Monthly Archives: November 2011

Christian Intolerance?

Courtesy of Reddit, this is an email someone received from a religious parent:
Subject: You and [girlfriend],
Hi [boyfriend],
I see that you and [girlfriend] are ratcheting up your relationship. As I said before, this puts your family in a very difficult situation.
Althought it seems you have made up your mind about this, I want to make sure that you are aware of the scriptures on this.
The most helpful passage about marrying an unbeliever can be found at 2 Cor 6: 14 Do not be yoked together with unbelievers. For what do righteousness and wickedness have in common? Or what fellowship can light have with darkness? 15 What harmony is there between Christ and Belial[a]? What does a believer have in common with an unbeliever?
Besides this there are numerous Old Testament passages in which Israelite men married non-believing women from other nations, always to the displeasure of the Lord. For example, in Ezra 10, Israel is rebuked for their marriage to foreign wives: 10 Then Ezra the priest stood up and said to them, "You have been unfaithful, you have married foreign women, adding to Israel's guilt. 11 Now make confession to the LORD, the God of your fathers, and do his will. Separate yourselves from the peoples around you and from your foreign wives." 12 The whole assembly responded with a loud voice: "You are right! We must do as you say.
When you think about it, it only makes sense. What is more fundamental to a person, their values, their world view, their preferences and convictions than their true religious beliefs?
More to the point for the Christian, how can we justify joining ourselves as one with someone who is opposed to what we believe and hold dear, our relationship to Jesus.
I say all this [boyfriend] because while I love you dearly, I am quickly coming to a point where lines must be drawn. As your relationship picks up, so does my unease with the two of you.
I am sorry it has come to this [boyfriend]. I sincerely hope that I am wrong. But nothing I see in your relationship, nothing in the way [girlfriend] presents herself, gives me any hope. And it grieves me that you do not seem moved by this at all. Quite frankly, this has struck me as one of those times when you set yourself to do what you want, regardless of the truth of the situation.
I suggest that you, [girlfriend], and I meet. Unless and until we hear her beliefs about Christ, this uneasy relationship will continue. In fact, it will become worse
Is this intolerance? From my anecdotal point of view, on the outside looking in, it's behavior like this that makes many people see Christians as being intolerant. The sad part is that many Christians don't see this behavior as intolerance, and are confused as to why people think that Christians are viewed as intolerant since they have other behavior in mind altogether when they think of "intolerance".
The above relationship did not last, mainly due to the pressure from this parent. Of course, I witnessed a similar situation happen: A Christian girl was convinced by one of her religious friends to end her relationship with her non-Christian boyfriend for the simple fact that he was non-Christian. Besides that example, I've seen this situation happen more times than just that one instance I wrote about in that blog post; Christians being intolerant of other people simply for not believing what they believe: Protestants refusing to date Catholics, Protestants refusing to date Mormons, etc. (for some reason it's always Protestants in my experience who are the intolerant ones…). Certainly, there has to be some intolerance from the other side too. Atheists who refuse to date Christians, Catholics who refuse to date Protestants, or what have you. But I've just never seen it.
For me, the problem isn't Christianity per se, here. It's religious Christians. The definition of "religious", for me, in the pejorative sense, is someone who thinks that what a person believes is more important than how that person treats other people. If a Christian had to choose between a fellow Christian who treated them badly over a non-believer who treated them well, I would think that a rational person would go with the person that treats them well, no matter what they believe. However, the religious Christian would choose the poor behavior Christian simply because they think that being a Christian necessitates good behavior (and by implication, that non-belief necessitates bad behavior). So a situation like the one between Biblical scholar, and agnostic, Bart Erhman and his wife Sarah – even though it's a marriage between a believer and an unbeliever – is not a relationship between a religious believer and unbeliever.
This mentality probably also explains the poor behavior from "well meaning", yet religious, Christians in their response to the LGBT community. What does it matter if someone is gay as long as they are a good person? But the implication for the religious Christian, again, is that homosexual "belief" (in this case orientation) is more wrong than actual bad behavior. Which, again, seems to be a staple of Protestant belief – the thought that beliefs, in and of themselves, can actually affect reality.
If the god of the Christians is love (1 John 4.8ff), then I would think that this would implore Christians to be more open to love no matter who it came from. But these examples only impress on me that their god is intolerance. The worst part is, that this intolerance will only breed more intolerance: The above Redditor will be skeptical of dating another Christian again since they'll want to avoid having to deal with that intolerance of orbiting religious Christians of a future relationship, just as my friend who had his Christian girlfriend break up with him explicitly told me.
ἐάν τις εἴπῃ ὅτι ἀγαπῶ τὸν θεόν, καὶ τὸν ἀδελφὸν αὐτοῦ μισῇ, ψεύστης ἐστίν: ὁ γὰρ μὴ ἀγαπῶν τὸν ἀδελφὸν αὐτοῦ ὃν ἑώρακεν, τὸν θεὸν ὃν οὐχ ἑώρακεν οὐ δύναται ἀγαπᾷν. – Ἰωάνου Α

