Tag: Bayes Theorem

It’s been a long while since I wrote about Jesus mythicism. I hope what I write now will present a slightly different and useful perspective.

I want to address what appears to me to be a widespread misconception about historical knowledge across various social media platforms and in some published works where this question is discussed.

Too often I hear that historians can never be absolutely certain about anything in the past and that they always, of necessity, can only speak of “what probably happened”. (When I speak of historians I have in mind the main body of the historical guild in history departments around the world. I am not talking about biblical scholars and theologians because their methods are very often quite different.)

So let’s begin with Part 1 of the question of probability in historical research. Richard Carrier is widely known for reducing the entire question of Jesus’ existence to a matter of probabilities. I agree with much of Carrier’s approach but I also disagree on some major points. A fundamental point on which I disagree with Carrier is the claim that the most a historian can say about any historical event is that it is “probably” true. Carrier writes:

All claims have a nonzero epistemic probability of being true, no matter how absurd they may be (unless they’re logically impossible or unintelligible), because we can always be wrong about anything. And that entails there is always a nonzero probability that we are wrong, no matter how small that probability is. And therefore there is always a converse of that probability, which is the probability that we are right (or would be right) to believe that claim. This holds even for many claims that are supposedly certain, such as the conclusions of logical or mathematical proofs. For there is always a nonzero probability that there is an error in that proof that we missed. Even if a thousand experts check the proof, there is still a nonzero probability that they all missed the same error. The probability of this is vanishingly small, but still never zero. Likewise, there is always a nonzero probability that we ourselves are mistaken about what those thousand experts concluded. And so on. The only exception would be immediate experiences that at their most basic level are undeniable (e.g., that you see words in front of you at this very moment, or that “Caesar was immortal and Brutus killed him” is logically impossible). But no substantial claim about history can ever be that basic. History is in the past and thus never in our immediate experience. And knowing what logically could or couldn’t have happened is not even close to knowing what did. Therefore, all empirical claims about history, no matter how certain, have a nonzero probability of being false, and no matter how absurd, have a nonzero probability of being true.

(Proving History, 24f – my bolding in all quotations)

A little further on Carrier raises again the exception of a “trivial” event like an “uninterpreted [direct personal] experience”:

The only exceptions I noted are claims about our direct uninterpreted experience (which are not historical facts) and the logically necessary and the logically impossible (which are not empirical facts).¹⁷ Everything else has some epistemic probability of being true or false. 

17. Of course “historical facts” do include direct uninterpreted experience, because all observations of data and of logical and mathematical relations reduce to that, but no fact of history consists solely of that; and “the logically necessary and the logically impossible” are empirical facts in the trivial sense that they can be empirically observed, and empirical propositions depend on them, and logical facts are ultimately facts of the universe (in some fashion or other), but these are not empirical facts in the same sense as historical facts, because we cannot ascertain what happened in the past solely by ruminating on logical necessities or impossibilities. Logical facts are thus traditionally called analytical facts, in contrast to empirical facts. Some propositions might combine elements of both, but insofar as a proposition is at all empirical, it is not solely analytical (and thus has some nonzero epistemic probability of being true or false), and insofar as it is solely analytical, it is not relevantly empirical (and thus cannot affirm what happened in the past, but only what could or couldn’t have).

(Proving History, 62, 302)

And again, in pointing out that historians can never be absolutely certain about any “substantive claim”,

Such certainty for us is logically impossible (at least for all substantive claims about history . . . )

(Proving History, 329)

Not even God can avoid reducing all knowledge of the past to “what probably happened”:

A confidence level of 100% is mathematically and logically impossible, as we never have access to 100% of all information, i.e., we’re not omniscient, and as Gödel proved, no one can be, for it’s logically necessary that there will always be things we won’t know, even if we’re God . . . 

(Proving History, 331)

I have to disagree. We don’t need “100% of all information” or to be “omniscient” in order to be absolutely certain about certain facts of the past. Historians are indeed certain about basic facts. We know for a fact that the U.S. dropped atomic bombs on Japan in 1945, that Japan attacked Pearl Harbor a few years before that event, that Europeans migrated to and settled in the Americas, Africa, Australasia in the sixteenth to the nineteenth centuries, that King John signed the Magna Carter in 1215, that Rome once ruled the Mediterranean, that the Jerusalem temple was destroyed in 70 CE.

