Your paper only argues that BT does not apply to anything stipulated not to exist. I agree. Bayes’ Theorem refers to empirical propositions only. Thus it has no application to things that aren’t real. But the declaration that a thing is or is not real is itself empirical, and thus subject to Bayesian analysis.

Needless to say, I have no interest in things that don’t exist—apart from counterfactual reasoning, but that stipulates reality hypothetically and thus is still about “real” things (in the sandbox of hypotheticals), and of course apart from how we can show unreal things probably don’t exist so as to warrant their being ignored in the first place, a project which remains empirical and thus applies BT to the reality of the evidence, to then arrive at a conclusion on the proposed explanation’s reality.

There are situations in which Bayes’ Theorem is not applicable. I have a paper on that. It is available at https://vixra.org/abs/2302.0081

Let me be a little clearer: It’s a complaint about Christians and their (mis)use of the BT.

They don’t just misuse BT. They misuse standard logic (look what they do in the Kalam Cosmological Argument, for example). This is not about BT. It’s about Christians rejecting logic, and substituting fake logic instead. That’s the actual phenomenon you are complaining about. The problem is Christians, not logic.

But rather on the question of establishing a probability without any mathematical method…

I have a mathematical method. It is detailed in Proving History and explicitly laid out and applied in On the Historicity of Jesus. Every probability is justified by appeal to evidence. Imprecision is modeled mathematically. And the consequences determined by proper mathematical means.

Even when probabilities are “pulled out of thin air” they are a fortiori, i.e. empirically as favorable to the opposition as the evidence permits. Thus they are not in fact arbitrary, but constrained by logic and evidence. There is a whole section on the logical validity of of this methodology in Proving History. You need to get up to speed.

The only difference that exists is: I am using the method correctly; they are not. That’s not a problem with the method. It’s a problem with them.

For an example, see Crank Bayesianism: William Lane Craig Edition.

Let me be a little clearer: It’s a complaint about Christians and their (mis)use of the BT. It’s my long experience with Christians that they don’t agree with Atheists on what constitute as evidence. So my concern is that people like William Lane Craig are using Bayes’ Theorem for their own purposes.

BTW, many Christians are not rejecting logic. In fact, many of them are very, very logical. It’s just their premises are different than mine and yours.

Also, my post was not about precision/imprecision. But rather on the question of establishing a probability without any mathematical method, which often occurs when discussing such things as the Jesus Resurrection (JR), or the Jesus Virgin Birth. Often in those cases, the estimation of the probability of an event occurring is pulled out of thin air. You might argue don’t worry, that with more evidence, you can refine the calculations. That’s fine if you are looking at finding an airplane that crashed, where each new evidence increases your precision, but airplanes and crashes are real. But in the Jesus Resurrection, how real is that? Would you accept that Osiris and Isis in Ancient Egypt are believed to have resurrected as evidence, that many gods in Ancients Greece and Rome were believed to have resurrected as more evidence in your equations?

My concern is that once you open the door to Bayes’ Theorem on such topic as the JR, then the likes of WLC will come with full force and bite you. Never mind that you would point, correctly, to their misunderstanding. It matters not to someone who believes that the Holy Spirit is inside of him, guiding his every step in defending the faith. And if Atheists believe they have discovered their “nukes” to destroy people like WLC, think again. Like in the video game CIV2 by Sid Meier, once a civilization develops nukes, every other civilization has access to those nukes.

Let me make sure I understand you correctly:

You have a problem with Bayes’ Theorem because it doesn’t allow any effect of “unreal events outside space and time” upon the probability of sometging being true or false.

That’s what you are arguing?

Because that’s not Bayes’ Theorem. That’s all logic whatever. There is no effect of such things on probabilities. Things that don’t exist have no effect. Nor do things for which no evidence exists. If you are worried Christians are rejecting all logic whatever, that isn’t a complaint about Bayes’ Theorem. It’s a complaint about Christians.

As for the “precision” argument, it is clear you don’t know what you are talking about. Bayes’ Theorem, like all mathematics, can easily model imprecision. My argument in OHJ uses very wide margins of error, not only fully acknowledging precision does not exist in this subject, but even measuring how imprecise the evidence must leave our conclusions to be. I even have a whole section on this as a general methodological point in Proving History.

