Several students and patrons have lately asked me a similar question. Apparently the new fad is for Christians to go around insisting Jesus is so historically unique that he cannot be subsumed under any other reference class by which to estimate any prior odds on any claims made about him being true. In practice, what they then do, is immediately put him in a reference class so unreasonably generic or so unreasonably specific as to guarantee a high odds on whatever claim they want. Of course. That’s how apologetics works. It’s about rationalizing, not testing, beliefs. But it’s important to understand why this approach is formally illogical. Because even non-Christians often resort to the exact same rhetoric when convincing themselves or others of some conclusion. And ignoring evidence and its effects on a conclusion’s probability is stock and trade for both Christian apologetics and pretty much any other tinfoil-hat conspiracy theory.

For example, some conservative pundits have tried claiming a certain rate of dying from a covid-19 infection by basing it on their naive use of global counts of cases and deaths. This is a classic example of a fraudulent reference class, because it literally applies to no one. No one on Earth lives in this “global” risk pool. For example, if you live in Greenland, your risk of catching covid are unusually low; as is your risk of dying from it should you get it. By contrast if you live in the United States, both risks are very much higher—and even more so if, as I write this, you live in, say, the eight states whose risks on both metrics are alarmingly higher than in the other forty two at the moment. But the global risk levels are an average—not just of all fifty states but all two hundred or so nations—and the latter have wildly varying reliability and completeness of record-keeping, and considerably varying conditions and policies. No one lives in that “global average” place. Everyone lives in some particular place. You aren’t in the imaginary kingdom of “Greenlandusa.” You are either in Greenland, or in the U.S.A. (or wherever else). Indeed, you aren’t just “in the U.S.A.,” either. You are, for example, either in Hawaii or in Florida (or whatever state and county); and both risk levels differ considerably from one to the other.

Bayes’ Theorem states that the final odds equal the prior odds times the likelihood ratio; formally: P(h|b.e)/P(~h|b.e) = P(h|b)/P(~h|b) x P(e|h.b)/P(e|~h.b). The terms b and e (“background knowledge” and “evidence”) together sum to include all available human knowledge. If you “leave out” of both b and e something that in fact you do know, you are only going to be producing a fraudulent result (if, that is, you then claim it applies to the real world; hypothetical runs of the equation, where you leave information out to see the effect of doing so, make no such claim). A Bayesian conclusion is only sound and valid if you are being honest with it, and thus actually doing what it instructs: including everything you actually know (leaving nothing out); and actually generating the corresponding dependent probabilities (each probability as it must be given the entire contents of e and b). If you conveniently “forget” the actual data for a resident of Florida, leaving it out or taking it into no account, and instead “pretend” that instead the covid risks for someone in Florida correspond to the “worldwide average,” you are producing a fraudulent conclusion. Because you know those are not the same numbers and you know the person you are talking about is in Florida. You can’t legitimately “ignore” things you know.

The Resurrection of Jesus

This same fact applies to Jesus. For example, suppose you want to test the hypothesis (the “claim”) that Jesus rose from the dead, and you need to determine a credible prior probability that someone rose from the dead. You know billions of people have lived and died and not risen from the dead (that data is in b and you can’t pretend you don’t know it); so you know the base rate of “just anyone” rising from the dead can be no higher than billions to one (and that’s even assuming you are not being picky about what might have caused it; the priors drop the moment you start getting particular about that). It is necessarily the case that a prior probability must be the same across all members of a reference class—because this is the probability prior to considering evidence particular to the member you are looking at. So you cannot treat Jesus any differently than anyone else unless you can produce evidence he does indeed belong to a different reference class with an observably different frequency; and even then the base rate is still what it is observed to be in that reference class. But since there is no reference class of people with a higher base rate of rising from the dead, you’re stuck with “just anyone.” And that’s even assuming you are still not being picky about how Jesus rose from the dead (e.g. you are letting “aliens did it” and “Jesus was a sorcerer,” and so on, an equal chance of being true).