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Posted by on November 30, 2011 in economics/sociology


17% of Aussies Think That Jesus Didn’t Exist

Y'know, I'm not sure what I think about this!
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Posted by on November 29, 2011 in historical jesus, jesus myth


An Analogy For the Progression of Science

A while back I was having a conversation with someone who professed to work with undead spirits and the supernatural. As you know, I don't think that appealing to the supernatural is a good explanation for whatever phenomenon we are attempting to describe. As a matter of fact, from a Bayesian point of view, it's much more likely that a naturalistic explanation that has an intrinsically higher prior probability, that can also explain the phenomena, is the better candidate for explanation.
I didn't actually get into a full-blown arguement with this person, I just sort of asked some Socratic-dialog like questions to see if she could quell my skepticism. One of the things I asked was how it was that these ghosts and other supernatural beings intake useful energy and release non-useful energy. She didn't seem to understand what I was asking, so I used a car and the human body as an example. Gasoline/food goes in, heat/methane/CO2 goes out. She simply asserted that supernatural beings consume "electromagnetic energy". This was an obvious attempt at using the literary genre of science to make it sound like she was doing actual science, but I obviously saw through that (i.e. I asked "what do you mean by that?" but she couldn't answer, since there are multiple types of E-M radiation).
What she then said was that science was wrong in the past, so it will probably be wrong in the future, and used the shift from a geocentric view of the universe to a heliocentric view of the universe as an example. "Laws of physics" she said, "were completely overwritten in the past, so they will be overwritten in the future". Therefore, she will be vindicated in some future physics that will show that her beliefs were always compatible with science. I actually do think that will happen, but not from the physical sciences. The part of science that will shed light on why she believes what she does will probably come up in neurology and psychology, or other areas of cognitive science, not from the physical sciences. Well, that part is already available, it's just that this scientific knowledge hasn't become common knowledge. Yet.
Anyway, if I had been thinking faster, I would have corrected her misrepresentation of the progression of science with the analogy I'm about to write. But all I could say was that previous theories were never really overturned, it was just that newer theories were less wrong than previous ones.
So yeah, here is the analogy: Imagine you live in an apartment building Harlem and you attempt to draw a map of all of New York City. Let's say you've never been outside of the block that your apartment building is on. This map might be accurate for say, your immediate neighborhood, but it won't be accurate for all of NYC. Let's say, then, that you decide to walk a 10 block radius around your apartment. Again, this map might be more accurate than your previous map; it will be accurate for the 10 block radius around your apartment and a bit beyond, but it still won't be accurate for all of NYC. Next, let's say that eventually, you decide to walk all around Manhattan island and then attempt another map of NYC. Again, this map will be more accurate than your previous maps, but it won't be accurate for the entirety of NYC.
Each update to this map, as you explore more and more of NYC with your own eyes, will be more accurate than your previous maps until you've been to all of NYC. Moreover, you will be able to see the logical evolution of these maps and why the previous maps got what they got right and got what they got wrong. No successive map will be completely unrelated to a previous map. Furthermore, each map follows a Bayesian updating scheme, where new information is included into previous information.
The scientific model of knowledge progression that the psi-ist person was promulgating was a wholly unBaeysian progression of science. As Isaac Azimov wrote, they think that one day science will say that the Earth is a sphere, and then the next day science will say that the Earth is a rectangle, the next day a trapezoid, the next day a donut, etc. None of those models has any logical progression between them, and none of those models follows any sort of Bayesian updating. They are just random.
So the next time I encounter someone who attempts to appeal to some future physics that will one day vindicate their psi beliefs, I'll have to remember to use that map analogy to set them on the correct path. Hopefully, any reader(s) of my blog will do the same 😉

