by Neil Godfrey
How do historians, comparative linguists, biblical and textual critics, and evolutionary biologists establish beliefs about the past? How do they know the past?
That’s the subject of Aviezer Tucker‘s Our Knowledge of the Past: A Philosophy of Historiography (2004). Tucker’s interest is the relationship between the writing of history (historiography) and evidence (p. 8). It is written for audiences interested in philosophy, history, biblical criticism, the classics, comparative linguistics and evolutionary biology (p. 22).
When I began to review Richard Carrier’s book, Proving History, I pointed out that far from substituting crude mathematics for historical inquiry, the application of Bayes’ Theorem merely expresses in symbolic terms the way historians evaluate the nature of evidence and test hypotheses to explain evidence for certain events and artefacts. Some fearful critics have objected to the application of Bayes because they have never understood this fact.
All Bayes’ theorem does is help us clarify our thinking. Bayes theorem is simply a symbolic way of expressing how we do our best thinking when seeking explanations for evidence or evaluating hypotheses against the evidence. The more complex the factors that need to be considered in addressing a problem the easier it is for us to overlook a critical point or draw invalid comparisons. Bayes’ helps us to clarify thinking about the most complex of issues, including those in the social sciences and history. *
Tucker writes as a philosopher and concurs with the above assessments of other authors addressed in my earlier posts. Philosophers like to clarify the complexities they are discussing and are apt to use illustrative symbols to this end.
Philosophers find often that formal representation, Bayesian probability in our case, clarifies and concentrates the discussion. Some historians and many classicists may not be as used to this form of representation as their philosophical colleagues. . . . When I use formal representation, I express the same concepts in words, for the benefit of readers who are not accustomed to formal notation. (p. 22)
Historians ask questions like the following:
To what degree does a piece of evidence contribute or not to the confirmation of a hypothesis, given background conditions? (p. 96)
To what extent does a similar saying in the Gospels of Matthew and Luke support, or not support, the Q hypothesis, given everything else we know that is relevant to the question?
To what extent does the passage “born of a woman” in Galatians 4:4 support, or not, the hypothesis that the author believed Jesus was an historical person in the recent past, given everything else we know about Galatians, that verse in particular and its context, and evidence for Jesus?
The Bayesian theorem purports to state formally the relation between a particular piece of evidence and the hypothesis. (p. 96)
In the fifty or so pages of chapter 3 Tucker demonstrates
that an interpretation of Bayesian logic is the best explanation for the actual practices of historians. (p. 96)
Tucker sets out Bayes’ Theorem thus:
Pr(H|E & B) = [Pr(E|H & B) x Pr(H|B)]:Pr(E|B)
Pr — the Probability of. . .
H — the Hypothesis, or any historical proposition about past events
E — the Evidence (often this means similarities between two or more independent sources)
B — the Background knowledge of theories, methods, other hypotheses
The vertical line | should be read as “given”. So the first part of the equation expresses:
The Probability of the Hypothesis being true given the evidence and background information.
Pr(H|E & B) translated into words:
The probability of the hypothesis that George Washington was the first president of the United States, given the massive amount of documentary evidence for it and background knowledge of the causal chains that led to this evidence, is almost 1. We are almost certain that George Washington was the first president. (p. 97)
The probability of the hypothesis that Jesus was the founder of what became the Christian Church, given the massive documentary evidence for it and background knowledge of the causal chains that led to this evidence, is . . . ?
Unfortunately we have no background knowledge of the causal chains that led to the Gospels and writings of Paul. We only have other hypotheses (e.g. oral tradition) to fill in these gaps.
Pr(H|B) in words:
This is the prior probability of a particular hypothesis being true given our background knowledge prior to knowledge of the evidence.
The probability of the hypothesis that there was a city of Troy that was destroyed in a war in the twelfth century BCE was low given the background information that had been known prior to the archaeological discovery of the city.
The probability of the hypothesis that there was a Gospel of Thomas that was the text of an “unorthodox” Christian group in the second and third centuries CE was relatively high given the background information that had been known prior to its discovery in 1945 (e.g. Hippolytus of Rome (c. 222–235) and Origen of Alexandria (c. 233) wrote about it.)