I covered all that in my previous article Crank Bayesianism: William Lane Craig Edition. Here my concern is with what this means regarding a “reference class.” If you are new to the concept, a “reference class” is a set, whose members share enough in common that a “prior” prediction of a frequency can be derived. For example, “people who live in Florida” is a reference class; from it you can ascertain, empirically, a “base rate” (an average frequency) of, say, contracting covid or dying from it, for every member of that set. You can narrow the set when you know more; e.g. “obese people in Florida” have a different base rate, so if you know you are talking about someone who qualifies as “obese” in medical terms (which is far easier to do than colloquial understandings of that word would have it), then you have to use that reference class. Because you can’t legitimately ignore information you have. Nor can you run that trick the other way around. You cannot legitimately claim Jesus is “unique” and therefore belongs to a “different” reference class in which the base rate of resurrections is higher. Because there is none. You have no data in b relating to any such alternative class. You therefore must stick with what you know. And what you know is that the prior probability against a resurrection is even at best billions to one, because that’s the actual highest possible frequency it can have in any known reference class. You can’t substitute hypotheses for facts. A Christian will want to claim, for example, that “surely” the base rate of resurrections among genuinely divine beings is “higher” than for “just anyone.” But we have no data confirming that, nor any non-circular way to establish Jesus belongs to that reference class. It’s just something the Christian is making up. It’s a product of their imagination.

Lest it not be obvious, we actually don’t have any database of “genuinely divine beings” to go to and measure here to see if this hypothesis about them is true. Nor can we “circularly” presume Jesus is even in such a class. Even if we had an empirically verified class of supermen, it is still a straightforward fallacy to argue “Jesus was a superman, because the base rate of real resurrections among supermen is high, and Jesus was claimed to have risen from the dead.” Because that assumes Jesus belongs to the class of supermen, in order to apply that class’s base rate, in order to get the conclusion that Jesus belongs to the class of supermen, in order to get the conclusion that he’s as likely to have really been resurrected as they were. But the question is whether he belongs to that class; and you cannot answer that question by presuming his membership. What we want to know is the base rate of claimed resurrections being actual resurrections, which is much the same as asking what the base rate is of claimed supermen being actual supermen (which we also have no examples of).

We do have several “claimed” ancient supermen; indeed, several even claimed to have risen from the dead (see Dying-and-Rising Gods: It’s Pagan, Guys. Get Over It). When you employ a definition of resurrection that includes only a bodily return to life, all the other members of this resulting reference class are mythical. And take note. Not only are their resurrections mythical, but they themselves are mythical. This does not bode well for Jesus. But for the present point, we cannot use this to determine the maximum reasonable base rate of real resurrections, as if to say that because there are only six or so “resurrected godmen” stories, then the Laplacean probability any of them enjoyed a real resurrection is (s+1)/(n+2) = (0+1)/(6+2) = 1/8 and therefore “one in eight.” Because to do that would again be to ignore information you otherwise have: that we have no confirmed resurrections of anyone, much less of these guys. You have to use the “billions to one against” reference class because you cannot ignore information you have, and you certainly can’t replace information you have with information you don’t have (like an “imagined” base rate of resurrection among “genuine godmen,” or indeed even of the existence of genuine godmen). And as I noted before, if you are testing not just the claim that Jesus rose from the dead—which would include “by technology”—but instead the more specific claim that Jesus rose from the dead by magic (in other words, that it was a miraculous resurrection), we are really talking about an odds against more like trillions to one, not billions.

“But Jesus is unique” does not get you out of this. Everyone is unique in one way or another. That fact is not usable here. I’m unique; yet my risk of contracting and dying from covid remains what it actually is. No amount of insisting “I’m unique” can change that; until you can prove it, which means, with data. “I have a unique hair color” would have no effect on my covid risk. Whereas “I uniquely lack a bloodstream” would indeed entail the base rates of covid infection and death in my geographical region don’t apply to me. But alas, I have a bloodstream. You can’t “speculate” I don’t and then use that to ignore the actual reference classes I belong to. Either way, if you only look at a reference class in which the only member is Jesus, you can extract no information from that class as to the expected frequency of anything about Jesus. You cannot use this as an excuse to then “forget” and thus “ignore” all the reference classes Jesus does belong to that contain quite a lot of members—like “humans.” You can only derive a prior probability from a reference class that contains enough members to empirically ascertain some usable frequency (see my discussion of this point in Kamil Gregor on the Historicity of Jesus and the further linked discussions there; see also McGrath on the Rank-Raglan Mythotype and the same regarding Litwa).