Religious Experiences Are Actually Evidence Against The Existence of God

Before I go over why I think the title of this blog post is true, let me go over the case of Oliver's Blood again:
In Bayes' Theorem, the Likelihood Ratio is how likely your hypothesis is in relation to all other hypotheses posited, and also shows how strongly the evidence favors, or disfavors, your hypothesis. This is simply dividing P(E|H) by P(E|~H). Let's say we're presented with the following scenario:
Two people have left traces of their own blood at the scene of a crime.  A suspect, Oliver, is tested and found to have type O blood.  The blood groups of the two traces are found to be of type O (a common type in the local population, having frequency 60%) and of type AB (a rare type, with frequency 1%).  Do these data (the blood types found at the scene) give evidence in favour of the proposition that Oliver was one of the two people whose blood was found at the scene?
So in this scenario, if Oliver accounts for the O type blood, then one unknown person accounts for the the AB. This gives us the P(E|H) = 1% or 0.01. You may say, at this point, that it fits the hypothesis of Oliver being there, since if Oliver was there, and he left blood, then at least one of the samples of blood would be type O.
On the other hand, if Oliver is not guilty, ~H, then this gives us P(E|~H). Or that two unknown people left blood at the scene. What is the probability of finding the evidence at hand if Oliver is not guilty? This means we have two people at random who at each random selection has to account for either the 1% or the 60%. This becomes 2 * 0.01 * .6, which is 1.2% or 0.012.
As you can see from this chart, a Likelihood Ratio that is lower than 1 means that it slightly supports the hypothesis that Oliver is not guilty! Or in other words, there's a higher probability of finding the evidence that we have if Oliver were indeed not at the scene of the crime and two other random people committed the murder. Going back to the simpler form of Bayes Theorem, P(E|H) would be the 0.01 and that is denominated by P(E). P(E) in this case would be the probability of finding the evidence at hand period, which is 2 * 0.01 * .6, which is 1.2% or 0.012. Again, P(E|H) < P(E). So even though the evidence intuitively fits the hypothesis that Oliver is guilty, it is more likely, due to the math implicit in the evidence, that Oliver is not guilty.
So I was just reading over my last post Extraordinary Claims Require Extraordinary Evidence. And like I said in that post, most people are convinced of the truth of their particular religion due to a religious experience. But what is the rate of false positives for religious experiences? What is the probability that if we polled a random person from the planet that their religious experience would be evidence for the "true" religion (whichever is) or the "false" religion?
We can actually get a rough estimate for this. Again, think about the totality of human existence. Most people who have ever lived – from the ancient Greeks, Aztecs, modern Hindus, Buddhists, Jains, etc. – have had religious experiences. To be a Christian (as an example) and think that only Christians have had religious experiences – the inner witness of the Holy Spirit, or the Burning in the Bosom – would be a pretty arrogant claim. Jews and Muslims, as well as Hindus, ancient Mayans, modern Native American shamans, etc., must have all had religious experiences that gave them absolute conviction that their faith is true.
Now if we actually do a rough estimate of all of these religious experiences, both modern and ancient, then from a Christian point of view, the overwhelming majority of religious experiences have actually pointed to the truth of some other religion. Equally so from a Muslim point of view, a Zoroastrian point of view, a Mithraist point of view, and on. This means that our P(E | H), the probability of having a religious experience given the truth of some religion, is insanely low, because the vast majority of people who have had religious experiences were not Christians (or Muslims, or Hindus, etc).
It would seem that this conditional probability is denominated by a much higher P(E | ~H). In this case, P(E | ~H) would be that physiological hiccup I mentioned in that "Extraordinary Claims…" post. It would even be lower than bare random chance (50%). And if the denominator is larger than the numerator, the Likelihood Ratio is lower than 1. This gives us an equivalent scenario to Oliver's Blood: Religious experiences are actually evidence against the hypothesis of the truth value of some religion, even though it might be intuitive to think the opposite.
So not only is the prior probability of the existence of the truth of some religion insanely low to being with, religious experiences actually make that probability even lower.
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Posted by on November 22, 2011 in Bayes


