There is a current push, in all disciplines really, to push toward reliability of conclusions, showing your reasoning is based on sound logic. For example, we want to be able to explain why a child received a B grade in Social Studies so that we don’t simply claim the child’s project felt like a “B” in my gut. Modern teachers adopt a dualistic approach quantifying (eg., seldom, sporadically, usually, often) and qualifying (with assistance, competently, proficiently) student work and reasoning, reflecting that in order to avoid evaluations based on gut feeling and relationality (the best project in the class must be an A), the quantitative and qualitative dimensions of the student’s work must be identified and evaluated.

Basically, what Carrier is doing is trying to move beyond “gut feeling” historical evaluations to those grounded in symbolic logic. In the history of Philosophy in the west, we tend to have two main streams, continental and analytic. Continental tends to deal more with the qualitative side, while analytic philosophy is more quantifying in nature. So, for example, an analytic judgement is one whose denial is a contradiction, to deny that all bachelors are unmarried is a contradiction. This is the hallmark of analytic thought, the principle of contradiction, which says “something cannot both be and not be, at the same time and in the same way.” Kant later clarified this to note “at the same time” doesn’t belong here because we are just dealing with the logical relation of concepts, so there is no reason for “time” to make an appearance here. Later critics like Heidegger noted the principle tacitly assumes a concept of “Being” that is left unqualified and basically borrowed without justification from Plato’s Sophist and the critique of Antisthenes.

Carrier says he tries to be as charitable as possible when weighing the evidence:

But that wasn’t the only evidence (neither in the Epistles, nor beyond). So many more arithmetical calculations were needed. But all of that—everything you are terrified of the moment you see it (such as reproduced in the Appendix here)—is just a repetition of the same simple steps I just walked you through.11 Sticking with the Epistles as a category, the last three subcategories of evidence within that I actually scored in favor of historicity (at least on the a fortiori side; not on the other).  Which are the three I devote chapters to at the end of this volume: whether Paul attests Jesus had a father; whether Paul attests Jesus had a mother; and whether Paul attests Jesus had brothers. I thoroughly addressed (then and now) the evidence and background information in each case, and demonstrated that, even at best, these are not strong evidence because of all the ambiguities surrounding them. Nevertheless, I concluded they could still be weak evidence for historicity.  Indeed I considered that these three facts might be stronger evidence than I just mentioned. I conclude each reference (in the form we actually have it) is twice as likely to come from Paul if Jesus existed than if he didn’t. Hence each one scored 2/1 in favor of historicity. Which means, together, they score 8/1 in favor, because 2/1 × 2/1 × 2/1 = (2 × 2 × 2) / (1 × 1 × 1) = 8/1. That means these three references together are eight times more likely to survive in Paul’s Epistles if Jesus really existed, than if he didn’t.  In effect, I am saying the non-existence of Jesus might not explain these very well. In truth, I think it’s the other way around; so on the other side, the a judicantiori margin (‘the more judicious’ or ‘more critical’ side), I find that they don’t support historicity at all. But erring as much as possible on the side of historicity, I conclude it could be otherwise—that in fact all this stuff could be eight times more likely on historicity.  If we now update our result with that, we get: 3/8 × 8/1 = 24/8; or if you want to spell it all out (as the prior odds times both likelihood ratios), then it’s 1/2 × 3/4 × 8/1 = (1 × 3 × 8) / (2 × 4 × 1) = 24/8. Which reduces to 3/1 (because 8 goes into 24 three times). So the odds favoring historicity are now 3 to 1, for a probability that Jesus existed of 75%. Because 3 plus 1 makes 4, and 3 divided by 4 makes 0.75. Or in this case, you can just notice there are four parts, so each is one quarter, and ‘three quarters of a dollar makes 75 cents’.  Hence the only reason I reach a final conclusion almost the other way around (2 to 1 against historicity, for a probability that Jesus existed of only 33%) is that my conclusion factored in all the other sets of evidence that we have been ignoring here (both in the Epistles and beyond), which all either have no effect or reduce the odds of historicity to some degree; which in the end pull its probability down from 75% to 33% (a loss of over half ).

Every discipline is going to have its kinds of reasoning. For historians this will be historical reasoning such as trying to derive history from ancient sources. Psychologists will work with statistics and experimentation. For Carrier, historical reasoning is ultimately grounded in Bayesian logic.

