A childish Philosophical Muser tried claiming there are “errors” in this month’s article on The Historicity of Aristotle. And boy, if only you saw my DMs from this bozo. You will already get an idea from the article I just linked. But his DMs are worse, reflecting someone painfully immature and emotionally irrational, with no interest in learning or understanding or engaging in any kind of intellectual discussion. For him it’s all just screeds and monkey scat. Which I’d normally just ignore as yet more dumb blather. But this is not a random aberration. It’s the mindset destroying the whole world: too many people are acting like this spoiled child; too few are checking their emotions to think and interact and actually learn things so as to understand them like a responsible adult. Too many people now are just raw bundles of emotions barking like savages. And filling the internet with slander.

I already covered a prominent example of this society-wide emotionalism in How Pseudo-Rationality Grounds Conservative Worldviews. Half the people like this can at least act calmly and almost take things seriously. But even they are acting purely on emotion, deciding what to believe on “feels,” and then rationalizing those feels with pseudo-logic and mythology, so as to look like adults being rational. But even for them it’s all appearance, little substance, as I found in my followup, How Being Bad at Reasoning Sustains Antifeminist Mythologies. The greatest folly is that this is the very thing that will prevent them ever admitting this and thus ever growing up to be a real intellectual, who actually thinks, and thus actually learns, and thus actually understands anything. And that’s why it’s all just “galactic clusters are a brain” and “women can’t build things” and “Haitians eat pets.” The world is regressing into drooling cave loons.

But the other half can’t even do the pose well. The Philosophical Muser in today’s saga opens his “response” to my article on Aristotle with two whole paragraphs of straight ad hominem and slander. Not a single thing relevant to the matter. Which is the absolute gutter of irrational thought modes. I responded here, above, with two paragraphs that are, by contrast, factually true and relevant: his recourse to childish slanders replaces thought and is devoid of demonstration; my description of his doing this, and what it takes to do this, describes the actual reality of what he did and why it demonstrates the unreliability of any opinion he could possibly have; and I’ve already shown before that this is a national, even global, problem. Telling the difference between baseless and irrelevant ad hominem and relevant and true documentation of a person’s intellectual values and capacity is one of those things that demarcates real intellectuals from flying monkeys.

So my introduction is itself a teaching example of what isn’t ad hominem and what is. And the main takeaway is that the irrational are the ones who can’t tell the difference. And that is destructive of productive discourse and education.

That out of the way, let’s be an adult, sit the child down, and calmly explain how math works.

How Do Prior Odds Work?

I discuss how to employ Bayesian methodology across dozens of articles here, and multiple academic monographs and conference presentations and journal articles. And many others have done the same (from Nathan Nadeau to Aviezer Tucker, now even in a Cambridge Element, and beyond). The lowdown is simple: the final odds on any claim being true always equals the prior odds on it being true, times the likelihood ratio, which is the ratio between the likelihood of all the same evidence on either competing theory of how that evidence came about. The likelihood ratio I simplify to “the odds consequent to the evidence” or simply “the consequent odds.” And that gets us the Bayesian model of all empirical thought: prior odds times consequent odds equals final odds. That’s it. Sixth grade math. And this describes all arguments ever made about any matter of fact ever, in any field at all (and I prove that by formal syllogism in chapter four of Proving History).

And it all starts with the prior odds: what usually has been the case before?

Muser claims of my Historicity of Aristotle:

His first amateurish absurdity is his invention of reference classes to predetermine the outcome.

This, his first relevant sentence, betrays three failures to read or think, or know what he’s talking about:

• I did not invent reference classes. They are fundamental to all Bayesian reasoning used across thousands of knowledge fields (see What Is Bayes’ Theorem & How Do You Use It?) and dozens of peer reviewed books and articles on empiricism and historical methodology, as documented where I said: in my original peer reviewed study and its ten-year followup study, which both reference my earlier peer reviewed study of Bayesian history, which discusses what reference classes are, how they are formed, and why they cannot be avoided in any other proposed method of doing history (or any other science). Searching the term “reference class” in the context of “bayes” in Google Scholar returns over 3,600 studies and discussions. It’s just simply stupid to act like “I made this up.”
  • Lesson: unlike a child, check your facts, and be honest about what you find. Don’t misrepresent professional facts as “absurd” or “amateurish.” Referencing classing is neither.
• My reference classes don’t predetermine the outcome. In that article I am explicit that I use a fortiori priors that are actually very generous to the alternative, estimating the prior odds on Aristotle of being historical way lower than is realistic and for Jesus being way higher than is realistic, to prevent predetermining the outcome. My exact words (which Muser evidently ignored): “In reality the prior for Aristotle would be higher (here I am using the most unfavorable lower bound of the error margin) while for Jesus it would be lower (I am using the most favorable upper bound … ).” Muser never defends any alternative priors nor explains how my selection of priors “predetermines” the outcome either way. I get the impression he doesn’t care if that is even true. He just wants to say this false thing because he is all emotional about it.
  • Lesson: don’t be emotional; be reasonable. If you genuinely think someone’s priors are wrong, present an evidence-based case for what the priors should be. Don’t just bitch about them not being what you want.

Muser then says:

He begins by dividing ancient figures into two “reference classes” – mythologised superheroes, who rarely exist historically; and ordinary mundane people, who usually do. He immediately places Jesus in the first class, Aristotle in the second, and then declares – based on his own invented categories – that Jesus must start with a very low prior probability of existence.

None of this is true. My selected frequency of existing in the set of all heavily mythologized people could never be described as saying they “rarely” exist or have “a very low prior probability.” I set the value at 1 in 3 (for odds of 1:2). That means heavily mythologized people are only twice as likely not to exist. That’s not “rare” nor “very low.” It’s actually quite common and reasonably high. If thunderstorms struck 1 in every 3 days throughout the year you’d be laughed out of the pub if you said thunderstorms there were therefore “rare” and “very improbable.” It is clear Muser is reacting hyper-emotionally, and thus hyper-irrationally, to the prior odds on Jesus being only mildly low.