I recommend you get up to speed here before criticizing something you haven’t even studied.

Finally, that people exist who abuse and misuse logic, is not an argument for not using logic. So your entire position is itself illogical.

My objection is not with Bayes’ Theorem but with how it’s been used with respect to interpreting historical events that involve religious beliefs. We must keep in mind that the BT is based on the following assumptions: 1) that one deals with real events in space and time, in other words, these events can be verified by any team of experts on the planet; and 2) that one can objectively determine the probabilities of their outcome as precise as that can be carried out. Needless to say that any failure of these two assumptions would invalidate the use of Bayes’ Theorem.

You might ask the question on how likely that the Jesus resurrection hinges on the probability of the body being stolen or reanimated, which to reasonable people it is a likely explanation. But to a Christian who believes that Jesus is the son of God, and as such, can resurrect. In other words, to that Christian the probability of Jesus resurrecting is 100%. You can see on that presumption what the BT would give as a result. Using the BT in debating with that Christian would get you nowhere. In fact, it might very well backfire on you. People like William Lane Craig are already doing that: using the BT to justify their beliefs. You might argue that they are applying the BT incorrectly. The point should be: you can’t use it. Period.

That isn’t how any logical syllogism works.

All empirical claims are probabilities. “Bayes’ Theorem” is just the correct logical way to do logic with probabilities. You can’t avoid it by doing something else.

So either you admit you cannot say whether anything is true or not (like whether Jesus existed or Julius Caesar crossed the Rubicon), or you admit you are getting a probability of that “somehow.” And there is only one way to do that: Bayes’ Theorem. I prove this in Proving History if you need to review that.

Like any logical syllogism, all BT does is tell you what has to be true when you grant certain premises. It thus prevents you making logical mistakes and thus forces you to actually say what your premises are, and why they are that.

Hence you still have to justify those premises with facts. The probability inputs in BT are premises. They are not arbitrary, but based on evidence and argument.

If you read On the Historicity of Jesus you will see how this works. That book also explains what you would have to do to get different premises (different probability assignments), which means what evidence (what facts) you need to justify different assignments.

This is where the objective grounding of all conclusions come from. The same way as with every other fact-claim.

Bayes’ Theorem is based on the assumptions that one deals with real events in space and time, that these events can be verified by any team of experts on the planet, and that one can establish the probabilities of these events to occur in some objective fashion. Otherwise it is an exercise in futility.

Paul does not mention Kephas separately “from being” a Brother of the Lord: he says he is an Apostle. All Apostles are Brothers of the Lord. So Paul didn’t have to “double identify” him.

The only distinction Paul draws is between apostolic and non-apostolic brothers of the lord. This is, in other words, just the word Paul used for “Christian.” He does not need to “add” that an Apostle is a Christian. Everyone knows that. He only needs to add that the other guy he met, who wasn’t an Apostle, was nevertheless still a Christian. But the word “Christian” hadn’t been invented yet. All Paul knows to call his fellow Christians was Brothers of the Lord. That’s who they were.

By contrast, Paul never once anywhere ever refers to biological brothers. He clearly had no idea he had to; the only brothers he knew, as he does say, where cultic. So there simply isn’t any evidence for your contention. The evidence is to the contrary.

As to Josephus, the evidence is extensive that he never wrote that. But even if he did, there is no evidence he knew the difference between cultic and biological brethren. As all baptized Christians are Brothers of the Lord, Josephus’s source would simply have called any Christian a Brother of the Lord, hence of Jesus Christ. There is no way to know how Josephus would know that was a cultic designation and not a biological one. So we can’t tell which kind of brother he means there.

I don’t know the relevance of the rest of your remarks. I actually say exactly the same things myself in On the Historicity of Jesus. They have no bearing on the above question.

No, I just pointed out that Paul mentions Kepha separately from the “brothers of the Lord”, that’s enough to show that Paul can distinguish between general “brethren” and actual biological brothers. Plus there’s Josephus who mentions James or Jacob or however you want to spell his name. Occam’s Razor: we shouldn’t multiply causes beyond their necessity. Jesus’ teachings aren’t super strange when taken together with the DSS, later Rabbinic teaching, etc. We only have seven surviving writings of Paul: there are more that he wrote that we do not have and that may contain all the extra nuances that we want.