Historical events are unique and unrepeatable and our knowledge of many of them can often be absolutely certain. Witness the “History Wars” around the world — the Americas, India, Australia. In Australia, for instance, the arguments over the killing of aborigines and removing children from their families is not about what “probably” happened but what the evidence tells us did actually happen — with no room for any doubt at all. The 1992 Holocaust trial of David Irving was not about what probably happened but what can be known as an indisputable fact to have happened.

To be certain about such events does not require us to possess 100% of all the related information. Further, being certain about such events does not mean we are certain about all the details. There are grey areas where probability does enter the picture but the core events themselves cannot be legitimately doubted.

A “brilliant and devastating critique”* of the probability approach to historical facts (in fact to the entire area of theoretical empiricism that once typically “characterised the academic social sciences and history”) was published in the 1972 book Systematic Empiricism: Critique of a Pseudo-Science by David and Judith Willer. The chapter that specifically addresses probability in this context was written by the sociologist Dr Cesar Hernandez-Cela. Here is what he says about probability in the context being discussed in this post:

A relative frequency is a probability only if the number of events taken into account is infinite. But when the number of instances is finite . . . the ratio is a relative frequency but not a probability. . . . . A relative frequency is a description, but a probability is a calculation. Although we may calculate a theoretical probability value of 1/2 for a universe in which A and B are equally represented when the number of instances approaches infinity, the most that can be said about the number of heads that will turn up when tossing a coin twenty times is that there will be a particular frequency which is unknown until we toss the coin. In other words, the assignment of a value of 1/2 simply because the coin has two sides is an error because we do not know that each side will be equally represented in any empirical case. Equal representation in probability is a mathematical assumption which is violated in finite empirical cases. . . . We may instead find that tossing a die results in a successive run of fives . . . .

The theory of probability . . . can be used in scientific theories, but it cannot be used to associate observables. Sociological statistical procedures are concerned with observables and therefore violate the conditions under which probability calculations may be legitimately used. But they are so often used that they are frequently accepted (in spite of their obvious absurdity) without question. We are told that the probability of rain tomorrow is 60 percent when, in fact, it will either rain or it will not. Such statements are unjustified, wrong, and misleading.

(Systematic Empiricism, 97f – italics in the original)

One is reminded here of Richard Carrier’s discussion of the “Rank-Raglan hero class”, a category of ancient figures — most of whom are mythical — who share certain mythical attributes.

This is a hero-type found repeated across at least fifteen known mythic heroes (including Jesus) — if we count only those who clearly meet more than half of the designated parallels (which means twelve or more matches out of twenty-two elements), which requirement eliminates many historical persons, such as Alexander the Great or Caesar Augustus, who accumulated many elements of this hero-type in the tales told of them, yet not that many.

The twenty-two features distinctive of this hero-type are:

1. The hero’s mother is a virgin.
2. His father is a king or the heir of a king.
3. The circumstances of his conception are unusual.
4. He is reputed to be the son of a god.
5. An attempt is made to kill him when he is a baby.
6. To escape which he is spirited away from those trying to kill him.
7. He is reared in a foreign country by one or more foster parents.
8. We are told nothing of his childhood.
9. On reaching manhood he returns to his future kingdom.
10. He is crowned, hailed or becomes king.
11. He reigns uneventfully (i.e., without wars or national catastrophes).
12. He prescribes laws.
13. He then loses favor with the gods or his subjects.
14. He is driven from the throne or city.
15. He meets with a mysterious death.
16. He dies atop a hill or high place.
17. His children, if any, do not succeed him.
18. His body turns up missing.
19. Yet he still has one or more holy sepulchers (in fact or fiction).
20. Before taking a throne or a wife, he battles and defeats a great adversary (such as a king, giant, dragon or wild beast).

and

21. His parents are related to each other.
22. He marries a queen or princess related to his predecessor.

Many of the heroes who fulfill this type also either (a) performed miracles (in life or as a deity after death) or were (b) preexistent beings who became incarnated as men or (c) subsequently worshiped as savior gods, any one of which honestly should be counted as a twenty-third attribute. . . . 