By contrast I did assign the absurdly low prior odds on Aristotle existing of just 5 in 6 (for odds of 5:1). In reality, if you added up even just all the merely mythologized people, the frequency of them existing is close to 99%, or 100:1 (this data and calculation has actually been done, also under peer review, by a team led by Kamil Gregor, as I discuss in chapter six of OPH). So 5:1 is indeed absurdly low. Yet Muser is calling that absurdly high, as if to “predetermine” the historicity of Aristotle. It’s clear from this that his analysis of my article is all emotion, no reason, and in result not even remotely accurate but reporting exactly the opposite of what it says and does, and then compaining about that—the thing it didn’t do.

You can’t ever land on truth or reality if you believe articles say exactly the opposite of what they say. So we are seeing a severe failure of intellect here. And yet this kind of failure is becoming increasingly common in the world. And I need to publish this as an example of that I can refer to from now on.

It gets worse:

Even a sketchy understanding of Bayesian probability would show Carrier that this classification is circular – where he’s basically argued: Jesus is mythologised, therefore low prior; mythologised means low prior, therefore Jesus is mythologised. If he had a proper grasp of history, he’d know that historians do not use “mythological superhero” as a category, much less use these invented accounts to lower the prior probability that the underlying person existed. Carrier’s entire Bayesian edifice collapses if his arbitrary priors are replaced by historically grounded ones.

This is embarrassingly confused. Of course my article does give “historically grounded” priors, entirely based on data that has passed peer review multiple times now. It is not circular to observe the fact that “heavily mythologized” persons usually don’t exist. We can count them and develop an actual data-driven frequency of this; and that’s exactly what I did in my original study, with a generous margin of error placing the prior odds on heroes like Jesus existing over a whole third of the entire probability space. The Gregor team’s study improved my results by narrowing that margin, yet ending up within (and thus confirming) my original study’s tolerances, by perfecting its empirical data. Their results now set the frequency of heavily mythologized persons who plausibly existed at 1 in 4, even lower than I assigned in my article on Aristotle, as I demonstrate in OPH.

That is what follows from their actual findings. While their own conclusion was to find that if we add up a common set of merely mythologized figures, the observed frequency of their existing is indeed just shy of 100%. So I was being very generous to Jesus in assigning Aristotle a mere 5:1 odds instead of 100:1. But they erred in placing Jesus in that set instead of the heavily mythologized set, which has a much lower observed frequency of existing. When you correct this mistake, the prior odds on heavily mythologized figures like Jesus existing drop from 1:2 to 1:3 (although, by contrast, the lower error margin rises considerably, but no one usually cares about the lower margin; nevertheless I redo all the math in an appendix in OPH accordingly). The Gregor team produced another paper (so far as I know, neither has actually appeared in print yet) that tried to argue for a different reference class, of “when” heroes get placed in history, but as that was always where in history their cult was believed to have originated, that reference class is uninformative as to historicity (which has no relevance to the “when” of their cult’s origin), and can’t even be constructed (as we don’t actually know when these myths began relative to their cults) and thus is not usable here.

The more obviously applicable classes are simply “heavily mythologized persons” tout court (Jesus, Osiris, Hercules, Moses, Dionysus, Alexander the Great, Mithradates, Apollonius, etc.) and “mildly mythologized” and “non-mythologized persons” tout court (Aristotle, Socrates, Spartacus, Hannibal, Pilate, Josephus, Alexander of Abonuteichos, etc.). Aristotle is not like Dionysus in the way Jesus is; and Jesus is not like Aristotle in the way Josephus is. They belong to different sets of people, with different observed frequencies of being made up. And this is all direct observation: if only 1 in 3 people like Jesus existed, then Jesus starts out with only a 1 in 3 chance of existing; only evidence can prove him one of the exceptions (one of the 1s out of every 3 who did exist after all, like Alexander the Great). Whereas this is not true of Aristotle. Almost all people like Aristotle existed. So it is more than safe to say at least 5 in 6 people like Aristotle existed; and again only evidence could prove him one of the exceptions (one of the 1s out of every 6 who didn’t exist after all).

To borrow his own inept phrasing, “if Muser had a proper grasp of history” (or even just actually read my article and its cited references), he’d know that historians do use “mythological superhero” as a category—variously named, e.g. the Rank Raglan class I specifically use as a proxy to all heavily mythologized heroes is taken as established by all expert peer reviewed literature for decades now, across more than a dozen studies, as cited in OPH. And it is routine among historians to admit that mythic superheroes typically did not exist. All I did was actually count them to see how many did.

Which is more empirical and more precise than all the historians Muser handwaves toward. If Muser wants to get a different result, he has to get better or more complete data, and find that the count is meaningfully different than I already allow. This is what Gregor’s team correctly did. They just counted the wrong ones. But they at least understood correctly that you have to actually count all the examples. You can’t just handwave and replace facts with feelings. The frequency is the frequency as observed. So you need to make some observations if you want to find the frequency to be different than it is. Merely not liking what that frequency turned out to be is to replace professional empirical methodology with reality-denying emotionalism.