Pr(E|H & B) in words:
This “expresses the likelihood of the evidence given the hypothesis in question in conjunction with background knowledge.”
Given the hypothesis that George Washington was the first president of the United States, and background theories and information about the nature of paper and its preservation and use over two centuries and our knowledge of paper trails that governments and politicians generate, it is highly likely that we can encounter today many contemporary documents that refer to Washington as the first president. (p. 97)
Given the hypothesis that Jesus was revealed through Jewish Scriptures, and background theories and information about the way Second Temple Jews used and adapted their Scriptures, it is highly likely that we can encounter many passages in the Jewish Scriptures that are alluded to in the Gospels and Epistles when talking about Jesus.
Given the hypothesis that education in Greek literacy required the study of Greek literature, and background theories and information about the way Second Temple Jews used and adapted Greek literature, it is highly likely that we can encounter at least some traces of Greek literary influences and ideas in the early Christian Greek literature.
Finally for now,
Pr(E|B) in words:
This is “the expectancy, the probability of the evidence given background information.”
If our evidence is an invitation to Washington’s inaugural, it is only to be expected, given all that we know. If, however, we find it in the archives of King George with a personal dedication from Washington saying, “hoping to see you there,” it is highly surprising and would require rewriting American historiography. (p. 97)
A early Christian studies example,
If our evidence is Christian apologetic writings that claim to quote a letter from Jesus to the king of Edessa, it can be dismissed as a fabrication given all we know. If, however, we found the letter in scientifically verifiable archives of King Abgar of Edessa, it would be very surprising and lead to a serious rethink about Jesus and Christian origins.
Pr(H|E & B) in words:
This is “the posterior probability of the hypothesis given new evidence and background information.” This is “the ratio of the likelihood of the evidence given the hypothesis and its prior probability, to the expectedness probability of the occurrence of the evidence whether or not the hypothesis is true.”
Let our hypothesis be that there was widespread literacy among speakers of the Y language in the time of X: . . . .
- New evidence comes to light. It is a book in prose in the Y language and from the time of X.
- Our background knowledge informs us that prose writings are associated with widespread literacy since the earliest (nascent) stages of literacy produce characteristically poetic (easily remembered) writings. Prose is a later development that accompanies growing literacy.
- The posterior probability of our hypothesis that there was widespread literacy at this time among speakers of language Y is almost 1.
Or let our hypothesis be that Chinese printing caused the invention of European printing:
- New evidence comes to light. It is a fourteenth century Persian text describing Chinese printing techniques.
- Our background knowledge informs us that there are many possible scenarios where a Persian author might know about Chinese printing that do not require that knowledge to be transmitted to Europe.
- Our posterior probability of our hypothesis that Chinese printing led to European printing is not increased by this new evidence.
Or imagine this (as per Tucker):
- New evidence comes to light. It is Gutenberg’s diary in which he recounts meeting a Chinese merchant from whom he bought a Chinese printed book before the time of his printing press.
- The likelihood of such evidence existing is very high given our hypothesis that Chinese printing led to the invention of printing in Europe. So the posterior probability of our hypothesis is dramatically increased by the discovery of the new evidence.
Discovery of new evidence does not necessarily mean tossing a stone into another cave and hearing the sound of it hitting a pot full of new manuscripts. Sometimes it can be an observation or record that has been in the literature but long overlooked.
I’ll cover more examples used by Tucker to demonstrate that Bayes’ theorem really does give us a symbolic representation of the processes by which historians really do evaluate hypotheses and test evidence.
Unfortunately, we will also see, by way of contrast, how theologians who think they are historians of the historical Jesus fail badly and really do not “do history like real historians do”. We will see that in fact many of them value what Tucker calls “therapeutic values” above “cognitive values”.
H/T Richard Carrier @ http://freethoughtblogs.com/carrier/archives/3923
Another critic of Carrier’s view, a theologian, has confused a Bayesian application to historical questions with classical logical-positivism. That, too, is a misinformed criticism: historians have long since (close to a hundred years now!) moved away from such positivism. Evidence is not theory-free. Theories are acknowledged today as necessary for deciding where to look for evidence, how we decide certain data is relevant evidence, etc. Clear thinking (which is all Bayes helps us to keep in mind) applies to more than just one philosophical approach to evidence and interpretation.