Undivided Looking

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:

Matthew: .1
Mark: .01
Luke: .001
John: .03
Papias: .05
Irenaeus: .001
Eusebius: negligible

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:

Matthew: .007
Mark: .0007
Luke: .00017
John: .0036

And for different numbers of gospels being genuine, the probability price you pay is about $10^{-2}$ for one Gospel being pseudonymous, $5 \times 10^{-5}$ for two, $3 \times 10^{-7}$ for three, and $3 \times 10^{-10}$ 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!

tradition.ods

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.

A common criticism of the Gospel accounts is that they are of low historical value because they are anonymous.  This is based on the observation that the authorship is never explicitly mentioned in the main body of the texts of the Gospels attributed to Sts. Matthew, Mark, Luke, or John.

If we use this criterion, then as far as I can tell from briefly sampling my own library and prior reading, the works attributed to these authors also seem to be anonymous:

• Aristotle's Poetics
• Plato's Republic
• Aristophanes' Birds
• Livy's The Early History of Rome
• Tacitus' The Annals of Imperial Rome
• Shakespeare's Hamlet
• Jane Austen's Pride and Prejudice
• Kant's Prolegomena to Any Future Metaphysics
• C.S. Lewis' Mere Christianity

Clearly this criterion is a silly one.  It is customary, both in ancient and modern times, for the authorship of a work to be stated, not in the main body of the text, but in the byline written in the title header, or else on the outside of the book.  The author may choose to begin his book by introducing himself by name to the reader (especially if there is a preface), but this is not the only way that an authorial name can be attached to a book.  It's certainly not the primary method we use today.  We're more likely to find the author's name on the spine or title page than in Chapter One.

According to this apologetics website, author names in the first century were typically written on a tag which was attached to the outside of the scroll, and possibly also in the title at the beginning or end of the document.  I have checked the earliest complete manuscript of the New Testament with my own eyes (via an online scan) and I find that the authors names are clearly stated on the manuscript itself, in a header (e.g. "The Gospel of Mark") which directly proceeds the text itself.  There is no evidence that an earlier form of the Gospels ever circulated which did not contain the author name.  In other words, it is reasonable to assume that the texts were probably written by their stated authors, for roughly the same reason that we assume that the modern-day books on your shelf were probably written by their stated authors.

A better set of definitions is as follows:

1. A document is anonymous if it was first published (i.e. distributed to a broad audience) in a way that did not have the name attached to the book.  Later readers may speculate about who wrote it, and the text may thereby acquire a traditional authorship, but it is still anonymous as originally written.  Otherwise, if there is a stated author:
2. Call it genuine if it was really written by that author;
3. Call it pseudonymous if it was really written by someone else.

Pseudonymous books are not anonymous.  They have a name clearly attached to them, it's just that the name is either fraudulent or fictitious (depending on whether the author intended the reader to be deceived).

A book of the New Testament which actually is anonymous is the Epistle to the Hebrews.  The author was clearly known to the original readers, but in its published form it says nothing about authorship.  Although it is traditionally attributed to St. Paul, the text itself nowhere says this, and there are significant differences in writing style (as I know from personal experience trying to translate it one time—the Greek is difficult and uses classical words; I only got four verses in).  The later history of Hebrews was exactly as you would expect for a truly anonymous document: discussion and disagreement about whether it was really written by Paul or several other proposed candidate authors, and uncertainty about whether or not it should be included in the canon.  From the 4th century on there was  a near consensus that the letter was written by Paul, but this consensus fell apart after the Reformation.  By contrast, the other 13 Pauline epistles have Paul's name clearly stated in the salutation, and are therefore each either genuine or pseudonymous.

Now, it's certainly logically possible that the Gospels were all originally anonymous.  However, achieving this would require a complicated historical process.  It would require believing that for each gospel 1) the gospel was actually written by some person of sufficiently little importance that their name was not recorded, 2) so that the document was published and first circulated without any names attached, 3) then, at some later time, someone speculated that it was really written by the proposed author, 4) belief in this authorship became widespread without any recorded dissent, and 5) all copies of the text which have descendants were modified to include the title.  This has to have happened, not once, but four times.