For example, Jesus belongs to a reference class of “people who have died” which contains literally billions of members. That’s a really good reference class: huge content, with very good dispositive data regarding the permanence of death per member. You have to use it. Unless you can find one that (1) is narrower, (2) has a different base rate of the phenomenon in question (in this case, of “actually rising from the dead”), and (3) has enough members to calculate what that different expected frequency is. For resurrection, no such set exists. Therefore, you cannot resort to inventing or imagining one. GIGO: if you derive a conclusion from a mere speculation, the conclusion itself is mere speculation. That’s a far cry from knowledge, and certainly no rational basis for belief. And as I’ll note in a moment, a set with only one or a few members is of little use mathematically, so trying to narrow Jesus down to a set of only one member gains you nothing. It simply leaves you with what you started with: Jesus’s membership in the set of “just any mortal man.”

The Historicity of Jesus

This all flips when we ask instead whether Jesus even existed. Because people placed in history who actually never existed are quite abundantly attested. Unlike resurrections, we actually have lots of confirmed examples of this phenomenon. It’s not miraculous. It’s rather ordinary, really. But now we are in a completely different situation evidentially. The Christian cannot now act like we can “skip over” all the informative reference classes Jesus belongs to in order to insist we should instead treat his prior probability of existing as being identical to “just anyone” claimed to exist. That would be like ignoring someone is in Florida and then insisting their covid risks equal the “global average.” This violates Bayes’ Theorem, by excluding information you actually have, or ignoring its effect on the dependent probabilities composing it. That’s fraudulent. I have already explained this in Okay, So What about the Historicity of Spartacus? (which I include and expand in my book Jesus from Outer Space).

If you know Jesus belongs to a narrower reference class with a different base rate of not existing, then you cannot ignore that knowledge, nor can you pretend it has no effect on the resulting dependent probabilities. Jesus actually belongs to a bunch of myth-heavy reference classes (I list them all here; I thoroughly discuss only four of those in On the Historicity of Jesus, Elements 45 to 48, Chapter 5). In fact, Jesus belongs to more such classes than almost any other person in history, which is quite peculiar; and several of those classes are quite specific or contain a lot of members. Not billions, to be sure. The largest of them contains fourteen other members; many of the others, from two to six (see On the Historicity of Jesus, Elements 44 through 48 in Chapter 5, and Chapter 6). We cannot ignore this information. Nor can we ignore the effects of it on our probabilities. The ideal reference class is one that has enough members to develop a usable frequency from, but that is narrow enough to represent the effect of specific knowledge about what we are discussing. If Jesus belongs to a set containing fourteen other members all of whom are mythical, that substantially increases the prior probability that Jesus is mythical beyond the base rate average for “just anyone.” Jesus being in that set is like you being in Florida: you can’t ignore that, and skip over it, and instead insist we use the “global” risk average for you instead. That is fraudulent.

Sure, we might be able to show that Jesus belongs to a reference class with lots more members. Let’s say we could prove he belonged to the set of all “godkings” and there were dozens of those and only half of all those godkings recorded in history were not historical. We might then want to latch onto that and say the prior probability Jesus existed is therefore “50/50.” But this would be the same fraudulent move. Because we also know Jesus belongs to a narrower reference class in which the prior probability of a member existing is as low as (0+1)/(14+2) = 1 in 16 and cannot reasonably be higher than 1 in 3. If we allow, for example, that four other members of it besides Jesus actually existed (which is well beyond plausibility and thus an error margin a fortiori favoring his historicity), then the base rate becomes (4+1)/(14+2) = 5/16, which is below 1 in 3, but close enough for government work. Indeed, treating it as fully 1 in 3 is actually even more generous to the possibility of his historicity. So by no means can we get the prior probability of Jesus to be higher than that. We cannot ignore this data. And thus we cannot “replace” it with some other data we prefer. Lest it’s not clear what I am saying here, I demonstrate mathematically for Kamil Gregor that the probability the “true” base rate of highly mythologized persons being nevertheless historical, using the Rank-Raglan set as our a proxy, is over 99% certain to be less than 33%. And that is not speculation, but a mathematically unavoidable fact, so you cannot ignore this when running a Bayesian test on the historicity of any member of that set—Jesus or otherwise.