In other words, a “historically grounded” frequency of existing is the one derived from an actual count of actual data. And I’m the one telling you what that turns out to be. With actual empirical data—the exact opposite of the “arbitrary” priors Muser falsely accuses me of using instead. So Muser is really just trying to deny that that is what happened (by curiously omitting that that’s what I did from his entire account) and then invent a claim that “no” historians already do this (as if “no” historians think heavily mythologized people are less often historical than mundane ones, when in fact veritably “all” historians do) or that this hasn’t been done by real historians under professional peer review—indeed, multiple times now, with no successful peer reviewed challenge. Distorting reality to bolster your purely emotional beliefs, and thus effectively lying about the scholar you are critiquing and lying about what they did and lying about what other historians think about things like this and lying about what has actually been professionally published under peer review about it, is the kind of pseudo-intellectual rot that is degrading the whole of society. And here we have a prime example of it.

The killer fail is when Muser hilariously straw man’s my argument as “Jesus is mythologised, therefore low prior; mythologised means low prior, therefore Jesus is mythologised.” This is an equivocation fallacy, where Muser has switched illicitly between two different meanings of “mythologized,” and ignored the actual data-driven process he is incorrectly describing. First “therefore Jesus is mythologized” isn’t a statement that he didn’t exist (because historical people are also mythologized). So “Jesus is mythologised therefore Jesus is mythologized” is not a circular argument but a tautology. It’s as true as “Jesus is a man, therefore Jesus is a man.” That Jesus is heavily (not merely) mythologized (unlike Aristotle) is a fact (not an argument capable of being circular). It is a thoroughly, professionally documented fact. The consequences of that fact are that Jesus starts out as likely to exist as anyone else heavily (not merely) mythologized (unlike Aristotle), which is empirically observed to be no more than 1 in 3 times.

Of course that does not mean Jesus only has a 1 in 3 chance of existing. This is the prior probability. Muser seems not to understand this, or what it even means. This is the probability before we take into account evidence particular to Jesus. It’s the same prior probability of existing as Alexander the Great. He also starts out with a 1 in 3 chance of having existed before we consider any evidence particular to Alexander. It’s just that, obviously, when we do take that evidence into account, it’s overwhelming and thus completely swamps the prior, leaving us with a final odds of millions to one. Which demonstrates that this prior does not predetermine the outcome. And indeed this is nowhere more clear than in the case of Apollonius of Tyana, whom I analyze in Obsolete Paradigm and whose final probability of existing I find is not confidently high but higher than for Jesus, enough to make his existence more likely than not, thus again demonstrating that my prior odds for him of also 1 in 3 does not predetermine anything.

Muser is thus just not paying attention. He doesn’t care about what I am actually saying or referencing in my article. He wants to emotionally rewrite reality so that 1 in 3 is “very low” when in fact it’s generously high, that this predetermines the outcome when it routinely doesn’t (and indeed couldn’t), that heavily mythologized heroes exist just as often as mundane people when obviously they don’t, and that an empirically documented frequency is a “circular argument” and “not grounded in history,” all while completely ignoring (and dishonestly failing to inform his readers of) what I actually said, argued, and demonstrated professionally with evidence.

This is SOP for internet goons now: to simply lie about what someone did or said, and never mention what they actually did or said, in the hopes that your audience won’t think to check and find this out. Sadly, most of any audience these days is too stupid to check and find out whether anything they hear or read is actually true, or a lie and hiding from them all the damning evidence of it. And that is the global failure mode ruining the world now. This is just one trivial instantiation of that. But I document this even for academic critics now (because standards in the field of biblical studies have degraded almost to the level of farce) in chapter three of Obsolete Paradigm, with countless examples.

How Do Consequent Odds Work?

Muser then says “he arbitrarily imputes likelihood ratios masquerading as mathematics,” which is false even as written, as I repeatedly explain in that article what makes my estimates non-arbitrary and what evidence would change them; and stating your beliefs in numbers is not “masquerading” as math, it literally is math. Muser has confused formulating propositions in mathematics with being wrong (being wrong does not make those statements non-mathematical) and with stating the empirical basis for estimates with giving “arbitrary” estimates (those are exactly the opposite). An adult would try to argue my estimates should be replaced with different ones, and present the evidence establishing that. Muser doesn’t even comprehend that that’s the only valid critique to attempt here. And then of course he never attempts it.

For example, Muser lies to his readers and claims I just “said” the collection of Aristotle’s writings we have are “100 times more likely,” as if I just made that up out of the blue. Here is in fact the actual statement in my article (I have put the evidential benchmarks in bold, which eliminates Muser’s claim that this estimate is arbitrary):

The probability that all of the extant writings of Aristotle are fakes (given all the pertinent data, internal and external, apart from what follows) cannot plausibly be higher than one percent, because most of what we have is at least a hundred times more likely to be authentic than not. Not even once in a hundred times do we have a vast faked corpus like this, [especially that is] plausibly contexted (internally, and externally, by all the ancient discussions of Aristotle [that are] not already counted below).

In other words, when we have a large plausibly contexted corpus, it is almost never fake. The cases that turn up fake count less than once in every hundred cases. If Muser wants the probability of this corpus being fake to be higher than 1 in 100, then he needs to present evidence that more than 1 in 100 comparable bodies of work are fake (or sufficient evidence to believe this one is fake). Otherwise, the conclusion follows: it is very unlikely for a non-existent Aristotle to have caused this kind of body of work (with all its internal and external markers of authenticity); whereas it is 100% certain on an existent Aristotle. This quantifies to 1 in 100 a fortiori (since fewer than 1 in 100 comparable sets of literature actually are fake, so I am even overestimating this). And this is empirically obvious (we are not awash in fake bodies of work from antiquity; they’re actually relatively rare, if indeed there even are any comparable examples). Which is the opposite of arbitrary.

I’ll put a pin for now in the point I made that this is even so when disregarding the other data I go on to present (note I state that qualification twice here, so it’s impossible to miss it—Muser missed it). When we import that data, this 1 in 100 becomes orders of magnitude less. But I account for that by accumulating that evidence independently, a point Muser also doesn’t understand. But as he treats that separately, so will I. Because that’s a different mistake from confusing an evidence-constrained likelihood with “arbitrarily assigned” likelihoods. That Muser doesn’t know the difference between those, or what that difference looks like, or how one can correct an evidence-constrained likelihood should it be at all wrong, is a separate embarrassment, and a separate example of his acting like a child rather than paying attention. Stay tuned for the other.

