Let Us Calculate

In this post I am going to outline what I consider the most relevant evidence for and against Christianity, in the form of a Bayesian probability analysis.  Now, just to be clear in advance, I'm not even going to take seriously the Jesus-myth crank theory that Jesus never existed.  No reputable scholar, no matter how hostile to Christianity, believes this, and one can only believe it by completely discounting almost all of the available evidence, including from nonbiblical sources.  And even the most skeptical or "liberal" biblical critics usually assume that at least some parts of the Gospels go back to real information about Jesus.  So I'm going to assume that Jesus existed, and that we know at least some minimal facts about him and his immediate followers.

Consider the proposition Christianity*, defined as something roughly like the following: "There exists one benevolent God who came to Earth in the form of a particular unique human being, died, came back to life again in resurrected form, and then departed again".  Note that: 1) Christianity* differs from Christianity in that it does not indicate which particular human being this is, whereas of course Christianity says that Jesus is that person;  2) We can, if we choose, add additional Christian doctrines to the proposition Christianity*, but I am going to argue that this doesn't matter very much for the end probability result, so long as the additional doctrines are supported by empirical testimony of the kind that I described last post, and we are willing to accept some rate of error in the correctness of our theological interpretations.  3) Although the conditional

P(\mathrm{Christianity}\,|\mathrm{{Christianity\!\ast} + facts\,about\,history})

is high, because Christianity is as far as I know the only historically credible example of Christianity*, nevertheless the prior probabilities of Christianity and Christianity* are quite different since there's lots of people, and Jesus is only one of them.

Let us now consider the prior probability of Christianity.  The prior probability (A) consists of a product of 3 terms which come from the following kinds of improbabilities in Christianity:

_____A1) Implausibility due to the fact that Christianity* makes a series of several specific claims, whereas prior probability of various hypotheses needs to be distributed amongst all possible kinds of religious claims.  (The size of this factor depends on how many doctrines we include in Christianity*, but I've been arguing in the comments to this thread that the large factor in A1 will be exactly cancelled in cases involving testimony.)
_____A2) Whatever implausibility is inherent in Christianity* due to the fact that it postulates new entities, which behave in weird ways.
_____A3) Implausibility due to the fact that if Christianity* is true, there are billions of people who might have been the special person, and Jesus is only one such person.

Next we have to consider whatever posterior arguments there may be for, or against, generic Theism (with a benevolent deity).  In my opinion there's only one really good philosophical argument against, namely the Argument from Evil:

_____B) One would expect a universe with a benevolent God to have little or no evil in it.  (If we define Christianity as including the existence of evil, this factor would be incorporated into the prior probabilities instead, but that won't make any difference.)

There's several possible arguments for Theism, some good and some bad, but I think the best one is the Argument from Design, which can be made surprisingly precise in the form of the Fine-Tuning Argument.  Eventually I'd like to talk about this in much more detail, but a short summary is here:

_____C) Since, in our current understanding of physics, the overwhelming majority of possible configurations of the constants of nature do not permit life, life is much more probable if those laws were selected by a deity interested in producing life.  The most plausible naturalistic explanations have to propose additional, ad hoc entities, e.g. a gazillion extra universes with different constants, or unknown physical mechanisms with surprising properties.

Next we turn to the arguments for Christianity specifically.  One could consider arguments from religious experiences, but to avoid wallowing in subjectivity I'll focus on miracle claims, particularly the historical testimony to the Resurrection.

Now remember from the Prosecutor's Fallacy how even rare events can be expected to occur so long as one draws from a large enough pool of candidates.  In the story I told, the prosecutor needs both the DNA evidence (something strongly correlated with guilt when taken on an individual basis) and also independent circumstantial evidence that the person who matched is among a small group of people more likely to have committed the crime.  We discussed how this circumstantial evidence may be quite weak, in the sense that it only suggests the possibility of guilt without in any way proving it.  Nevertheless, it can make the critical difference when combined with stronger evidence.