The Gospel of John is a special case, because the author is mentioned in the text specifically, although not by name, by the title "the disciple whom Jesus loved".  There's been a lot of ink spilled about the identity of this person, but I think much of it is an effort to deny the obvious.  The scenes with this person strongly indicate that he was one of the Twelve Apostles.  Moreover, the statement of authorship in John 21:24, "This [disciple whom Jesus loved] is the disciple who testifies to these things and who wrote them down. We know that his testimony is true," doesn't make much sense if the identity of the apostle was intended to be mysterious.  But it all makes sense if the Gospel was originally circulated with the name "John" attached to it (as it is in every copy we have).  This isn't a watertight proof by any means, but I think it is significant when combined with the other evidence.

So I think the skeptic would do better to say that the Gospels are pseudonymous.  However, they have to pay a probability price for this too.  In addition to bucking the standard presumption of genuine authorship, we also have testimony from other early documents.  This includes the writings of St. Papias (as preserved in Eusebius) and St. Irenaeus explicitly stating the authorship of the Gospels, and even providing details about how they were written (e.g. that Mark was based on St. Peter's preaching).  These two individuals are connected by very short chains to the original generation of apostles.  In fact, both Irenaeus and Papias assert that Papias was a disciple of John, although some scholars try to argue (in my view unconvincingly) that this was a different John than the apostle.  In any case, he seems to have been related by multiple two-step chains to the original apostles, so it would be hard for a pseudonymous work to fool him.  Irenaeus, in turn, was a disciple of St. Polycarp who was a disciple of John, again a very short chain of transmission.

This is excellent evidence for the traditional authorship of the Gospels, although it may be a more efficient investment of "improbability" for the skeptic to dismiss Papias and Iranaeus rather than accept the fact that two of the four Gospels were written by direct eyewitnesses to the events in question.  (The question of whether apostolic authorship is consistent with textual evidence of date and style will have to wait for another post.)

I'm reminded that at one time it was popular for scholars to believe that Homer never really existed.  Somehow, contrary to all modern experiences of authorship, they thought that the Illiad and Odyssey must have precipitated out of the folk-consciousness, without any definite author.  That's pretty crazy.  But let's suppose that there was some definite author, and we simply don't know what his name was.  Seem plausible?  Well, this would require believing that a class of professional singers, specially trained to memorize over 27,000 lines of poetry, were completely unable to remember a single word accurately.

UPDATE: I should clarify that Papias only refers to the circumstances of the authorship of Matthew and Mark; he does not (at least in the fragment preserved by Eusebius) discuss the authorship of the Third and Fourth Gospels.  Irenaeus, on the other hand, bears witness to all four canonical Gospels.

A lot of people think that the New Testament documents must be unreliable because (like all published texts from the ancient world) they are based on translations of copies of copies.  So how can we know whether the original version of the text is the same as what's printed in our Bibles?  Isn't it like a game of telephone, where eventually the message becomes distorted beyond recognition?

This issue came up in the comments section of the previous article, but I think it is important enough to justify its own post, especially since there are interesting connections to evolutionary biology.  (Yes, really!)

First let's consider translations.  All modern translations of the Bible are based entirely on direct translation from the original Greek (for the New Testament) or Hebrew (for the Old Testament).  They are not translations of translations (except insofar as the original texts may already be translations of e.g. Jesus' words from Aramaic into Greek).  Now I won't deny that the translation into English may obscure or distort features of the original language.  As the Italian proverb has it, traduttore, traditore.  However, this problem is mitigated by the fact that there exist lots of different scholarly translations of the Bible with different agendas, and we can check them against each other.  Or, if we are really dedicated, learn ancient Greek or Hebrew ourselves.  So let's set aside the translation issue, and just consider the question of whether the Greek text used by the translators is the same as the original Greek text.

In fact, we can be extremely confident that—with a couple important exceptions that I'll discuss below—the Greek New Testament used to make your Bible is in almost all important details the same as in the orignal text penned by the author (or more likely, dictated to a scribe).  And, in cases where the text isn't certain, we almost always know it isn't certain, and a scholarly edition of the Bible will point out the possible variants in a footnote.

So how do we know this?  The answer is using a field of study called "textual criticism", a procedure which is sufficiently methodical and precise that it almost qualifies as Science rather than History.  The idea is that manuscript copies don't just form a straight line, they form a tree with branches.  That's because a single manuscript may be copied more than one time, and hence have multiple descendents.  The root of the tree is the original manuscript (the autograph), and the branches are the various families of manuscripts which descend from it.

