I posted a couple of weeks ago. I’m not sure if you receive the post.

Everything you’ve submitted has been cleared through the queue.

Models such as yours involve deriving numbers from non-numerical data, a process of numerisation.

False. I have countable data for my prior, and I frame all my likelihoods in terms of countable data and expectancies.

If you think there is something incorrect about my counting, then you need to pick an actual example and explain how the count is different than I estimate.

You have yet to ever do so.

My objection to your use of Bayes’ theorem has nothing to do with its internal consistency, or the soundness of your reasoning when discussing the internal mathematics of it.

This is a lie. You started saying exactly that, and I refuted you. Now you are pretending none of that ever happened. This is dishonest.

My objection is that using Bayes’ theorem has led you to numerise the historical data in a specific way, to give numbers that can be the used as a substrate for Bayes’ theorem. Furthermore it has led you into a branch of mathematics which is particularly intolerant of errors and uncertainties in the numerisation process.

False. It is very tolerant when you allow for those uncertainties in your margins of error. Exactly as I do throughout OHJ. Explicitly.

And that was not your objection originally. If it is your “new” objection, then you have to actually show it: pick a case where my numbers don’t fit historical data, and show what number range would better fit, and why.

My position is that your numerisation process is so weakened by its inexactness, its variability from one observer to another, and its lack of repeatability that it cannot form the basis of any convincing model, especially one where your numbers are used directly in probability calculations.

It’s entirely repeatable. And is explicitly inexact: the uncertainty is built in to my estimating. If you want to show you get different results from the evidence, you have to show you get different results from the evidence.

You have only two options here: show different numbers are more defensible on available data; or show no numbers are defensible on available data. The latter gets you historicity agnosticism: if no probabilities can be estimated, then the probability Jesus existed cannot be estimated. This is absolutely necessarily the case: as I demonstrate in Proving History, Chapter 4. As I have said to you, repeatedly. Stop ignoring me.

This leads me to think that neither of you understood what I’m actually suggesting which is not to develop a new method using the same input data but to develop a different method of numerisation and then build the mathematical model around that method.

You have to. You cannot say “Jesus probably existed,” which is a mathematical statement, and not be able to justify that statement. And as it is a mathematical statement, only a mathematical justification is possible for it.

So by what means do you derive the conclusion “Jesus probably existed”? If it’s not Bayes’ Theorem, then what is it? And how is it logically valid?

You can’t dodge this question. If you cannot show you have any logically valid way to get that conclusion, then you have no logically valid basis for asserting that conclusion. By contrast, I have shown I have a logically valid way to do that. So you have none, I have one. One beats zero.

These are your options.

There are no other options.

We have told you this repeatedly.

Stop dodging what we keep telling you.

Many mathematical models ultimately fail to be convincing. When they fail, they all fail in the same way. There is never a problem with the internal consistency of the model because that part of the modelling process is easy. The problem always arises with the interface between the model and reality. Models such as yours involve deriving numbers from non-numerical data, a process of numerisation. It is this numerisation which is the most vulnerable link in your chain of reasoning. This is such a significant issue that most modelling exercises concentrate on optimising the numerisation process and justifying it rather than on the internal mathematics of the model.

My objection to your use of Bayes’ theorem has nothing to do with its internal consistency, or the soundness of your reasoning when discussing the internal mathematics of it. My objection is that using Bayes’ theorem has led you to numerise the historical data in a specific way, to give numbers that can be the used as a substrate for Bayes’ theorem. Furthermore it has led you into a branch of mathematics which is particularly intolerant of errors and uncertainties in the numerisation process.

My position is that your numerisation process is so weakened by its inexactness, its variability from one observer to another, and its lack of repeatability that it cannot form the basis of any convincing model, especially one where your numbers are used directly in probability calculations.

Now Johan says I should demonstrate an alternative method that uses the same input data and produces less wild swings in the output. He also says he does not believe it is mathematically possible and you have agreed with his point.

I had previously assumed that a Scholastic estimate of p(e|h) would be the same as a Scholastic estimate of p(h|e). You rejected this assumption and I accept your rejection of it. That in turn also means that I too agree. It is not mathematically possible to do what Johan asks.

This leads me to think that neither of you understood what I’m actually suggesting which is not to develop a new method using the same input data but to develop a different method of numerisation and then build the mathematical model around that method. This is what we commonly do when building models for non-numerical data. We concentrate on modelling the weakest link in the process, numerisation, rather than on some underlying theory of epistemology about the data itself. And such methods lead us into areas of mathematics like ranked statistics or fuzzy logic where the models do not describe either the theories under test or any philosophical understanding of truth, but rather the numerisation process and its susceptibility to errors and bias.

The first task in such an approach would not be to develop a model but rather to agree a numerisation process. This would have to give at least some form of consistency between observers. There is no prospect of your method achieving this consistency but alternative approaches may do. One would be to consider arguments in turn and decide whether they support or detract from historicity. This first attempt may be easiest to gain consensus on but there are likely to be issues about how much weight to place on different arguments so it would be necessary to add some indicator of argument strength.

