There is no fourth alternative. That some conclusion is then always entailed I demonstrate with a logical flow chart in the appendix page , where BT conclusions are shown to follow even from the simplest trichotomy here proposed, that is, that each premise has a value of either 0. But the same analysis follows for any degree of precision your knowledge can honestly claim. This becomes all the clearer as your certainty increases. This was already evident in chapter 3's opening example of the sun being supernaturally eclipsed for three hours.
It follows that no other method of inference, such as using ordinal or qualitative rankings of confidence absent any reference to probabilities, can supplant BT. It can work alongside it, as a heuristic or simplified way of getting the same result. But you can't get a valid conclusion from any other method and have that conclusion contradict BT. And for every hypothesis, BT entails some conclusion for whatever state of knowledge you are presently in.
Because for any probability in BT whether the prior or either consequent , you will always have some confident belief that it is at least some value or higher, or some value or lower, and this belief logically requires you to accept the conclusions that follow from that belief, in the very manner BT entails. Resorting to other methods of inference simply cannot extricate you from this obligation. At best they can only confirm the same result, and thus simply corroborate BT.
My conclusion is therefore inescapable. That probability is then the only one that will entail a conclusion you can be confident in—because to get a different conclusion out of BT, you must input a different probability, yet if you are inputting a probability you are not confident in, then you cannot be confident in whatever conclusion that that probability entails. Because every weakness in an argument's premises always translates to the conclusion. Thus a conclusion that can only be arrived at by affirming premises you are not confident are true is by definition a conclusion you are not confident is true.
There is no way around this. Because no matter how ignorant you claim to be, some value always necessarily follows for P h e. This is due to the key difference between epistemic and physical probabilities as demarcated in chapter 2 page With regard to physical probabilities, you can legitimately say you simply have no idea what the probability is and therefore you are not obligated to pick any one of the only logical possibilities available , but you cannot legitimately say this with regard to epistemic probabilities.
So even denying there is a probability always entails there is a probability—for you, and given the information you have at that point in time. BT therefore underlies all valid empirical reasoning. Or so I contend. Applying this knowledge now allows us to test the validity of any methodological principle in the study of history. We immediately rule them out as fabrications. We usually don't investigate.
I find that last bit to be dead on. March into a meeting of the Sanhedrin. Rhetorically, this is a great place to start. Obviously something is fundamentally wrong with the methods of the entire community. Nevertheless, it was a real scholar in very recent history taking the hypothesis seriously.
We don't wait until we can find evidence against the claim. We know right from the start the tale is bogus. Yet the only basis for this judgment is the Smell Test.
Is that test valid? It is certainly ubiquitously accepted by historians in every field. They ground this rejection in the claim that we shouldn't be biased against the supernatural, and God can do anything. We can't reject them—because God can do anything. Ghosts confirming to the living that heaven is run by a Chinese magnate and his staff? We can't rule it out. That would be bias against the supernatural. Honestly living that way would be impossible. You would have to believe everything you read or hear unless you can specifically present evidence sufficient to discount it: an impossible task.
You would be left with a belief system hopelessly frightening and contradictory—and mired in a thousand false beliefs. The Smell Test thus represents an intuitive recognition of: a the low prior probability of the events described i. Both c and d can raise the consequent probability of nonmiraculous explanations, and also reduce the consequent probability of the miraculous. But condition a is the point just made: such claims are contrary to reality as we know it. This doesn't just mean only miracles, but all wonders, like implausible coincidences and unrealistic social reactions and behaviors.
Hence, the issue is not the presumption that miracles never happen, but the documented fact that, if they happen, they happen exceedingly rarely just as implausible coincidences and unrealistic human behaviors do , whereas false tales of the fantastic happen with exceeding frequency; and likewise, the fact that miracles suspiciously happen all the time only in historical periods or geographical regions that are comparatively illiterate, superstitious, or unenlightened, in conditions lacking the means of verifying no shenanigans were involved in either the event or its telling , whereas in ages and places where we have widespread education and organized skepticism and the tools and opportunity to test wild claims, the phenomena always disappear.