It's a lot like the "Tree of Life" in evolutionary biology.  The different species we see can be classified into a tree structure based on how recently they diverged from their most recent common-ancestor species.  By comparing the DNA of different species, you can identify at what points in history various specific mutations must have arisen (e.g. if the mutation affects chimps and humans but not bonobos, it must have occured after the proto-bonobos split off, but before proto-chimps and proto-humans went their separate ways).

Well, it's the same with manuscripts of the New Testament.  From time to time, copying errors were introduced, either accidentally or on purpose.  These errors propagated into the copies of that manuscript, but unrelated manuscripts were unaffected.  What that means, is that the only way an error could go undetected, is if it occured before the first branch point such that we have surviving manuscripts for both branches.  (Or if there was a giant political conspiracy to change every copy of the New Testament in existence, but there's no evidence of any such thing, and once the Chrisitan church had enough centralized political power, the manuscripts were circulated far too widely for this to be feasible.)

If the error occurs after the first branch point, we'll have different manuscripts which say different things in some place.  It's a separate and harder question to figure out which of these variants was the original.  One could just count them (the "majority text") but this might not work since the branch with the error could have proliferated more widely than the others.  Instead, most scholars try to reconstruct the family tree, and weight more heavily manuscripts which don't seem to be closely related to each other (the "critical text").  However, since these variants usually don't affect major points of Theology, mostly I only care that we can identify the passages where there might be a discrepency—in these cases, pick whichever variant is your favorite, and I'll argue based on that edition of the New Testament.

In the case of the New Testament documents, the first branch point has to have been incredibly early.  That's because the New Testament was extremely popular: we have thousands of different manuscripts before the printing press, some of which are quite early, starting with fragments in the early 2nd century, and going onwards from there.  The runner-up is Homer, who was also well-liked, and therefore we have a few hundred copies.  By comparison, for most other ancient Greek and Roman texts (e.g. Aristotle) we're happy if we can find a few dozen copies from the high medieval ages.  The results of textual criticism are usually regarded as reliable in these cases; how much more so when the available "fossil record" is so much more detailed!

Let's try to quantify the probabilities a bit more closely.  I'm not a professional textual critic, so I'm only going to attempt a rough back-of-the-envolope estimate here.

The only way that an error could sneak in unnoticed is if it occured before the first branch point.  Consider as an example St. Paul's letter to the Galatians (which nearly all scholars think was written by Paul himself).  Let us define the "Publisher" of Galatians as the first person who arranged the text to be copied many times, where "many" means enough times to ensure that at least two copies have surviving descendents.  In the case of a famous person such as Paul, whose writings would be in high demand in many churches, it seems likely sufficient to copy the manuscript a mere 5 or 6 times, and then send them to geographically diverse regions in the Roman empire.  Now, the most likely person to be the Publisher is Paul himself.  However, we cannot rule out that the autograph was copied once or twice, maybe even three times, before the Publication.  (More than this seems unlikely to me; why would people be interested enough in a text to copy it once, several times, but not interested enough to distribute multiple copies?)

To estimate the rate at which copying produces errors, let's consider the Textus Receptus (the line of descent which gave us the King James Version), circa 1500.  Let's suppose this is about 50 copies removed from the first branch point (that's about one copy per 30 years)  There are about 8,000 verses in the New Testament.  Of these, two large sections of the Gospels, the longer ending of Mark (12 verses) and the Woman caught in Adultery in John (12 verses), were probably not in the original manuscripts (although they are early enough that they may well date back to the first century).  In addition to these, Wikipedia lists 100 verses (I counted, that's the exact number) with major discrepencies between the Textus Receptus and the accepted critical text.  There would be a lot more if we counted minor variants, but since most of the "major differences" on this list don't significantly affect interpretation, I'll draw the line here.

Putting all this together, we arrive at a "major error rate" of about .0003 per verse per copy.  If we allow for 3 copies before the first branch point, you still have to pay about $10^{-3}$ in probability ratios for each (noncontiguous) verse of the New Testament you'd like to dynamite.  Since the most important claims in the New Testament are typically found in several places, that's a very inefficient form of skepticism.

So the evidence suggests that a modern critical New Testament is at least about .999 accurate to the original text.  To be clear, this doesn't tell us anything about whether the books were really written by their traditional authors, or whether the original claims are true; that's a subject for other posts.  It does tell us, though, that the original claims were in fact made, by some first century person (whoever wrote the book in question), who was able to pass himself off to some audience, as a person with apostolic credentials.