This is important because factor (A3) is large, and we need to be able to cancel it out by showing that Jesus is more likely to be special than other people.  This evidence has to be independent of the Resurrection claim, so it's best to look at features of Jesus' earthly life prior to that time.  Exactly how one goes about this will depend on which fraction of the New Testament one accepts, but even from a "liberal" perspective I think it's extremely probable that at least some of the following facts are true:

  • Jesus was Jewish (Note here that P(\mathrm{Judaism} |\mathrm{{Christianity\!\ast} + facts\,about\,B.\!C.\,history}) is moderate to high since Judaism is one of the few successful monotheistic religions, and if Judaism is true the Messiah should be Jewish—indeed, descended from King David, but that is more difficult to prove.)
  • During his lifetime Jesus claimed to be, either the Son of God in a unique sense, or the Messiah, or at the very least he made some highly unusual claims about himself which were understood by some as implying such things.
  • Jesus was one of the most provocative and insightful moral teachers who ever lived.  (Of course, if Jesus is the Incarnation of a benevolent God, we'd expect him to be the most insightful moral teacher.  But this is difficult to prove because there are disagreements about morality.  Nevertheless, judging based on the fact that his teaching is widely regarded as great even by saintly people from different religious traditions, it's fair to say he at least makes the top 100 list.)  Note also that even the "liberal" interpretation of New Testament scholarship accepts many of the sayings in the Gospels as really going back to Jesus, and even if some of the insightful sayings were made up by his disciples, those disciples would have had to become unusually morally insightful somehow in order to do that.
  • At least some people prior to Jesus' death believed he had performed miracles involving healings, exorcisms, and/or power over Nature.  Otherwise it's difficult to explain the enormous number of realistic-seeming scenes in the Gospels where the crowds are pushing and shoving each other in order to try to get healed, and Jesus has to continually keep escaping from them and hiding in various places to get any rest at all.  Note also that the event where Jesus miraculously feeds 5,000 people is contained in all 4 gospels.

The following data point would also suffice for circumstantial evidence, for those willing to accept more details from the Gospels:

  • Some facts about Jesus' life could reasonably be interpreted as fulfilling some of the prophecies found in the Hebrew Scriptures, to a greater degree than expected by chance.  (Note that this counts as circumstantial evidence even if the fulfillment of the prophecies is intentional, because even if this is easy to do, very few people bother to do it.  So it still picks out Jesus as special.  But it doesn't count if the fulfillments of prophecy are fictional reading-back into Jesus' life as a result of the Resurrection experience.)

Let's call this set of facts, and any similar ones, as (D).  Regardless of the precise details, the conjunction of these is sufficient to pick out Jesus as one of a very small number of people who were especially likely, prior to their deaths, to be the special person of Christianity*.  Consequently, the factor (D) cancels out the factor (C).

Since there are multiple circumstantial facts in (D), one could conceivably use them all by themselves to mount a cumulative case that Jesus has the features expected of the Messiah.  However, this would be tricky to do, since the 5 factors listed above aren't very independent of each other.

Next we turn to the testimonial evidence for the Resurrection.  Now, no one claims to have seen the actual instant when Jesus came back to life again, but the New Testament does claim that the tomb was found empty (except for angelic messengers) and that hundreds of people witnessed him physically alive afterwards, on several different occasions before the Ascension.

That's going by the New Testament, but what are the core facts that even someone fairly skeptical of the Gospels should accept?  There has to be some plausible origin story for how Christianity came into being: there must be some core set of claims which led to the later formation of the New Testament.

It would be extremely unparsimonious to postulate the existence of a completely different form of Christianity, of which we amazingly have no records, which transmuted into a completely different thing in just a few decades.  And besides, even the more skeptical biblical critics say that we have genuine letters of St. Paul dating from the late 40's or 50's (recall that the Crucifixion took place around 30), which make reference to doctrines and events taking place many years earlier.  Using just Paul's letters which are agreed to be authentic, together with some not-particularly-controversial chronological details from the Acts of the Apostles, one can date Paul's conversion to just a few years after the Crucifixion, sometime in the 30's.

Furthermore, while Paul might have been able to foist new doctrines off onto Gentile converts to Christianity, it's not very likely he would be able to seize control over the leaders of a previously existing religious group, which he had formerly persecuted, and convince them not only to accept the Resurrection, but also to claim to be witnesses of it.  As Paul says here:

For what I received I passed on to you as of first importance: that Christ died for our sins according to the Scriptures, that he was buried, that he was raised on the third day according to the Scriptures, and that he appeared to Peter, and then to the Twelve.  After that, he appeared to more than five hundred of the brothers at the same time, most of whom are still living, though some have fallen asleep.  Then he appeared to James, then to all the apostles, and last of all he appeared to me also, as to one abnormally born.