By contrast, we could ignore that if competing applicable base rates overlapped. For example, Jesus belongs to several reference classes with only a few members, which are also considerably more myth-heavy than the “just anybody” set. But because their membership is so scant, the margins of error for any frequency derived from them are considerably high, to the point even of being almost wholly uninformative. For example, Jesus belongs to a reference set including only two other members: Socrates and Aesop; one historical, the other probably not (OHJ, Element 46). Jesus definitely belongs to the set. The attributes he shares with them are so numerous and coherently particular that, indeed, no one else ends up matching them, and the probability of this being true is too low to be a chance accident; in contrast to matching only one other person and only on a litany of incoherent trivia, such as the “Lincoln and Kennedy” coincidences, which is quite probable on chance accident. Not so, the Socrates-Aesop-Jesus set. But that there are only two other members to derive a frequency from in that set leaves us with a large probability of anomalous observation, and therefore a large margin of error.

For example, if the “true” base rate for historicity of that set were 4 in 5, the probability we’d pick two members at random and they’d be 50/50 historical is still 80% x (100-80%) = 0.8(0.2) = 0.16, or 16%. That’s 1 in 6. If we ran that math for “true” rates and summed the results, the margins of error would similarly run from quite low to quite high. If for example we found it left us with a 10% to 90% range (meaning, it’s between those two, but we don’t know where in between), that’s pretty much useless. It is not informative. If we wanted to be, say, 95% certain of our result, we can’t use this one. If we did the math for every possible “true” frequency and calculated the ensuing range of results, such that we could claim a 95% certainty that the “true” frequency was within that range, we’d still end up with an upper margin above 50%. Which is essentially the same conclusion we got with that hypothetical “godkings” set, only (in that hypothetical) we have a set with many more members, so we would be even more certain of a frequency around 50% than we can be from the Socrates-Aesop set. Ergo, we are getting more, and more accurate—and thus more usable—information from that godkings set, and therefore must use it. Because we cannot ignore information we have.

Now, I’ve been using this “godkings” set only hypothetically. I’ve never counted up all the godkings in antiquity and assessed their historicity; but it wouldn’t matter what the result of such an inquiry were, precisely because of the mathematical principles I am elucidating here: a narrower class would simply always override it; just as “is in Florida” overrides “is on Earth” and even “is in the United States.” Yes, the latter two sets contain many more members; but the first set is more informative of someone in Florida. In like fashion, do we have an actual set Jesus belongs to that has more, and more accurate—and thus more usable—information than the Socrates-Aesop set? Yes. The Rank-Raglan set. And it gets us an upper bound no higher than 1 in 3. We therefore cannot pretend that fact does not exist in our background knowledge and choose to use “instead” the “godkings” or “Socrates-Aesop” set and insist the prior is as high as 1 in 2. The Rank-Raglan set is a subset of the godkings set; and contains many times more members than the Socrates-Aesop set, entailing a substantially smaller margin of error for any frequency we derive from it. We therefore have to use it.

So the fact that Jesus belonged to that subset of godkings and not just the generic superset of “just any godking” is information we cannot ignore, nor can we ignore the fact that the Socrates-Aesop set is too small to reliably get any different frequency from (although, notice, it still does not get us a strong base rate favoring historicity, either). Just as we cannot ignore that you are in Florida and use “instead” the covid-risk base rates for the “generic” superset of “all people on Earth.” Neither can we use the subset of “the only two people in Florida who own a Mickey Mantle baseball card,” as that’s too small a set, so we have no usable base rates there. But we know you are in the subset “people in Florida” and we know what the base rates are in that set to a reasonable margin of error. We therefore have to use that set. We only could ignore it if that set were so small or so particular that our margins of error for it included the base rate of the superset, and that superset gave us a narrower margin of error. If we knew nothing about Florida, for example (if we didn’t even know whether it’s a state in the U.S. or a town in Greenland), then the global average would be our most accurate and thus most usable—it would represent what we know. And Bayes’ Theorem is all about telling us what the posterior probability is given what we know (hence, when you know more, that probability can change). But we are not in that condition with respect to Jesus. When we look at godkings who are also Rank-Raglan heroes (or, the hypothetical example I use in On the Historicity of Jesus, “Josephan Christs” who are also Rank-Raglan heroes: “The Alternative Class Objection,” pp. 245-46), we simply end up with a prior probability of historicity no higher than 1 in 3. We cannot pretend we don’t know that.