Last time I wrote a long discussion of what I think is the best evidence for and against Christianity.

When it comes to the historical testimony to the Resurrection, I analyzed the data in terms of a set of minimal facts which I think even a "liberal" biblical critic ought to accept.   By the "liberal" view I mean someone who thinks that the Gospels, Acts, half the letters of Paul, and the general epistles were pretty much all written in the closing decades of the 1st century, by people other than their traditional authors—but that nevertheless the texts are based on identifiable earlier sources which go back to some real, and much earlier, written or oral traditions about Jesus.  (Because some parts of the Gospels are obviously rooted in actual historical events.)

This was a concession, not my actual beliefs: in reality I think this "liberal" view, despite its acceptance by the majority of secular biblical critics, is supported mostly by circular reasoning, and is more than a little reminiscent of the claim that Bacon wrote Shakespeare.  Nevertheless, if a good case can be made for Christianity even under such hostile circumstances, then obviously things would work even better on a more "conservative" view.  For a Bayesian approach based on a somewhat more conservative view of biblical criticism, see this paper by Timothy and Lydia McGrew (they argue for the conservative biblical view, but don't incorporate it into their probability analysis).

I also made no reference to the "inspiration" of the Scriptures by the Holy Spirit; rather I am treating them as ordinary historical documents containing what is claimed to be testimony.  Just to be clear, I do believe that the entire Bible is inspired by the Holy Spirit, and that therefore all of it is an important communication from God to us.  I disagree with fundamentalists in that I don't think the point of the Bible is to communicate scientific facts, or even matters of historical trivia.  For this reason it doesn't bother me that the Gospel accounts contain apparent contradictions: although most of these contradictions would probably be resolvable if we knew the full circumstances, it's not important to me whether if the documents contain mild inaccuracies regarding trivial matters, as all genuine eyewitness testimony does.

So now I have to analyze how I think the probability analysis actually goes.  To summarize the previous post, the main factors weighing against Christianity are:

(A1) prior probability due to specificity of Christian doctrine,
(A2) prior probability due to the weirdness of Christian doctrine,
(A3) prior probability due to Jesus being only one of billions of people.
(B) the Argument from Evil

while some of the factors weighing in favor are:

(C) the Fine-Tuning version of the Argument for Design.
(D) circumstantial facts of Jesus' life prior to his death, making him more likely to be the Messiah
(E) multiple testimonies to the Resurrection,
(F) modern-day miracles.

This is by no means a complete list, but I think it contains most of the highlights.  I've excluded some other arguments for Theism, and various Christian experiences, as less likely to be persuasive to someone coming from a skeptical point of view, even though I rate some of these things as significant.

Each of these factors leads to a shifting of the relative odds of Christianity : Naturalism.  (I'm assuming here that Naturalism is the main rival hypothesis to Christianity for skeptics of a "scientific" sort.)  Since these factors are approximately independent, each of them multiplies the relative odds by some number.  Since we aren't going to agree on precise ratios, I'm going to just estimate how persuasive these are to me, in terms of orders of magnitude (i.e. powers of 10).

I think that (B) and (C) are both good for about 2-4 orders of magnitude and therefore they approximately cancel each other out.  Each of them, despite being grounded in certain observable facts about the universe, is a controversial philosophical argument about metaphysics, and I think it's quite rare for any such argument to establish a conclusion with an error rate less than $10^{-3}$ or $10^{-4}$.  You could say that I'm skeptical about Philosophy, but that's not really fair since shifting the odds by a factor of 1000 should count as a "success" even if this can be easily overwhelmed by more definitive evidence.  For similar reasons I don't think (A2) should be much less than $10^{-4}$.

(A3) and (D) cancel each other out nearly exactly, because if Jesus is in a very small group of people more likely to be the Messiah, then it doesn't matter how many other people there are in the control group.   See the discussion of the prosecutor's fallacy.

(E) contains a factor which cancels out (A1) exactly†.  That's because the Christian testimony is to Christianity specifically, and not to any other religion.  Whereas a made up religion is going to be selected from some large set of possible religions.  See the discussion of the Farmer Jones case in the comments of this thread.

The remaining part of (E) has to do with how plausible the testimony is, leaving aside its specificness.  Now the testimony of a single individual is has to be worth at least 2 orders of magnitude, because most of the time people don't lie about things.