For I am the least of the apostles and do not even deserve to be called an apostle, because I persecuted the church of God.  But by the grace of God I am what I am, and his grace to me was not without effect. No, I worked harder than all of them—yet not I, but the grace of God that was with me.  Whether, then, it was I or they, this is what we preach, and this is what you believed.  (1 Cor 15:3-11)

Unless one thinks that Paul made up all of these people, it's clear from this list that the Christian belief in the Resurrection predated Paul's conversion.  So, using Paul's letters and the extremely broad details common to all four gospels (allowing for distortion as time passes), I think one should accept the following Resurrection facts (E) as nearly certain, even from a fairly "liberal" biblical criticism perspective:

  • Jesus had an inner circle of twelve disciples, who (except for Judas) later were important leaders in the early church, especially St. Peter, St. James, and St. John.
  • Jesus really died on the Cross.  (The theory that he swooned and then recovered is monstrously improbable.  Not only does it require Jesus to be sufficiently "dead-seeming" that the Romans and his friends didn't realize it, he then has to somehow regain enough health to persuade people he's not only alive but triumphant over death.  It doesn't explain Paul's conversion, and it's grossly inconsistent with any of the Gospel narratives.  Since the skeptic is still going to have to explain these things with some independent hypotheses, it's rather a stretch to have a medical improbability on top of all that.)

Furthermore, within a few months or years, the following were all true:

  • At least some Christians believed that the tomb was found empty after the Resurrection.
  • At least some female disciples believed (or else claimed to believe) that they were the first people to see Jesus, after his Resurrection.  (Since women were not considered reliable witnesses in the 1st century, male disciples would be unlikely to invent this detail out of whole cloth.  It must go back to some original historical fact.)
  • Some group of male disciples, including at the very least the Twelve Apostles, believed (or else claimed) that Jesus had appeared to Peter, and to the whole group on more that one occasion, after his death.  (This is only going with the groups mentioned in both the Gospels and Paul.  Paul's list includes St. James, the brother of Jesus, and more than 500 other witnesses, while the Gospels include two additional disciples on the road to Emmeus.)
  • Furthermore, either (a) many of these male disciples were originally inclined to be skeptical, or (b) the early Christians liked to invent stories portraying the faith of their most cherished leaders as weak.  Furthermore, they knew that persisting in this testimony was likely to lead to their deaths, which would have been obvious from (i) the fate of Jesus, (ii) the fact that their testimony was inherently uncomplimentary to the Jews and the Romans, and (iii) Paul himself (see below).
  • We have Paul's testimony against himself that before his conversion he "persecuted the church of God and tried to destroy it" (Gal. 1:13).  Then, as a result of an experience which he interpreted as a Resurrection Appearance of Jesus speaking to him, he become a Christian and immediately began to preach the new faith.  (If one additionally accepts the accounts in Acts 9, this experience was accompanied by phenomena which affected his travelling companions, and resulted in his temporary blindness until 3 days later, when someone named Ananias came to see him as a result of a vision of his own, after which "something like scales" fell from his eyes.)

This last fact is staggeringly implausible from a naturalistic point of view, even ignoring the additional details from Acts.  This can be seen by imagining yourself in the situation beforehand and then asking how surprised you'd be if it happened.  It's a lot like Hitler converting to Judaism after being struck by lightening, and then later being accepted into the Jewish community and becoming a highly respected rabbi.  That's a 1-in-a-million event right there, folks.  If Christianity isn't right, it's still true that they were fantastically lucky in the case of Paul, at a very critical moment in their history.

If we were to accept even one of the additional corroborating circumstances in Acts, the event becomes even harder to explain naturalistically.  Yet in general the book of Acts (which records 3 different versions of the conversion of Paul), even if it was not written by St. Luke, is filled with so much realistic detail and mundane trivia that it's impossible for me to believe it doesn't incorporate at least some memoirs which go back to the time of Paul himself (especially in the chapters which use the "we" pronoun).

Finally, some of the Apostles were not only willing to die for their testimony, they did die for it.  Christian tradition says that all of the Twelve except for John were martyred, but the later lives of many of the apostles are known only through fanciful legends.  However, at least 4 cases are fairly certain:

  • Peter, Paul, the Apostle James (brother of John), and the other James (brother of Christ) were all martyred.  The Apostle James was killed by Herod in the 40's, as described in the book of Acts (hard to imagine why they'd make this up).  That Peter and Paul were martyred in Rome is described in several early post-New Testament Sources, and the martyrdom of the other James in Jerusalem is described by the Jewish historian Josephus.