What’s Really Wrong With The Middle East

I don't have anything to add to this article, and I obviously don't have access to the interior of the Arab world to corroborate, so I just thought I would post some highlights from this article:
[There are] three concentric circles that complete the picture of the current Middle East.  What makes these circles all the more significant is that they all touch upon religion.
The first and most important of the circles addresses the Sunni-Shiite divide… …The second circle involves the recent uprisings in the Arab world, better known as the “Arab Spring,” which have granted power to Islamists everywhere, and made the Sunni Muslim Brotherhood (or affiliated parties) the dominant political force in Tunisia, Egypt, and now in Syria… The intolerance of the MB towards non-Muslims (Jewish Israel for instance), Christians and Shiite Muslims (whom they consider as “errant” Muslims) is connected to the first circle. The third circle is that of the conflict between Arab countries as well as non-Arab Muslim countries (Iran and Turkey) and their ethnic and religious minorities.  These include the Jewish state of Israel, the Coptic Christian minority in Egypt, the Kurds in Turkey, Iran, and Syria, and the Sunni Baluch minority in Iran as well as the Ahwazi-Sunni Arabs in Iran.
What the three circles have in common is religious and ethnic hatred and intolerance…
Israel, an advanced Western democratic state, gets a disproportionate amount of press and criticism, to the near exclusion of coverage and analysis of intolerant Arab-Muslim states by the mainstream press.  The ease of access Western journalists have in Israel compared to the absence of secure access in the Arab and non-Arab Muslim Middle Eastern states, makes for unfair and inaccurate reporting in the Western media, which results in holding Israel responsible for the lack of regional peace.  Moreover, secular western reporters and editors, who are disconnected from religion, fail to grasp the overarching role religion plays in Middle Eastern conflicts.
Contrary to the reportage written and distributed by Western media sources, conflict in the Middle East is less about territory and almost entirely about religion. True also for the Arab (Palestinian)-Israeli conflict is that its foundation is in Islamic religious intolerance rather than territory or Palestinian victimhood (Palestinian Arabs could have established a sovereign state under the Peel Commission in 1937 over 72% of Mandatory Palestine, and again under the UN Partition Plan of 1947.  They rejected both plans with the demand for all of Palestine or nothing — no compromise with infidels). Palestinian Arab-Muslims seek to replace Israel rather than live side-by-side with it.  And, the Israeli-Palestinian conflict, which is fueled by arms, funds, and propaganda provided by Shiite Iran and Sunni Saudi Arabia to the Palestinians against the Jewish state, still pales in importance, to Shiite Iran’s encroachment and hegemonic ambitions in the Gulf.
I think the whole article is worth reading, and it's only two pages so it's pretty short.
Now, I don't think that getting rid of religion will rid the world of all our problems. All of our problems are human problems that, by themselves, have nothing to do with religion. What religion does is intensify all emotion that humans have towards something. If it's love, then it's more intense love. But if it's hatred, it's more intense hatred.
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Posted by on November 21, 2011 in economics/sociology