Somewhat counterintuitively, the value of testimony towards implausible claims like miracle reports is actually somewhat greater than this, because people are less likely to make up claims that are implausible.  There are many people who claim to have crossed the street, but only a few people claim to be abducted by UFO's.  The number of people who claim to have seen people physically resurrected is quite low; certainly much less than $10^{-2}$ of the population.  To the extent that this effect exists, (E) also partially cancels (A2).  But this cancellation only works up to a certain point, since nothing says that the rate of false claims has to mirror the true a priori probabilities.  For the small fraction of the population who is willing to make absurd claims, there is no limit to how unlikely their assertions may be.  So some residue of (A2) may remain.

What remains to be considered in (E) is the gross improbability of seeing testimony as strong as this about anything false.  The multiplicity of eyewitnesses, the priority of the women, the apparent unanimity in the pre-existing group of Twelve (minus Judas), and the fact that they were willing to die for their testimony all weigh in its favor.  All of these facts are strongly supported by the historical data.  Their initial skepticism and doubt, mentioned explicitly in almost all of the Gospel accounts, weighs heavily in its favor, so the skeptic is probably better off trying to argue (somewhat less implausibly) that this was made up later to prove a point.  The lack of any reasonable ulterior motive also makes the testimony less likely given Naturalism.

St. Paul presents a special case: since we know he was previously hostile, his testimony is more or less independent of the others.  That in conjunction with the unusual circumstances surrounding his conversion is a factor of $10^{6}$ all by itself; the group testimony of the remaining apostles is at least $10^{8}$, and that's rather generous, since on that hypothesis we'd expect to find about 100 similarly strong examples of false dramatic claims by large groups, in the most recent generation of $10^{10}$ people alone.

Taking everything together I think that the implausibility of a set of testimony looking like (E) given Naturalism is at least $10^{-14}$, and much lower if one takes a more conservative approach towards biblical criticism.  If this is right, then (E) pretty much overwhelms every other factor in play, and (F) is just icing on the cake.  Therefore, with high probability, the Resurrection seems to have really happened.  In other words, (some unspecified version of) Christianity is far more probable than Naturalism is.

[UPDATE 5/30/15.  Much later, a reader St. James wrote in to ask for clarification of the probability values.  My response to him included the following, which I think is worth appending for any clarification value it may have:

Thanks for your comment.  As is clear from the date I'm coming back to this post after a couple years, so I need to reconstruct what I was thinking.  I'm pretty sure I meant for (D) to cancel (A3) specifically, and for (E) to include a piece which cancels (A1), but I think I wrote (A3) by mistake so I've fixed it in the post above.

(D) as I've stated it is rather vague, so it actually contains the potential for more evidence than just that which cancels (A3), for example based on the greatness of Jesus' ethical teaching.  My point was just that, if we have even vauge circumstantial evidence that the pre-Resurrection Jesus was the type of person who might be the Messiah, then the common atheistic objection (at least people have said it to me multiple times) that Christianity is unlikely because Jesus is just one out of many people, and that resurrections are extremely uncommon in a group of $10^{10}$ people, is irrelevant.  So I shouldn't have said (D) exactly cancels, but I should have said it includes a factor which approximately cancels (A3).

Similarly, testimony (E) has the magical property that it can compensate for almost any amount of improbability due merely to specificity, since P(witness tells the truth) and P(witness is lying) both have to be equally specific.  That's why I threw out (A1) and just concentrated on the probability of a group this large having a conspiracy to lie, (or being misled, or being legendary, etc. etc.)

With respect to that probability, I guesstimated 14 orders of magnitude but as you can see from the comments section that was really controversial, and the main point of controversy concerned whether any ancient historical documentation can ever get us probabilities that large.  This is an important question and looking back I'm not at all certain I didn't run the numbers much too "hot"; it's possible the whole thing should be scaled back a bit.  But then I think the philosophical numbers should probably also be diminished proportionally, since I'm fairly certain that History provides better quality evidence than Metaphysics in general.

But I still think the posterior probability that Julius Caeser wasn't really assassinated must be several orders of magnitude tiny (though not as small as I estimated below), and that the apostolic testimony for the Resurrection has a comparable in strength likelihood ratio.  So that without tiny prior probabilities or other substantial arguments against, Christianity winds up being highly probable.

UPDATE 8/30/16: For a more recent take on analysing the probabilities, see my recent post:  Just how certain can we be? ]