Far from “none of Carrier’s ratios are derived from data, statistical analysis, or historiographical practice,” they are all exlicitly derived from data and historiographical practice. If Muser thinks a more careful statistical count of comparable cases would get a different expectancy, then he should produce one. Otherwise, the evidence remains as it is. Merely legendary people in the literate Greco-Roman era almost never generate massive comparable bodies of work that exactly suit their context. And “almost never” is actually far less than once every hundred times. So I’m being overgenerous to deniers of Aristotle’s historicity here (as I also explained).

The same goes for all my other likelihoods.

• The Callisthenes inscription “being a fake is damn near impossible” is an evidence constraint. If Muser wants this likelihood to come out differently, he needs to show us data whereby more than 1 in 1000 Greco-Roman-era inscriptions are fake, in order to claim the probability that this one is fake is higher than that. Evidence constrains my estimate: here, the evidence of fake inscription frequency from the relevant era. It’s directly evident that merely legendary people generate fake inscriptions thousands times less often than real people do from this era. So my saying it happened only a thousand times less often is again being overgenerous to deniers of Aristotle’s historicity. And the only way to gainsay this is to present evidence of it happening more often than that (or evidence that this one inscription is fake—without which we have only the base rate of any inscription being fake). I welcome the effort. That’s how real progress gets made in any knowledge field. I just know such a project is unlikely to get a different result, because I’ve been a professional in this field for twenty years, and I am very familiar with the epigraphic data and why scholars have reached the conclusions about it that they have.
• The attestation by Aristoxenus, “mere years after Aristotle died” that “is not a mythology but an ordinary science textbook” is again not met with a massive body of fake science textbooks faking attestations to people. My estimate that one out of every ten science textbooks attesting to people is a fake is absurdly high. Experts in the field of ancient science well know the rate is closer to one in a hundred. But if Muser wants the frequency to be even higher than one in ten, he needs to show us that it is: present the evidence that, say, one in every eight or five of these is fake. Then that will be the corrected likelihood and we can run the math with that new finding—as I did for Jesus in OPH after the Gregor team published corrected data, their effort being an example of not acting like a child but actually paying attention, understanding what’s going on here and what’s actually needed to change a previous empirical result, and seriously making an effort to do that.
• I did the same with Arrian (“I’ll be absurdly skeptical and say it’s only ten times more likely, again allowing a 10% chance it’s all fake or mistaken somehow”), and all the early sober accounts (“It would be hard to have faked all of this” and “if authentic, none of it makes sense unless Aristotle existed,” halving the ten into five and thus allowing this all being fake to be twice as likely), and all subsequent sober well-sourced histories (which I reduce further to only twice as likely if Aristotle is real).
• That last category of evidence illustrates my point best: I said that “for all the far better material we have for Aristotle to be faked or mistaken, with dozens of otherwise trustworthy scholars being duped by forgeries and legends, is harder to believe” and thus “can’t be any less than twice as likely.” In other words, we have no evidence that this scale of successful dupery for Classical-era events happened a third of the time in antiquity, so it is absurdly generous to deniers for me to say that it did. If Muser wants to claim it happened more often than that, he has his empirical work cut out for him: he would have to prove the entirety of ancient histories of the Classical period (or their contents) are half fake! Since he can’t do that (the evidence just isn’t there), he can’t gainsay my absurdly generous 2:1 (for 1 in 3). I am simply describing the evidence when I say “less than a third” of fake people generated that kind of historical footprint as real people did.

Muser thus lies when he says I gave “no empirical calibration of likelihoods” (I stated the constraining evidence repeatedly) and that my “numbers have no grounding in actual frequencies” (I grounded them all in explicitly-stated empirical frequencies). He also falsely accuses me of “inflating the totals” by counting dependent evidence twice, but he never gives any example of my doing that. There isn’t any. He also lies when he claims “small, uncertain datasets cannot sustain precise Bayesian ratios.” Not only is this mathematically false (small, uncertain datasets can sustain imprecise Bayesian ratios, and as I am arguing a fortiori, I am stating imprecise Bayesian ratios, not precise ones—but Muser doesn’t even understand what error margins are, or that using an a fortiori margin is a mathematization of imprecision), but it’s also factually false: the relevant data sets (all ancient inscriptions, all ancient literature, all ancient historiographic writing, and so on) are huge and very well established, not “small and uncertain.”

The likelihood of a certain cause (e.g. a mere legendary person, or a historical person, the two hypotheses being predictively compared against the evidence here) derives from the background facts of the frequency of such causes producing such effects. Real revered scientists always produce more or less this kind of evidence (even if medieval selection destroyed most of it). Merely legendary scientists almost never do (the frequency of that in the available massive datasets is not always zero, but is definitely low). Muser does not appear to understand what likelihoods measure, or how they derive from extensive field-generated background evidence of what has typically happened in the relevant period. He has no idea what he is doing. Yet he acts like he does. Which is just another kind of lying: feigning a competence you know you don’t have.

A non-childish critique of my article on Aristotle would entail documenting different frequencies of these kinds of things happening then, thus re-calibrating my estimates to a more precise examination of the data. Muser will never do this because (I suspect) he knows the evidence doesn’t go that way, that in fact I am already under-estimating the impact factors of the evidence for Aristotle here. And that would become obvious the moment you started listing and counting relevant datasets, such as adding up all the Greco-Roman inscriptions we have and counting how many are fake. Pro tip: we have over a million such inscriptions; and if you check, you’ll find documented fake or dubious ones are in the low thousands, and most of those are medieval or modern fakes, while the Callisthenes inscription would have to be an ancient fake; the ensuing math does not go Muser’s way (nor would any other math, as I explain in an endnote here). An alternative approach would be to show the inscription I discussed is an exception, with evidence that it is a forgery or a fake. And that means: not armchair assertions; evidence. But Muser does neither.

