I've created a spreadsheet model, in Open Office format, to illustrate the probability calculus for whether the Gospels were written by Matthew, Mark, Luke, and John. This post probably won't make much sense if you haven't read the comments on the previous one; if you're not a mathy person just skip it. The spreadsheet file is at the bottom of this post.
It's just a model: I don't claim to have incorporated every possible effect that could be important. I'm just trying to illustrate how the short chains of oral transmission to Papias and Irenaeus can provide significant information. This is a dynamic spreadsheet, so if you change one box the rest of the numbers will change accordingly. The idea is that if you don't accept my numbers, you can change it yourself to see what happens, rather than just griping at me that it should be different.
I've used the following hypothetical likelihoods for each Gospel/early writer to be pseudonymous instead of genuine, from the perspective of a person who isn't sure whether or not to believe Christianity:
This is based on the names attached to the documents, as well as internal evidence and the fact that they were received as genuine by the Church, but not yet taking into account the testimony of Papias through John (concerning Matthew and Mark), as quoted by Eusebius, and Irenaeus disciple of Polycarp disciple of John (for all 4 gospels).
The odds for Matthew are higher than the others because that is the only one where there were significant arguments for pseudonymity, instead of just arguments that it could have happened. For me, the actual names written on the documents, and their acceptance by the church, are better evidence than any of the evidence against, hence the numbers above. Papias is more likely to be pseudonymous since other than the few fragments preserved by Eusebius, we have to rely on the judgement of the early church about this.
I haven't taken into account possible lack of independence between the pseudonymity of the 4 gospels. Although the Gospels do incorporate text from each other, they were almost certainly written by different individuals, so they aren't strongly dependent. Nevertheless, there's some probability dependence here in their later cultural acceptance by the Church. If you want to consider different odds for their dependence, you could put that in by hand in the "scenarios" section at the bottom (where e.g. "13" would mean the probability of the 1st and 3rd Gospels are pseudonymous, relative to the probability of all of them being genuine.)
In accordance with the arguments here, I've assigned odds of .001 per century until the first branch point for each document. I've assumed Eusebius had only one copy of Papias, and I just guessed 4 centuries for Irenaeus since I couldn't figure out the first branch point for him from what I could find online. I'm pessimistically assuming that if an textual corruption has occured, it makes the entire document unreliable. I'm also assuming that any given nongospel writer has a .01 chance of being totally unreliable due to e.g. deliberate deception.
Finally, I'm assuming that for any two people related by an oral testimonial link, there's a .05 chance that a given fact about authorship will be garbled. I'm assuming optimistically there was only one John and that Papias interviewed him directly, but this is balanced by not including any of the numerous other chains back to the apostles which Papias cites. I'm giving the garbling more odds than any other form of error, but unlike the other errors I'm assuming that because this is inadvertent, if one piece of data in the document is garbled, the rest are all unaffected.
(In order to make the math easier when considering multiple gospels, I had to break out the total errors, the garbling errors and the nongarbling errors into three separate rows).
I haven't included the possibility that we might be wrong about the chains of testimony themselves, but you're free to play around with inserting extra people or changing their dependence or such.
I got the following probability odds for the Gospels being pseudonymous:
And for different numbers of gospels being genuine, the probability price you pay is about for one Gospel being pseudonymous, for two, for three, and for all four. This is before considering prior probabilities.
Interdependence between the four Gospels will make these last figures smaller, but I think any reasonable model will have some significant suppression of probability there.
All right then, here it is. Enjoy!
UPDATE: Replaced incorrect "genuine" with "pseudonymous" above.
UPDATE 2: Fixed a bug in the spreadsheet. See the comments section below. This doesn't change things much for the numbers I provided, but might affect things if you change the input assumptions. See oldspreadsheet to look at the old version.