Even if you are a firm believer in the miraculous, the facts remain the same: most wondrous claims by far are bogus. And like the Tibetan peasant claim in chapter 3 page 72 , when we lack specific evidence to confirm a claim, or lack the means to verify it by reliable tests, the priors must dictate what is reasonable to believe. That reasoning is both logically valid and sound.
Thus, BT confirms that the Smell Test is valid, even on point a alone. Conditions b , c , and d only strengthen this conclusion. Even outside the context of wondrous claims, ancient texts are full of lies and falsehoods, even when generated by eyewitnesses, contemporaries, and critical historians, or anyone who ought to have known better. The darkening of the sun predicts a vast quantity of evidence that, by not existing, disconfirms the story. Likewise, the frequency of resurrection stories in antiquity entails a phenomenon that should still be observed with the same frequency, yet is not except in such mundane ways as to refute any miracle claimed to be analogous—such as from the application of CPR and ordinary cases of misdiagnosed death.
Thus, the disappearance of this phenomenon is an unexpected piece of evidence on the theory that any resurrection is real, just as the disappearance of angels and gods who used to descend and deliver speeches with surprising frequency in antiquity is unexpected on the theory that these things ever really happened.
Any logically valid argument must take this improbability into account. Which means the Smell Test reduces to BT. Negatives are often quite easy to prove and we prove them all the time. In fact, logically, every positive claim entails a converse negative claim, thus merely in the act of proving a positive we have always proven a negative; often a great number of them. The question of whether Jesus existed, for example, would be decisively proven in the negative by the recovery of an authenticated letter signed by the Apostle Peter outright saying that Jesus was only a cosmic being whose sojourn on earth was merely a symbolic myth, and who was only known to anyone through mystical perception.
And we could have had a great deal more evidence than that—as we do for the ahistoricity of Betty Crocker, for example.
The ahistoricity of Moses and Abraham and all the other patriarchs is now generally accepted by scholars the world over as an established fact, quite rightly, and yet without even need of such a smoking gun as a contemporary epistle declaring them a fiction. Unfortunately, no, because we have little reason to expect such evidence to have survived for us to now have it. If that only happened after Peter died, he won't ever have written a letter gainsaying it. For the present, our concern is with when an Argument from Silence is valid and sound—and when it is not.
The logical conditions have already been correctly stated:. To be valid, the argument from silence must fulfill two conditions: the writer whose silence is invoked in proof of the non-reality of an alleged fact, would certainly have known about it had it been a fact; [and] knowing it, he would under the circumstances certainly have made mention of it. When these two conditions are fulfilled, the argument from silence proves its point with moral certainty. That would be a slam-dunk case.
But a relatively weaker deployment is possible, to the extent that either condition is less certain.
Not having more evidence of the sun going out examined in chapter 3 is a strong Argument from Silence, but not having a letter from the first Apostles explicitly declaring Jesus a fiction is weak. The examples of Caesar shaving or playing dice with a hooker examined in chapter 2 are weaker still, being exactly what historians have in mind when declaring absence of evidence is not evidence of absence. Yet as the sun case proves, that rule does not always apply. Once again, BT describes the logic of this argument.
In my next volume I will discuss this oddity and how it might be dealt with. The point to observe here is that the Argument from Silence is a commonly accepted historical tool, and is logically valid precisely and only when it conforms to BT. What else will Bayes's Theorem teach us about the methods particularly used by Jesus scholars? To that we now turn. BT is a logically proven theorem. No argument is valid that contradicts a logically proven theorem.
Therefore, no argument is valid that contradicts BT. If B, then A.
Accordingly, I propose the following testable hypothesis: P5. That means the following is true by definition: P6. Either C, D, or E. Therefore, either D or E. P5 and P6. Therefore, only D.
The logical conditions have already been correctly stated: To be valid, the argument from silence must fulfill two conditions: the writer whose silence is invoked in proof of the non-reality of an alleged fact, would certainly have known about it had it been a fact; [and] knowing it, he would under the circumstances certainly have made mention of it.
My thinking would be that Philo was directly involved in all Jewish affairs, defending the Jews of Alexandria against Greek propaganda to Augustus, no less. As it so happens, I am finishing a PhD in the theory of probability. I may not be recognized as a world-class expert on the subject, but I may be able to contribute some useful thoughts here.