Either would be an achievement worth publishing under peer review. But I doubt Muser will even try to get either such kind of “study” published under peer review. Because he is not being sincere. I don’t believe he really thinks the frequency of faked inscriptions is any higher than my a fortiori estimate, or that he has any actual reason to believe this inscription is itself a fake. He’s just talking shit. Because he is behaving emotionally, not rationally. Whereas I am simply repeating the state of the field after a century of extensively published research. I am deriving my likelihoods from the evidence. Muser is just gainsaying them because he’s a chest-thumping butt-hurt child. He offers no alternative likelihoods, much less presents any evidence for them.

That this is all an irrational childish bender rather than a serious critique is illustrated here by Muser’s final statement on this second point, complaining that if I heeded his vacuous assertions here (though he never explains how anyone could or what heeding them would consist of) then I “wouldn’t assign arbitrary values that produce a desired outcome of Jesus’ non-existence.” But he only complained about my likelihoods for Aristotle. How would reducing the probability that Aristotle existed increase the probability that Jesus did? There is no logical connection between these two points. It’s thus clear Muser only has “feels” about Jesus being found improbable, and is childishly lashing out at a case for Aristotle because he doesn’t emotionally like how it contrasts so poorly with Jesus, and thus it is an existential threat to something he is emotionally attached to. (Muser also says I don’t “compare incomparable social strata” here, but he never explains what that means or how it would get a different result here either.)

So, should my likelihoods for the evidence I presented for Aristotle be lower than I landed on? How much lower? And why? What evidence do you have that they are lower (not just that you wish they were or need them to be)? If you have no answer, you have no rebuttal to my case. You’ve lost the argument. Adults admit that. Children don’t. And if you do have an answer, adults present the relevant evidence and validly show the effect it has on revising my likelihoods. Children don’t. And that’s how you tell the difference.

Forget Aristotle. What about Jesus?

Muser pauses mid-screed to complain about my case for the evidence for Jesus. But since he is responding to an article about Aristotle, that has no relevance here. If he has complaints about my generation of priors and likelihoods for Jesus, he needs to engage with the extensive evidence we presented for that in our peer reviewed studies. But I know he never will, because he didn’t do it here, even for Aristotle. For example, here he childishly complains that I “artificially reduce[d] all early Jesus evidence to zero by redefining everything as dependent, mythical, or derivative.” This is mathematically inept (obviously no “zero” is involved here, so I never do this; Muser does not appear to understand how the math works here). But it’s also just lying. My finding that a lot of the evidence has dependent likelihood ratios of 1/1 (which is 1, not 0) is not “artificial” but thoroughly empirical and extensively argued.

I also did not find “all” the evidence like that: for some I find ratios against the historicity of Jesus; and for some I find ratios on my a fortiori side to be in favor of historicity: a combined 8/1 in fact (from three items each at 2/1: see the last three chapters of OPH, and its appendix; in reference to §11.9 and §11.10 of the original study and the corresponding sections of Lataster), so all that evidence together could be eight times more likely if Jesus existed than if he didn’t. Whenever a critic reveals they did not know I counted some evidence as for Jesus, then I know they literally do not know what my study actually said and have no idea what they are talking about. It’s the best litmus test: just ask a critic if I counted any evidence in favor of historicity, and then what evidence, and then how much I weighed it that way. If they can’t answer, never talk to them again. They have demonstrated that they are not even interested in knowing what I argued. And thus they will never have any worthwhile opinion of it.

Muser goes on to illustrate this again and again by listing a bunch of evidence that I either already refuted or a fortiori even agree with, thus further demonstrating he has never read my study and doesn’t even know what it argues. He is therefore offering no actual reply to it. He’s just emotionally repeating his beliefs, and not any intellectual evaluation of professional challenges to those beliefs. He doesn’t even know what those challenges are.

What Counts as Independent Evidence?

Muser’s final winge is the accusation that I multiplied the likelihoods “as if each piece of Aristotle’s evidence were independent when they are all connected to the same Peripatetic tradition, preserved by the same Hellenistic libraries, and cross-quoted within the same literary networks.” This is false. I explicitly made each estimate independently of the other evidence (I would have gotten different specific results had I accounted for dependency—but the mathematical outcome would be the same: see my explanations of dependency in OPH, pp. 172–78, and 379–80) whereas each item of evidence’s dependence on a mere “Peripatetic tradition” (as opposed to a real Aristotle) is exactly what I am calculating. That’s how Bayes’ Theorem works.

Muser doesn’t understand what dependent probabilities are or how they multiply together, or how all Bayesian posteriors are a dependent probability. Every probability in every application of Bayes’ Theorem is a dependent probability. And item by item you can run strict dependency in likelihoods by iterating for each item of evidence in chronological order. But when this has no effect on the outcome, there is no reason to do it, because it requires needlessly complex arithmetic, to no improved result. Muser certainly shows no effect to consider here. He does not argue that any item of evidence’s dependency on any other even exists, much less produces a different likelihood than I estimate. And that’s what an adult needs to do if they want to make this accusation seriously.