If that could be achieved, and I am not at all sure it could be, then an appropriate mathematical model could be easily developed to analyse the resulting numbers.

Thanks, Johan.

Superb point.

Patrick Mitchell wrote:

“Any method that allows minor adjustments to multiple pseudo-formal *probabilities* as you aptly wrote it, leading to wild swings in the result is never going to achieve that.”

For that claim to make any sense, you would have to demonstrate an alternative method that, for the same input data, leads to less wild swings. You have not done that, and I do not believe it to be mathematically possible.

You are blaming the method for the fact that there is wide disagreement. That is not a flaw in the method, rather the method is simply reflecting – and clarifying – a disagreement that would be there regardless of the method used. Any method that did not “swing” wildly in the face of profound disagreement would be fatally flawed.

You can’t say my upper bound is too low, if you can’t explain how any of the premises that entail that are false.

That’s how logic works.

I’m not the one avoiding issues here. You are. You’ve avoided admitting all the errors I caught you at and called you out on. And now you’ve dodged, into a new whack-a-mole game, into some other argument about how you can prove Jesus probably existed without ever doing any logically valid probability reasoning. Which is inherently illogical. And here you just assert that my pro-historicity estimates are too low. Just “because.” Without any evidence or argument that they are too low.

That is dodging logic. Not using logic.

You can’t say “Jesus probably existed” and not be making a mathematical statement. That the word “probably” is in English doesn’t make it not a mathematical statement. There is no escaping that fact. You cannot say Jesus probably existed, and not be able to show mathematically that he probably existed. If you can’t show mathematically that he probably existed, you do not know he probably existed. By definition. This is already obvious, from the definition of “probably.” But again, I formally prove it in Ch. 4 of Proving History. And yes, when historians refuse to admit they are making mathematical statements, they are rejecting logically necessary facts. And that’s a problem for the field as a whole. See the analysis, again, of Aviezer Tucker.

There is no logically valid way to reach conclusions about what probably happened in history without making assertions of mathematical probability. Even if those assertions are in English and vague.

You are right in that this is a totally pointless debate. I hold that there are two alternative methods that give the same result. You hold that they boil down to the same method and so give the same result.

But, you have user this pointless debate to repeatedly avoid answering the issues that I have repeatedly raised. Your estimates are not independent for the reasons I previously given and also because they all involve an element of judgement and they were all made by the same person, you, and moreover there is reason to believe you have axe to grind and therefore there is concern about a systematic bias.

You point out that your treatment of historicity is being very generous and so if there is any bias it’s towards rather away from historicity. That is true but there’s a reason for that isn’t there Richard.

That reason is that you needed your probability results to be as they are. The lower bound needed to be low and you made it good and low. The upper bound was more of a problem. It had to come in under 50% or evens but if it was too far under it would make the overall result too far from the mainstream scholastic consensus be taken seriously. You felt that odds of 2-to-1 against historicity was about right. So you got the upper bound to come in just on the right side of 2-to-1 odds. This was easy to do because small adjustments to multiple probabilities using your model lead to large changes in the result. It had the happy side effect of making you appear generous towards historicity but that was not its purpose.

Now only you know whether or not you did this, but no amount of protestation and abuse will make any difference. You need to show that you didn’t do this and you can’t can you? Because if you could it would have been in the book.

Your approach is analogous to that of David Baggett when he used probability to “show” that the resurrection happened. The ease of doing this and the difficulty of detecting it is the very reason why you should not use formal probability calculations without addressing their assumptions.

It’s a pity, really, because otherwise you made a good case.

All that is true and you cite an an amusing example that I shall look up. The problem here is that you need to have a method that reflects scholastic issues that are not numerical, a method where, if you must use numbers, you use categories that are broad enough to allow a fair consensus between scholars. Any method that allows minor adjustments to multiple pseudo-formal *probabilities* as you aptly wrote it, leading to wild swings in the result is never going to achieve that. And that’s basically the reason why most scholars don’t do it. There are areas of scholarship where precise mathematical analysis is appropriate and very powerful, such as in statistical textual criticism, and the growth of such methods has meant that scholars are aware of them. In general it’s not ignorance that stops them it but prudence.

If we came up with a method which allowed us to sit around a table with historicists and agree rules and values with them, and reach a conclusion that none of us could escape, then we’d be onto something.

Patrick Mitchell wrote:

“You then look at the evidence sequentially and when each item is considered, you adjust probabilities away from or towards the default position. These adjustments are usually cumulative rather than geometric.”

I have seen this done in a reasonable way, but then it is not dealing with *probabilities*, but rather just with a very simple overview of available evidence. If you do this with probabilities, you are doing it wrong. I have an actual live example to illustrate where such nonsense leads:

A Swedish man, Thomas Quick, confessed to a large number of murders and was convicted of eight of them. After journalists investigated, it was found that he had been encouraged to give false confessions while under psychiatric care, and that the evidence presented in the trials had been skewed and deeply flawed. His convictions were all overturned, and most observers agree it is highly unlikely that he was involved in any of them.