More importantly, Fischer’s whole through-line is to pursue a single question: by what logic are any historians’ conclusions justified? There must be one. Yet if we do not know what it is, then we cannot know whether any of their conclusions are justified, least of all when.13 As Fischer points out, “assuming that this logic of historical thought does tacitly exist,” as otherwise historical thought must be devoid of logic and thus illogical (and if that’s the case, we may as well just pack it in), “the next question is to raise it to the level of consciousness,” and thus start working out what that logic is, so that it is no longer tacit…People rarely realize it, but all arguments over what happened in the past are really arguments over just these three numbers: the prior probability (how likely the thing claimed usually turns out to be true)—which measures what is sometimes colloquially referenced nonnumerically by such vague expressions as ‘plausibility’—and the two consequent probabilities that comprise the likelihood ratio. Which measure how likely all the evidence is if the thing claimed is true, and how likely all that same evidence is if something else caused it instead…We are talking about logic. We mean merely that Bayes’ Theorem proves how conclusions in history logically follow from their premises—and thus what kinds of premises sound conclusions require, and when conclusions are soundly reached at all…And that begins with admitting that the probability Jesus existed is proportional to the difference between the probability that the evidence would exist if he did and the probability that that same evidence would exist anyway even if he didn’t…We don’t have anything like this. Which is the problem. But the point here is to illustrate how evidence works: to say that something is evidence ‘for’ Jesus’s historicity is to say that there is something improbable about that evidence but for Jesus having actually existed. However, if anything about the context makes that evidence not improbable anymore, then it is no longer evidence for his historicity. But it also wouldn’t be evidence against his historicity, either. 

However, there are going to be interpretive disputes. Carrier says:

Which is crucial to understand, lest you be triggered by a confusion over this point: it is possible for some item of evidence to have no effect on the historicity of Jesus. Saying it does not make Jesus more probable is not saying it makes Jesus less probable. It simply is saying that that conclusion doesn’t gain the probability you had hoped. Only when we have some item of evidence that is (to some degree) improbable if Jesus existed do we have evidence ‘against’ his historicity. For example, suppose Cluvius wrote that Paul and his Christians reported their belief to be, as confirmed by his accusers in court, that Jesus was a mystical being slain in the heavens and not yet come. That would pretty much end the historicity of Jesus as a hypothesis. Yet we don’t have this sort of evidence, either.  So not having evidence for Jesus is not equivalent to having evidence against Jesus. Which means that knocking the probability of Jesus down on the conclusion that you had incorrectly raised it does not constitute presenting ‘evidence against Jesus’. Hence here in chapter nine, my demonstrating that Paul is only speaking of mothers allegorically in Galatians 4 does actually remove evidence for Jesus, but only because it never really was evidence for Jesus. So it does lower the probability of his existing, but only because you shouldn’t have raised it on that evidence in the first place. The net effect of that result is that we simply don’t know whether Paul thought Jesus had a real mother, because in the one place he speaks of Jesus having a mother, it turns out, he isn’t talking about biology either way. That is therefore not evidence Jesus didn’t exist. It’s just not evidence anymore than he did.

It is precisely the “brother of the lord” passage and “seed of David” passage in Paul that strike historicists as conclusive, whereas the just strike Carrier as ambiguous. This is where the mathematical breaks down. Similarly, two teachers using the same rubric and benchmark may come up with a very different evaluative grade for the same student’s work during consensus marking, just as three UFC judges may be using the same criteria but score the match very differently. Carrier finds it striking that the ancient Jews may have considered it normal for Christ to be killed in the upper realm by demons:

I documented that the popular imagination filled all those spaces with versions of everything on Earth, including thrones and halls and gardens, and wars (and hence deaths), and burials (see chapter two). In that context, a message that the messiah was killed and buried (and raised) there is not only intelligible, but resonant. It is thus no longer unexpected that a movement then would begin believing or even just preaching such a thing, particularly if that solved a number of pressing problems faced by Jewish messianism at the time (as evidence suggests it did).30 So it cannot be argued that that would be contextually improbable at all. 

But this seems to fail to note that all the evidence seems to point to the idea that the elite Jews were responsible of Christ’s death. This is conveyed in a seemingly authentic portion of Josephus. Paul notes the Jews killed Jesus (Carrier claims this passage is an interpolation), as does Matthew. The Jews killing Jesus was later blamed for God’s wrath being poured out on the temple via the Romans. And we know from multiple sources the Jewish elite from the time of Jesus were seen as corrupt, which the gospels satirize with the ridiculous trial of Jesus before the Jewish high council with the plethora of transgressing of Jewish custom and law, only to have the crafty legal experts find loophole after loophole!

Carrier comments:

All the conceptual difficulties here are not arithmetical (the math is relatively easy), but logical; and historians must learn logic. You need to be able to understand a chapter like this, because you need these concepts to understand why your own arguments regarding probability are sound (or not sound). It should be required of all history graduate students to master at least basic level logics, in particular how to derive conclusions from premises and fallacy-test their inference models, as well as the basic principles of probability logic as here described. ‘But it just feels right in my gut’ can no longer be an accepted mode of reasoning. You need to be able to explain why your conclusion follows from your premises.

As I said, what Carrier proposes is not fundamentally different from other disciplines, but I think he overestimates what quantifying can actually accomplish.