Muser is not an adult. But he also doesn’t understand how likelihoods even generate. He claims that all the evidence I present is “all connected to the same Peripatetic tradition, preserved by the same Hellenistic libraries, and cross-quoted within the same literary networks.” But that is not a dependency relation between the evidence. That’s a hypothesis of the evidence. He is basically saying, “What if all that evidence was faked in agreement with a single original ‘Peripatetic tradition’?” Which is simply the hypothesis we are testing against the evidence. If Aristotle didn’t exist, then indeed that is the only remaining explanation of all that evidence. So the question is not whether that hypothesis could be true, but how well it predicts each specific item of evidence.

So, if that hypothesis is true, then it still faces the same problem of the rarity of successfully forging isolated inscriptions, for example. Most such mythical traditions didn’t do that. And there is a reason they didn’t: it’s hard to even anticipate the need to, much less succeed at it. That’s why it almost never happened. And that’s why its likelihood is low. Such a thing is simply unlikely even if Aristotle didn’t exist and everything was created by some expansive effort to reify a ‘Peripatetic tradition’. And notice this is regardless of all the other evidence I list—so I am not considering that all that evidence exists when I estimated the likelihood of this inscription on either hypothesis. I am therefore generating an independent probability. There is no dependency with the other evidence.

There is only a dependency on each hypothesis, which is already baked into Bayes’ Theorem. That is precisely the dependency relation we are calculating when we derive the likelihood for each hypothesis: the probability of that evidence dependent on each hypothesis being true—and dependent on all human background knowledge, because each likelihood is P(e|h.b), where the probability of e is dependent on the truth of h and the entire contents of b (such as all inscriptions from Greco-Roman antiquity and their empirically observed frequency of forgery). This is Bayes’ Theorem.

How All Likelihoods Are Hypothesis-Dependent

So if “no Aristotle” is true (and thus “a single mythical Peripatetic tradition” is instead the cause of all the evidence), then what is the probability we’d get such a mundane yet successful inscription forged? It’s very unlikely. Whereas what’s the likelihood dependent on the hypothesis that Aristotle really existed and really did the thing the inscription is an eyewitness testimony to? Well, effectively 100% (minus a coefficient of contingency that is the same on the alternative hypothesis and thus cancels out: see Proving History, index, “coefficient of contingency,” also described in the endnote below). The ratio follows. This inscription simply is more likely to exist if Aristotle did, and all we can debate is how much more likely. Muser doesn’t even debate that. He gives no alternative likelihood nor any evidence supporting one.

Muser’s goof here becomes obvious when we turn the tables. Suppose we had an inscription in Nazareth, dug up from a soil collapse dated to the early first century and thus incapable of being forged afterward, which declared the contents of a now missing ossuary to be that of the messiah Jesus Christ, son of Joseph, lawfully restored to that ossuary after his year’s atonement in the Jerusalem graveyard of the condemned, and payed for by a collection taken by all twelve named and patronymed apostles, with the date of interment. Would Muser be mocking anyone who cited that as evidence for historicity because their likelihoods are arbitrary and made up? Unlikely.

I doubt Muser would even question their assigned likelihoods, or try to document that they should be adjusted somehow in light of the evidence of the frequency of Christian forgery (which is higher than could ever be claimed for Peripatetics: most early Christian literature and archaeology is fake). No. It would be obvious to him that the existence of this find increases the probability of Jesus, and equally obvious to him that its weight would be at least 1000:1. He’d instead be defending me then, and complaining about anyone who said it was less. But that’s him now. He’s the one absurdly claiming it must be less—as soon as it’s an inscription attesting Aristotle and not Jesus. Because, emotionally, Muser can’t have that count as evidence when it’s Aristotle; it’s supposed to only count when it’s Jesus. Which demonstrates his irrationality. His entire critique is built out of pure childish emotionalism, not any reasonable evaluation of the weight this kind of evidence has whenever we do indeed have it.

So the conclusion remains. If Aristotle didn’t exist, there is nothing about the mere Peripatetic Tradition that would assuredly “cause” the obscure Callisthenes inscription. That’s possible. But it’s not probable. It would be a weird thing to fake, and hard to fake so early in the very city full of eyewitnesses. So, how likely would that be? Maybe, say, 1 in 1000? If you want it to be 1 in 100, on what evidence do you claim such weird and difficult results were so common then?

Muser doesn’t even know this is the question he is supposed to answer, much less how to answer it. He’s wholly incompetent here. The funniest thing is that I already refuted his entire article before he wrote it (this almost always happens)—because he is so incompetent, he didn’t actually pay attention to what my article said, and thus he missed my saying in the end that “even if you wanted to be absurdly skeptical and cut every high likelihood ratio down to 10/1, the evidence is still a hundred thousand times better for Aristotle.” In other words, even if we declared one out of every ten ancient inscriptions fake (or just “declared” there was evidence that this inscription was 10% likely to be fake), Aristotle is still a hundred thousand times more likely historical than Jesus.

The same simply follows for all the other evidence. The inscription is not related to any of the other evidence I assigned a likelihood to, so no further dependency relation exists there. It’s independent evidence. It’s all dependent on which hypothesis we are estimating likelihoods for, but after that each item is independent of every other. Even if what it records were in the Corpus of Aristotle, it would still be independent corroboration of that—because it’s always more likely something a text recorded is true if it’s also attested in an inscription that does not cite that book as its source but independent eyewitnesses of the event (as the Callisthenes inscription does). Again, this is obvious as soon as you turn the table (Muser would himself argue that an inscription corroborating a Gospel increased the probability of that being true, and would likely even assign the same likelihood I do).

Likewise, the eyewitness testimony of Aristoxenus contains information that can’t be dependent on either the Inscription or the Corpus, so it has to be evaluated independently: what is the probability the Aristoxenus text was forged or that Aristoxenus lied? It’s not 100%. So, what is it? Again, turn the tables to decide: if we had a mundane eyewitness memoir of Peter attesting his travels with Jesus, what probability would you assign that to be a forgery or a lie? Anything more than 10%? If “No,” then you can’t assign anything more than 10% to Aristoxenus. My assigned likelihood is thus the very one you are agreeing I should.