And So On

People who chafe at this will try to “get around it” in other fraudulent ways. For example, they will try to expand Jesus’s reference class to an even broader and more general one: like, say, all Rank-Raglan-scoring heroes in the whole of history, thus roping in everyone from Darth Vader to Hong Xiuquan, and then try to claim the “new” base rate of historicity this expansion produces should apply to Jesus. No one has ever actually done this; they always apologetically just cherry pick the members they want rather than completing a full count, e.g. disingenuous historicists will ignore Darth Vader and Superman, and include Hong Xiuquan and David Koresh, while disingenuous mythicists will ignore the latter and include the former. But it doesn’t matter, because even a correctly circumscribed set would be inapplicable to Jesus. Because once we have Christian dominance of world culture (even Hong Xiuquan was basing his own creed and legend on it), we are no longer in a relevantly similar causal system; as one can show by looking at how different the base rates are between the pre-Christian-dominance set and the post-Christian-dominance set. Quite simply, Christian dominance changed everything. That was not the cultural and literary environment Christianity arose in or that the Gospels were written in. It’s therefore not an applicable context. This would be just like trying to “skip” the Florida set and jump to an Entire Earth set that’s even more generic, now including decades of previous years, conflating previous coronaviruses with the current one. Wrong context. Not an applicable reference class. Historians cannot substitute anachronism for actual context.

If you want to know the base rate of highly mythologized persons being historical in pre-Christian antiquity, you have to look at the base rate of highly mythologized persons being historical in pre-Christian antiquity. That’s the only applicable context, and thus the only applicable base rate. You would include overlap only with pre-dominance, i.e. the context remains “pre-Christian antiquity” until Christianity becomes so widely known and respected as to begin dominating cultural influence and discourse, which could be no earlier than the 3rd century, and no later than the 4th (e.g. attempts to reconstruct the mythology of the pagan Apollonius of Tyana in parallel with Jesus Christ begin in the 3rd century; whereas, apart from converts, in the 2nd century almost no one even knew what Christianity was, and those who found out, were disgusted with it, not keen to emulate it). Even if one attempted to make an argument to a “causally similar context” with the Middle Ages (observing, perhaps, the similar scale of fabrication and gullibility and poverty of reliable record-keeping, and correspondingly similar effects, e.g. the proliferation of historically dubious Saints), that could not extend to Modernity. Darth Vader, Superman, Hong Xiuquan, David Koresh are all post-1800, an era of radically different scale in respect to critical scholarship, availability and reliability of records, and cultural change (e.g. it marks the rise of fiction replacing mythology as the defining cultural touchstone), precisely things that we should causally expect would reduce the success of any attempt to invent non-existent people (and yet even then such proceeded, albeit more rarely, as we have examples ranging from Ned Ludd to John Frum, as I discuss in On the Historicity of Jesus, cf. index).

In the end, you simply can’t use fraudulent reference classes to “get a different result.” Because doing so can only ever produce a fraudulent result. Bayes’ Theorem entails its probabilities given what is known. Thus if you know something, you have to include it—and that means, you have to include its effects. You therefore can’t use more general reference classes when you have more specific ones (you can’t skip “Florida” and replace it with “Earth”). You cannot use reference classes too small to generate any usable frequency from (like sets with only one or two members), because you will always know some other reference class applies that has more members and thus a more determinable frequency margin (because logically, necessarily, that is always the case: every thing that exists belongs to countless sets of many members). You cannot use contextually or causally irrelevant reference classes; because you know you have contextually or causally relevant reference classes to consult instead, and you know only those are actually applicable. And that’s just that. So if you want to get a different prior probability for Jesus than I did, you have to actually do the work of finding an actual reference class that produces a more applicable and usable base rate of historicity, which does not ignore the effect of other classes he belongs to. Making an excuse to ignore data is just that: an excuse to ignore data. And that’s epistemic fraud.

For more on all these points, see my discussions in Proving History (index, “reference class” and “prior probability”); and as applied to Jesus, in On the Historicity of Jesus (Ch. 6).