However, Göran Lambertz, a justice of the Swedish Supreme Court, could not let go of the case, and has vigorously and publicly kept arguing that Quick is guilty. In a book, he gave probabilities for various evidence he believed were indicative of Quick’s guilt, and summed them. Just as you describe. He concluded that the probability of Quick being guilty was 183% (yes, he actually wrote that himself).

After being ridiculed for this, he updated his calculation using Bayesian calculations, arriving at a conclusion that is at least not *mathematically* insane.

“Garbage in – garbage out is how programmers express the problem.”

But that problem does not in any way diminish if you use bogus math. Lambertz above has absolutely ridiculous arguments, but his flawed math made the problem even worse, not better. Moreover, if you believe the arguments to be “garbage” then you need to provide arguments for this, rather than attacking the mathematics used.

Patrick, you started with a video making claims about Bayesian reasoning and probability theory. Those claims were false. And worse, they betrayed an ignorance of even basic principles of Bayesian reasoning and probability mathematics. I pointed that out in my article.

Now you are making shit up about some other method no one has ever heard of and that I never used and that has no demonstrated validity anywhere. That’s not what you were talking about in your video.

So please admit you fucked up. Before continuing this tedious exchange. If now you want to change the subject and argue that you have a better method than Bayes’ Theorem for determining how likely a hypothesis is, you need to actually do that: prove to the field of mathematics that you’ve discovered a better way of doing that.

Otherwise, admit you have no idea what you are doing.

You then look at the evidence sequentially and when each item is considered, you adjust probabilities away from or towards the default position. These adjustments are usually cumulative rather than geometric.

That’s the Bayesian method. It’s called starting with a neutral prior and updating the priors as evidence is added. Each iteration converts the added e into the contents of b for the next run of the equation. I explain this in Proving History. Look at the index under “iteration, method of.”

Of course it will never give you a credible answer if you leave evidence out. For example, all human background knowledge has to go into the equation at some point. Otherwise, it will not give you a correct probability. This is indeed how Christian apologetics works: leaving evidence out, so as to get a probability they want. That’s invalid because we have the missing evidence, so we have to put it in—and when we do, the conclusion changes, to what we actually know it to be, because it is arguing from knowledge and not from engineered ignorance: see Bayesian Counter-Apologetics.

A difference is that when you look at the evidence sequentially, you can organise it in different way.

That cannot make any difference to the outcome. If it does, your method is formally invalid.

Thus, order is irrelevant in Bayes’ Theorem, too.

It is clear that Richard organised 0HJ into bodies of evidence rather than arguments …

Every body of evidence is an argument. Every argument is a declaration that some body of evidence changes the posterior probability. They are the same thing. You cannot have a relevant argument for any h, that does not reference any e, or make any assertion about how e increases (or decreases) the probability of h. And Thomas Bayes proved there is no valid way to make such an argument, but through what Laplace later articulated as Bayes’ Formula.

You can’t escape Bayes’ Theorem. The moment you make any claim that the probability of h is P given everything we know, you are making a Bayesian argument. See formal proof, again, in PH.

because this suites the Bayesian approach better but I’m sure you know that David Fitzgerald in Nailed organised the book into 10 arguments, as is more commonly done, as this suits the non-Bayesian approach better.

Dude. That’s just an order of presentation. It’s still Bayesian.

He gives no other equation, and derives probabilities in no other way.

He uses no such baloney method as you describe.

He reasons the way all historians do: each chapter argues from a body of evidence, to a conclusion about the probability of h. And the reasoning he uses is Bayesian (whether he describes it that way or not, and whether he knows that or not).

So the commonest non-Bayesian approach from non-numerical data, such as historical data, is to consider arguments in turn, assess which side of the issue they support, then allocate a numerical value to them proportional to their power and add that value to the side of the issue that they support, there are several ways of allocating numerical values.

That’s arbitrary nonsense. It has no logical validity whatsoever. And isn’t used by any historian, ever, anywhere, in the history of peer reviewed history.

Indeed, the numbers you’d be using in such a method, and getting out of such a method, would be meaningless. And as such, their relationship to each other would be completely incoherent and incapable of producing any logically valid conclusion.

And any attempt to make it coherent and valid, will just convert it into Bayes’ Theorem. Hence I prove one version of the method you describe, the Inference to the Best Explanation—an argument historians actually use and thus one more coherent than this nonsense you just made up—is actually reductively Bayesian: Proving History, pp. 100-03.

You need to stop making shit up.

You have only two options.

Admit all historical methods are Bayesian.

Or show us a logical proof of a method that (a) doesn’t reduce to Bayes’ Theorem and which (b) gives us a logically valid conclusion as to how likely one hypothesis is relative to another. That is, show us the formula, and prove it is logically valid.

That’s it.

Do one or the other.

Or go away.