This no dependency on “a Peripatetic tradition” has any effect on this estimate, because the question is whether Aristoxenus is fake or a liar, not where he got his notions from. On Bayesian reasoning we are assuming Aristoxenus got it from just ‘a Paripatetic tradition’ on the contrary hypothesis, and so we are already accounting for its dependency on that tradition. Our likelihood is a dependent probability in that sense, because it has to be: that’s what Bayes’ Theorem is doing. We then put that in ratio to the other hypothesis, where we assume Aristoxenus got it from being an eyewitness partner of Aristotle, and asking how likely the text we have is then. Those two probabilities then sit in a ratio, to give us the weight this evidence has in attesting that Aristotle existed or not.

Muser seems not to understand any of this.

Similarly, Arrian is completely independent of Aristoxenus, the Callisthenes inscription, and the Corpus. Moreover, he reports he is writing independently of any Peripatetic tradition as well: he exclusively used three eyewitness sources to Aristotle. So the only question is what the probability is that he or they were all lying or fake. That probability does not depend on the existence of a Peripatetic tradition. Whether Aristotle existed or not, the probability that Arrian or his sources are lying or fake is the same. The difference between the likelihood “dependent on” Aristotle existing and the likelihood “dependent on” there only being a mythical “Peripatetic tradition” is simply that probability. Because “Aristotle existing” does not require that evidence to be fake, but “mere Paripatetic tradition” does. The latter is therefore dependent on an assumption that has an improbability. All we are doing is asking what that improbability likely is. And I said the background evidence entails it’s no higher than 10%. And if we turned the tables and had this evidence for Jesus instead, Muser would then agree. He’d flip-flop and defend my likelihood rather than winge about it.

Even when I add in the later evidence, of historians within a century, and then historians later, I then account for the possible dependency on mere tradition rather than factuality by lowballing their likelihoods despite their vast quantity. I am thus doing the thing Muser accused me of not doing: taking this into account. It’s showing up in my math, exactly as it should. I assume Muser wanted this evidence to be all 100% expected on “mere tradition” and thus exactly balanced with “Aristotle existing” thus adding nothing at all to the historicity of Aristotle. Though I expect he would react in horror the moment he realized this meant we have to do the same to all the century-and-beyond evidence for Jesus. But since my article was about pointing out the difference between this evidence for Aristotle and for Jesus, the real issue here is the thing that, again, Muser ignored, and thus childishly hid from his readers: the fact that this category of evidence is better for Aristotle than it is for Jesus.

For Aristotle we have numerous “ordinary attestations … within a century” while for Jesus we have “only overt myths and implausible legends,” a significant difference in evidence quality that must mathematically be represented in the likelihoods. I then give examples proving the point. And conclude “It would be hard to have faked all of this” and “if authentic, none of it makes sense unless Aristotle existed,” unlike the Gospels and Apocrypha, which do make sense if Jesus didn’t exist, and have abundant markers of being faked or fabricated. And surely that difference is “at least five times more likely” if Aristotle existed, based on all our background knowledge of mundane histories and textbooks, mythographies and novels, scientific literature versus religious literature, stylistic and contextual evidence, and so on. So all this evidence remains unlikely even if it all was based on a mere “Peripatetic tradition,” whereas it is exactly what we expect if there was a real Aristotle. And that difference is the likelihood ratio.

This is just as true of “historians who we know in general relied a lot on original documents and contemporary sources,” who are always more reliable than writers who don’t meet this criterion, and “more reliable” is a colloquial statement of the mathematical difference in likelihood between fake and real stuff getting into those histories vs. into mythographies. The more so when they actually quote eyewitness and contemporary documents (no source does this for Jesus). And we have a ton of this for Aristotle, and none for Jesus. And yet I still account all this evidence as weighing only 2:1 in favor of Aristotle existing.

There is no possible way for Muser to claim all this is “just as likely” whether Aristotle existed or not, as we well know, because if we had this for Jesus, then Muser would vilify anyone who said so—and thus vilify himself, as soon as his own argument was turned against him. More importantly, though, this is the case even considering the dependency relation Muser refers to: we are assuming this evidence was all caused by a mythical “Peripatetic tradition” when we compare that likelihood of it with its likelihood if caused by a real Aristotle. We are already taking that into account. The point is that even if this evidence was all caused by a mythical “Peripatetic tradition” it is still unlikely to be what we’d have. It’s unexpected on that hypothesis. Because it requires far too much fakery and dupery to produce this kind and quality of evidence, but it does not require that much fakery and dupery to produce nothing but fanatical mythography. And we know that from vast empirical experience with how real things and fake things get documented and believed.

And Then the Final Boner

In the end, Muser also gets wrong how priors and likelihoods work.

Muser confuses the fact that we have evidence specific for Alexander the Great that keeps his posterior probability high with meaning his prior probability should also be high. It’s the other way around: if all we had were the wild myths of Alexander, his prior and posterior probabilities would be low, and all historians would agree—as they do for Hercules and Osiris, for example. The only reason we conclude Alexander existed is because of the evidence specific to him. Therefore, mathematically, his prior probability, which is the probability prior to considering all that evidence, cannot be affected by that fact. It therefore would not go up. It would stay low. It would remain in fact exactly what it would be if that evidence didn’t exist.

That’s literally the point of the prior probability.

Only when we add that evidence does it go up, but that’s then the posterior (not the prior) probability; and all of the change from the one to the other is in the likelihood ratio, not the prior. Alexander’s prior stays the same as for Jesus, which I set at 1 in 3 in my article on Aristotle, same as my original study (it has since been reduced to 1 in 4, as I there explain, but I set that aside to argue a fortiori). That Muser doesn’t know this shows he has no actual understanding of Bayesian reasoning or mathematics, and thus is not at all qualified to critique any application of it.