1. Oedipus (21)
2. Moses (20)
3. Jesus (20)
4. Theseus (19)
5. Dionysus (19)
6. Romulus (18)
7. Perseus (17)
8. Hercules (17)
9. Zeus (15)
10. Bellerophon (14)
11. Jason (14)
12. Osiris (14)
13. Pelops (13)
14. Asclepius (12)
15. Joseph [i.e., the son of Jacob] (12)

This is a useful discovery, because with so many matching persons it doesn’t matter what the probability is of scoring more than half on the Rank-Raglan scale by chance coincidence. Because even if it can happen often by chance coincidence, then the percentage of persons who score that high should match the ratio of real persons to mythical persons. In other words, if a real person can have the same elements associated with him, and in particular so many elements (and for this purpose it doesn’t matter whether they actually occurred), then there should be many real persons on the list—as surely there are far more real persons than mythical ones. . . . 

So there is no getting around the fact that if the ratio of conveniently named mythical godmen to conveniently named historical godmen is 2 to 1 or greater, then the prior probability that Jesus is historical is 33% or less.

(On the Historicity of Jesus, 229-231, 241 – italics original)

First, we have fewer than a quarter of 100 instances in our group so a per centum figure is misleading. The total number Raglan studied was twenty.

Second, on what basis can we validly decide to count only those figures who score more than half of the listed attributes? Carrier identifies ten of the twenty-two listed features as applicable to Alexander the Great and acknowledges (though disputes) the possibility of assigning him thirteen. Half seems to be an arbitrary cut-off point (or at least tendentious insofar as it excludes the exceptions, historical persons who would spoil the point being made) especially when we know that Raglan himself said that his list of twenty-two was an arbitrary number. Other scholars of mythical “types” produced different lists:

Von Hahn had sixteen incidents, Rank did not divide his pattern into incidents as such, and Raglan had twenty-two incidents. Raglan himself admitted that his choice of twenty-two incidents (as opposed to some other number of incidents) was arbitrary (Raglan 1956:186).

(In Quest of the Hero, 189. — Raglan’s words were: I have taken twenty-two, but it would be easy to take more. Would a more complete list reduce the other figures to matching fewer than half….? So we begin to see the arbitrariness of Carrier’s deciding to focus only on those with more than half of the attributes in the Raglan list of 22.)

Alexander the Great and Mithridates are not the only ancient figures to whom “hero attributes” were attributed in the literature. Sargon and Cyrus were also studied in the same context by other scholars:

Raglan wrote in complete ignorance of earlier scholarship devoted to the hero, and he was therefore unaware of the previous studies of von Hahn and Rank, for example. Raglan was parochial in other ways too. For one thing, the vast majority of his heroes came exclusively from classical (mostly Greek) sources. The first twelve heroes he treats are: Oedipus, The­seus, Romulus, Heracles, Perseus, Jason, Bellerophon, Pelops, Asclepios, Dionysos, Apollo, and Zeus. Raglan could have strengthened his case had he used some of the same heroes used by von Hahn and Rank and other scholars, e.g., such heroes as Sargon and Cyrus.

(In Quest of the Hero, 187 – my bolding)

One might even argue that the further east one went from Greece the more likely it was that historical persons matched the mythical hero reference class! Much fun can be had with statistics.

Let’s continue with Hernandez-Cela’s discussion of probability as it applies to the social sciences and history:

Social empiricists, when presenting numerical values such as the “probability” of churchgoers giving alms to the poor, might state that only in 5 percent of cases would an association as large as 60 percent or larger not obtain when instances are randomly selected. But, observing individuals, we may only say that they either do or do not give alms. In the first observation we may find that 60 percent of the total sample gave alms, but in succeeding observations this value may differ. We cannot, in fact, have any expectations of probability of giving alms to the poor, no matter how many samples we take. If, on the other hand, the sample approaches or is equal to the total population of churchgoers, then the figure represents a simple proportion, a frequency, not a probability. On the other hand, specification that only 5 percent of samples will not result in the .60 or more is meaningless. If we chose several samples all of the same size, and found that in only 5 percent of them the figure was under .60, then we still can draw no conclusions, for we know nothing about the empirical conditions prevailing in future samples. Such a claim has no basis either in theory or in observation. What the claim means is that if there were an infinite number of cases whose composition was on the average like that of the sample, then in only 5 percent of them would the percentage be smaller than .60. But, we cannot assume that any other empirical cases are on the average like the sample studied, and we cannot assume that they are infinite in number. Theoretical cases can be infinite in number, but empirical ones cannot. Such statistical claims, of course, cannot be violated empirically because they are not probability statements at all but disguised frequencies obtained by observation. Future observations cannot verify or falsify frequencies but only slightly modify their numerical value in the light of new cases. Furthermore, the statistical procedures themselves are not open to any kind of empirical verification or falsification . . .

(Systematic Empiricism, 99)

So a sample of a score of mythical heroes cannot be the basis for predicting the likelihood of any particular figure being historical or not.

The statement, “All As are Bs,” . . . . really means no more than “As have been observed with Bs.” But this statement is not a universal statement, but limited to a population. . . . Consequently no empirical generalization can act as a major premise in a deductive explanation, and empirical generalizations can never be used deductively to explain or predict.

(Systematic Empiricism, 130 — no longer from Hernandez-Cela’s chapter; italics original)

An illustration of the fallacy is set out thus:

Premise A: The probability of recovery from a streptococcus infection when treated by penicillin is close to 1.

Premise B: John Jones was treated with large doses of penicillin.

Conclusion: The probability that John Jones will recover from his streptococcus infection is close to 1.

(Systematic Empiricism, 130)

One might rephrase this as:

Premise A: The probability of a figure in the hero-class being non-historical is close to 0.

Premise B: Jesus is a figure in the hero-class.

Conclusion: The probability that Jesus is non-historical is close to 0.

But as D. and J. Willer observe,

Predictions and explanations cannot be made from [such a statement]. John Jones either does or does not recover. If he does recover the probability value of statement A is slightly increased by his case, and if he does not the probability value decreases. . . . [T]he event itself cannot be predicted with any certainty. Furthermore, if John Jones either recovers or does not, he does not recover with a probability of close to 1.

Individual facts either occur or they do not. Certain facts cannot be explained by uncertain statements. Even in ordinary everyday practical empiricism we do not make that error.

(Systematic Empiricism, 131, 135)

No two historical events are ever exactly alike. People and societies are not like that. There are always variables that make each historical event unique. Of course there are common experiences such as war or economic depression but no two wars or depressions are the same. Human events are not governed by laws in the same way geological forces or the weather are governed by scientific laws. Historians do not observe the results of “laws” in the historical data. They cannot make predictions about a unique historical event or person  — all historical events and persons are unique in some respect — on the basis of limited samples with variable (“arbitrary”) attributes. Generalizations can be made about the impacts of technologies on various kinds of social groups but particular historical events are each unique in some way. But generalizations cannot predict what a historian will find in the sources.

The most that probability (in the context of Richard Carrier’s discussion) can tell us about the likelihood of Jesus having existed is that Jesus was one of a few historical exceptions (or even the only exception) to general notions about mythical persons.

In the next post I’ll show what historians say about the certainty or otherwise of “their basic facts”.

Carrier, Richard. On the Historicity of Jesus: Why We Might Have Reason for Doubt. Sheffield: Sheffield Phoenix Press Ltd, 2014.

Carrier, Richard. Proving History: Bayes’s Theorem and the Quest for the Historical Jesus. Amherst, N.Y: Prometheus Books, 2012.

Hindess, Barry, and Paul Q. Hirst. Pre-Capitalist Modes of Production. London: Routledge & Kegan Paul Books, 1975.

Raglan, Lord. The Hero: A Study in Tradition, Myth and Drama. Mineola, N.Y: Dover Publications, 2011.

Rank, Otto, Raglan, and Alan Dundes. In Quest of the Hero. Mythos (Princeton, N.J.). Princeton, N.J.: Princeton University Press, 1990.

Willer, David, and Judith Willer. Systematic Empiricism: Critique of a Pseudoscience. Englewood Cliffs: Prentice-Hall, 1973.