From Paul's uncontested letters we can also know this:

  • Paul believed (or at least claimed) that he and certain other Christians sometimes had the power to do miracles, and that these miracles had been witnessed by the churches he writes to.  (Additionally, the book of Acts records several miracles by Peter and Paul).

Finally, if Christianity is true, one would expect that God would continue to sometimes perform miracles even up to the present day.  And there is indeed evidence for this.  But it would take a whole 'nother post to go into any details, so I'll just reserve a parking space for this by calling it (F).

About Aron Wall

I am a Lecturer in Theoretical Physics at the University of Cambridge. Before that, I read Great Books at St. John's College (Santa Fe), got my physics Ph.D. from U Maryland, and did my postdocs at UC Santa Barbara, the Institute for Advanced Study in Princeton, and Stanford. The views expressed on this blog are my own, and should not be attributed to any of these fine institutions.
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5 Responses to Let Us Calculate

  1. g says:

    More comments to come later, probably -- at the moment I'm away from home and using suboptimal equipment for reading and writing -- but there seems to me to be an obvious huge omission here.

    You consider the prior probability of Christianity, evidence for and against theism generally, and evidence for Christianity specifically -- but not evidence against Christianity specifically.

    Many people who aren't Christians would say there's quite a lot of that. They might say that the Bible ought to be more impressive than it is, or that Christians ought to be morally better than they are, or that there ought to be more evidence of contemporary miracles than there is, or that various details of Christian doctrine don't make enough sense, or whatever.

    Also: There's more than one argument from evil, and some don't involve claiming that there should be "little or no evil" in the world.

  2. Aron Wall says:

    I didn't claim that the arguments were a complete list: just the highlights. However, mostly I didn't include any other arguments against Christianity either because I think they're already factored in, or because I don't think they rate very highly. I don't think I've left out anything on the anti-Christian side worth many orders of magnitude, anyway.

    If the statement about the "impressiveness" of the Bible is meant as an allusion to the apparent moral atrocities in the Old Testament, this is probably best taken in conjunction with (B), the Argument from Evil---it's certainly not independent of the existence of natural evils in the world. I agree though that my summary of the Argument from Evil is inadequate and should have read more like "would not have the kinds of evils which are observed, or else which are implied to exist by Christianity". I meant for this factor to include all the different permutations of the Argument from Evil.

    If it's something else about the Bible (like an argument from supposed contradictions) then I doubt I'll find the argument impressive since most "contradictions" come from reading over-literalistically, and I think the Bible does an extremely good job of doing what I think God intended it to do for Christians: convicting our consciences, educating our minds, equipping us to do good works, and comforting us in distress.

    If Christian doctrine doesn't make much sense, that's already factored into (A2), "new entities which behave in weird ways".

    Modern day miracles are already factored into (F); you're right that (F) could turn out to count against Christianity if there's significantly less evidence for miracles than one would expect, but in fact I think there's positive evidence here: in other words not only is P(F | Christianity) fairly high, but P(F | Naturalism) is quite low.

    Regarding the morality of Christians, let me be brutally honest here. As far as I can tell from my own personal experience rather than what I've heard from others, on average Christians are in fact significantly nicer and more moral than non-Christians. The existence of some religious hypocrites doesn't really count against Christianity seeing as it predicts them (see: practically anything Jesus says about ethics in the Gospels, plus the fact that he was condemned to death by the religious leaders of God's chosen people). And the most morally impressive people I know are nearly all Christians, although one is a convert to Judaism from Catholicism.

    I may well have been lucky in the churches I've attended, but I think a lot of the disdain for Christians in popular culture is due to distaste for people with intense moral opinions. Anyway, if we open the door to things this subjective on the anti-Christian side, to be fair one really has to include pro-Christian arguments from religious experience as well. We all have many moral deficiencies, but most of us at least have a sense that God is turning us into better people than we otherwise would be.

  3. g says:

    (Again, more will probably follow when I've found more time. For now, just continuing the existing discussion.)

    I wasn't intending to offer any specific arguments; just to point out that there's a big general category of evidence that you'd missed out. But, just to give a clearer indication of the kind of thing I had in mind:

    Unimpressiveness of the Bible: I was thinking of (1) failed predictive prophecies, (2) moral atrocities apparently endorsed by God, (3) inaccurate factual claims, (4) internal inconsistencies, and (5) a shortage of really impressive positive things to offset (1-4). The point, of course, isn't the Bible is an exceptionally awful book in these respects when compared with other roughly contemporary documents, but that if Christianity -- especially evangelical Christianity, but this applies in slightly different ways to lots of other kinds -- is correct then it ought to be exceptionally, supernaturally good and skeptics would argue that it doesn't seem to be nearly good enough for "divinely inspired" to beat out "ordinary human documents".