Anyway, I agree with you that the Bayesian approach cannot produce precise numerical values for the probability of historical events. I do think, however, that the Bayesian framework can still be useful in a more qualitative way. The basic Bayesian idea is that we have some set of mutually exclusive hypotheses H1, H2, and so on. We then make some observation O. There will be some conditional probability P O H1 , which is the probability of observing O given that H1 is true. Likewise for all the other hypotheses.
These conditional probabilities are called the likelihoods. The inputs to the theorem, then, are the prior probabilities and the likelihoods. The nice thing about the approach is that you can keep on applying it as new observations come in. Hoffman seems to think there is some sort of problem in applying the approach to hypotheses about the past. I think I can unequivocally say he is mistaken about that. I am not merely stating my own personal opinion here; it is the general consensus among theorists of probability.
If probability is understood as rational degree of belief, then past events can have all sorts of probabilities and we are free to use any valid theorem of the probability calculus to help us evaluate those probabilities. The problem, rather, is that the prior probabilities and the likelihoods are both impossible to evaluate, or even to give rough estimates for. The prior probabilities P H1 and P H2 are, respectively, the probabilities that Jesus did or did not exist—as considered without regard to any more specific evidence on the matter.
The Bayesian approach allows us to be quite vague about those probabilities, so it is reasonable to set both of them equal to one-half. Let O, for example, be our observation of what some ancient manuscript of Mark says. We will also need to know P O H2 , i. Clearly, there is no way to precisely evaluate those probabilities. Taking the Bayesian approach just amounts to detour. How do I think Bayesianism can be qualitatively useful, then?
I think it can help us to zero in on which pieces of evidence are most critical. When people disagree about some large hypothesis, applying the Bayesian approach can help identify which pieces of evidence matter most to the overall disagreement.
Maybe you think it is extremely unlikely that the followers of a purely mythical messiah would make up a story about his powerlessness, while it is extremely plausible that if Jesus was real he would have little effect on those who had always known him as merely a humble carpenter. That would amount to significant albeit not overwhelming! You could then debate this particular issue. The approach is not an alternative to the usual criteria of historicity embarrassment, and so on ; rather, the approach offers one way of formalizing those criteria.
It is an estimate, and producing such estimates always involves an element of art. You may not be prepared to assert there is a By using the Bayesian framework, we can see which pieces of evidence have been most important in leading you to that conclusion.
Proving History: Bayes's Theorem and the Quest for the Historical Jesus [Richard Carrier] on ykoketomel.ml *FREE* shipping on qualifying offers. This in-depth. Anyone with an interest in historical methods, how historical knowledge can be justified, new applications of Bayes's Theorem, or the study of the historical Jesus .
Carrier perplexes me, sometimes. On the one hand, he makes very interesting, and very valid points— whether I agree with the conclusions he draws from them or not, these contentions do deserve some thought and response. Carrier would be much more convincing if he simply stuck to attacking confirmation bias and perceived issues with historical methodology. Just make up whatever probabilities fit your purpose and then use those to prove your point.
You can use the same logic to prove the story of Joseph Smith and the Book or Mormon, or the validity of the Koran, or the existence of leprechauns. Five days, three days, one day? I listened to your debate with Craig. Yup, true. Ok, well… My math skills are weak and I found Dr.
So — I gather that the theorum can be used for real world events like the wedding hypothesis but for historical events the theorum has to be altered to the point where it is no longer useful. So, in effect Carrier creates his own theorum which is based on Bayes?
Is that right? Or am I still missing something? I gather from Dr. Hoffman that the way Carrier uses the theorum that almost any outcome can be manipulated. So, if my premise is that the Battle of Agincourt never happened and is just a fictional event I could manipulate Bayes to support that? Sorry, this is odd and confusing — but still kind of interesting. Thanks… SBD. I guess Bart really is ignoring Mythicists. I can prove Luke is not recording history, but that evidently has no bearing on his veracity. You say that we should hear what some of your friends say about Mythicists.
What do they say? I was just on a chat blog on Amazon with a guy who claims Tacitus mentioned Jesus. Christians, I find, do these leaps routinely. Their points really did seem stronger than yours. If your case is solid, then you should have no qualms about engaging Mythicists.