This is also demonstrated by the fact that he didn’t know my likelihoods for Aristotle not existing already take into account that evidence’s dependency on “a Peripatetic tradition.” He didn’t even know that this is always the case, that it is literally what you are doing when you estimate likelihoods in Bayesian reasoning: you assume the one condition is true (“Aristotle existed”) and then assess how likely the evidence would be dependent on that being the case; then you assume the other condition is true (“it was just a Peripatetic tradition”) and assess how likely the evidence would be dependent on that being the case; and it is the ratio between those two likelihoods that tells you whether that evidence argues for or against either condition (or neither), and the size of that ratio (the difference between those two likelihoods) tells you how weak or strong that evidence is for that conclusion.

The only independence we need to assure is that we are not citing evidence as independent that is fully dependent or not assuredly independent of evidence we are already assessing. So, someone quoting the Gospels is only proving the Gospels exist, not that what they say is true. Whereas when someone is quoting a different eyewitness to Aristotle than someone else is quoting, that is giving us independent testimonies to Aristotle’s existence. The one arguing Aristotle nevertheless didn’t exist therefore needs to posit that this is an accident of some convoluted process of lying or forgery, an ancillary hypothesis historicists have no need of and thus aren’t dragged down by. The degree to which the Aristotle historicity denier is dragged down by these unproven suppositions is precisely measured by their collective improbability, which is reflected in the likelihoods (and trying to hide that by pretending the suppositions are instead givens only moves the improbability back into the prior).

Muser understands none of this, and thus isn’t even capable of articulating a relevant critique of my article. Yet the nature of the internet is such that anyone can stumble across his article and mistakenly believe he has made a relevant critique, based solely on his arrogant confidence and blustering posture—in other words, based on emotion, rather than fact. It is not worth the bother of responding to every crank, loon, and idiot like this. It is barely worth the bother of responding to any of them. But here I wanted to make an example of this one that I can point to as typical of everyone like him, and thus what is needed to not be duped by their bullshit. While in that process I can use his garbage as a foil for teaching important principles of how Bayesian historical reasoning really works.

Conclusion

I am coming to realize that a common thread binding all cranks, hacks, trolls, and idiots, and all propagandists and apologists, is a cooption of the appearance of rationality over its substance—hence, literally, pseudorationality. They will construct arguments that share the seeming form of real arguments but lack the requisite features that would make it real and not bogus. One of the most common forms of this is accusing someone of lying or being incompetent, or a crank or a loon, without any real evidence—which looks like a valid point against them, except, without real evidence, it fails to meet the rational bar of actually being a valid point against them. It only satisfies the emotional bar, as people biased against its target will simply believe any accusation whatever, and never ask for evidence. Which means that they do not form evidence-based beliefs. And this defines them as a person. It’s not just an occasional mistake. It is a property of their immoral character. And it is indeed immoral to behave this way, because it is irresponsible—and you know it is irresponsible. For you will complain the moment this same irrational emotionalist fallacy is turned against you or someone or some thing you like.

Muser’s opening and closing are full of false accusations like this. He documents or demonstrates not a single one. Look for the evidence. He doesn’t present any, outside demonstrable lies. By contrast, I have clocked Muser as a liar and a crank, a pure emotionalist with no competence, in either Aristotle or ancient history or Bayes’ Theorem or even math, or even in baseline rationality. But unlike him for me, I have presented extensive evidence that these assessments of him are true.

And I know that because he is irrational and a child, he will ignore this distinction and accuse me of hypocrisy or a double standard, or attempt some tu quoque “both sidesism” fallacy, sliding right past the fact that the difference is that I proved my case; while he merely asserted his. His accusations are false. Mine are true. And that is empirically confirmable. I have provided you with all the evidence, or ample breadcrumbs to it. So you can check this yourself. And if you care about the truth, and care about being a rational and honest person, and only heeding rational and honest people, if you don’t already see that this is obvious, then you will put in the effort to find out. But if you are an emotionalist child like Muser, you’ll just pick a side based on feels and not facts.

And that is the core wedge that divides our nation and the world on almost any issue whatever: which sort of person you are. One who checks. Or one who just believes what they feel. One who wants to really understand something, and thus endeavors to. Or one who doesn’t give a shit about understanding anything, but only pretending to. And you need to figure out who is who.

⌘

Endnote: For those who want to get hyper-technical: the precise likelihood of the Callisthenes inscription (or any other evidence here) is not necessarily the frequency of fake inscriptions tout court, but the frequency with which mythical traditions produce fake inscriptions (and that means not “an” inscription, but an inscription pretending to be authentic and contemporary). But in the absence of any evidence that this frequency would differ from the frequency of fake inscriptions generally, the likelihood is, so far as we know, simply the frequency of fake inscriptions altogether. Conversely, the frequency of a real person causing an attesting inscription is not precisely 100%, but 100% times the contingencies of producing an inscription at all. But that latter probability is always the same on either hypothesis, and thus cancels out, leaving the likelihood “given the contingencies producing a particular inscription,” which is ≈ 1 for real events and < 1/1000 for fake ones, which is why experts correctly assume attesting inscriptions are usually real. That’s why they exist: it’s usually real events that produce them. To argue that we could not tell if an inscription is real is to say that it’s 50/50 (the likelihoods are the same) that any inscription is real. Which is obviously, on all observed evidence, not the case. One could try to move the numbers around, and say that real events outnumber fake ones by a thousand times while each is as likely to produce an attesting inscription, but that cannot change the mathematical outcome, as you are just relocating the improbability of an inscription being fake from the likelihood to the prior, which makes no difference to the outcome.