    I don't think moral atrocities in the Bible belong with the argument from evil. Here's one way to see that they don't: Suppose for the sake of argument that none of those atrocities really happened. Then their endorsement by the Christian scriptures would still be evidence against Christianity (or at least look like evidence against Christianity) despite the absence of any actual evils in the world corresponding to them. The argument here is more like "If Christianity is right then the Bible should be the sort of thing that a god with the attributes claimed by Christianity might have caused to be written; a document endorsing genocide is not the sort of thing a good god would have caused to be written; the Bible endorses genocide; so much the worse for Christianity", rather than "If Christianity is right then there shouldn't be genocides; the Bible reports genocides; so much the worse for Christianity" which I agree would be an argument from evil.

    I suppose you're right that not-making-sense is largely contained in your A2. (I was focusing on the "new entities" rather than the "weird ways" bit.) In that case, I think A2 could easily contribute somewhat more improbability than the 40dB you allow. Perhaps you're right that any single problem of "philosophical" type shouldn't be allowed to count for more than about 40dB, but arguably Christianity has several such problems. (It depends, as usual, on what you take "Christianity" to mean. But note that if some weak-seeming simplified "Christianity*" really entails all the weirdness of full-blown Christianity, then that weirdness has to count against Christianity* too.)

    I hadn't realised that you were intending to allow (F) to include every case of unanswered prayer, alleged miracles that turned out to be fake, obvious opportunities for intervention where God appears not to have intervened, etc. In which case: yes, I agree, that is the right place to put those things (though some might be better filed under "argument from evil"); but then you can't blithely go on to say, as you do elsewhere, that (F) obviously goes under "evidence for Christianity" and that you don't need to account for the associated probabilities because it's "icing on the cake". It might point in the wrong direction.

    The existence of religious hypocrites could count against Christianity despite being an explicit prediction (if Christianity implicitly predicted that there shouldn't be any, and if that were a more robust prediction despite being implicit, on account of following from more fundamental doctrines or being based on more solidly established textual evidence or something). As it happens, though, I don't think the mere existence of religious hypocrites is much evidence of anything. But "the plural of anecdote is not data", and the fact -- I'm assuming for the sake of argument that it is one, as it very well may be -- that among your personal acquaintances the Christians are nicer isn't really relevant to the point I was gesturing towards. Because the argument I had in mind goes like this. If Christianity is right, then Christians should not merely be a bit nicer/better than (say) atheists or Taoists or Sikhs; they should be spectacularly nicer/better. Because (1) Christians are supposed to have actually living within them the god who is the source of all moral goodness and value; (2) they pray to an allegedly supremely good and powerful being, repeatedly, that he will purify their hearts and cleanse them from sin and lead them into righteousness, and this seems like an absolutely ideal case of the sort of prayer that God ought to be willing and able to answer positively if he has any influence at all over what happens in this world -- because answering positively wouldn't violate anyone's free will (the people in question are begging him to do it), doesn't require any violation of the regular operation of the universe beyond what it takes to nudge human thoughts and feelings, and pretty much by definition has consequences that are morally good rather than bad. So saying things like "be patient; God hasn't finished with me yet", while it sounds clever and sensible and nice, doesn't (I suggest) actually make any sense on closer inspection; there is no good reason why whatever moral improvements God wants to make to Christians should be slow.

    If Christians are, on balance, a bit better than others, should we consider that evidence for Christianity over, say, naturalist atheism? Probably not much, even if an answer to the argument above is forthcoming; I don't think it would be very surprising on naturalist atheism for there to be some correlations between religious affiliation and character or behaviour. I wouldn't be surprised to find moral differences between rich and poor people, or intelligent and unintelligent people, or English and American people, or [etc.], either.

    I absolutely agree that we should allow for pro-Christian arguments from religious experience. (And pro-other-religions arguments from religious experience, which might end up anti-Christian on balance.) But I think those arguments are terribly, terribly weak.

  4. James says:

    May I save this article to my hard drive?

  5. Aron Wall says:

    Yes you can save any of my posts if you like.

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