The Nazis Were Atheists and Darwinists

On the contrary, Nazi racial ideology was religious, creationist, anti-materialist, and anti-Darwinian in nature. Some highlights from that blog post: 
Chamberlain is totally dismissive of the Darwinian idea that man could ascend from “a bestial past” and that “… natural selection, in its blind choice, is forsooth to transfigure us into an exalted being”.

This passage is worth quoting more fully, since the usual accusation is that the Nazis took from Darwin an idea of using selective breeding to create a “master race”. Chamberlain, the foremost intellectual founder of Nazism, totally and explicitly rejects this, instead wanting to preserve the past:

“Darwin specially recommends his theory for our acceptance in that it also promises to mankind that all corporal and mental endowments will tend to progress in the direction towards perfection. I, on the contrary, should have thought that we might have contented ourselves with the gifts of a Plato, a Descartes, a Leonardo, a Goethe, a Kant … how far better this than that we, fooled by delusions out of a bestial past that is no past … should with outstretched greedy hands, without cease or rest, clutch at a phantastic future in which natural selection, in its blind choice, is forsooth to transfigure us into an exalted being, the like of which is beyond the imagination of the great and holy and sublime men of the present generation!”

Thus, to Chamberlain, Nazi theory was not about using selective breeding to perfect a master race, Nazi ideology was that the Aryans were already a master race, and had always been, since an original creation by God. And that the Aryan master race was now threatened by interbreeding with “lesser” races of human, which it was their duty to prevent. This theme was later to make up a large swathe of Mein Kampf.

[Nazis] disliked Darwinism precisely for the reasons that other Christians do, that it points to man as a product of material, natural world, whereas the Nazi’s preferred to regard man as divine special creation endowed with a spiritual soul.
Ironically, the blaming of “atheism” for the Third Reich is itself a Nazi-style tactic: the Nazis blamed the ills of society on Jews, building on centuries of antipathy towards a group that refused to acknowledge the Christian god. Blaming the ills of society and history on “atheists”, as by Ratzinger and other Christians, has the same motive: antipathy towards a group that refuses to acknowledge their god. One can excuse Ratzinger for having joined the Hitler Youth at the impressionable age of 14, at a time when it was expected of all German boys; but he should not be excused for displaying Nazi-style prejudice at an age when he should know better. 
Hitler, and many other Nazis, actually equated Jewishness with atheism
Mein Kampf does not mention Darwin even once. Where atheism is mentioned (twice) it is pejorative, associating atheism with Jews and Marxism (e.g. “They even enter into political intrigues with the atheistic Jewish parties against the interests of their own Christian nation” and “… atheistic Marxist newspapers …”).
It might stand to reason that Hitler hated Marxism (thus Communism) because it was Jewish in origin; Karl Marx was Jewish. Hitler even went out of his way to eliminate freethought organizations:
One of the early acts of the Nazis one gaining power was to disband and outlaw atheist groups. By 1930 the German Freethinkers League had 500,000 members. It was closed down in 1933, with Hitler saying in a speech that year: 
“We have therefore undertaken the fight against the atheistic movement, and that not merely with a few theoretical declarations: we have stamped it out.” (Adolf Hitler, in a speech in Berlin on Oct.24, 1933) 
Chairman of the German Freethinkers League was Max Sievers, who was arrested by the Gestapo in 1943 and executed.
Nazi ideology had the same hatred for “materialism” that modern Creationists have: 
In the introduction to “Foundations” [Houston Stewart] Chamberlain writes of Darwinism as “A manifestly unsound system”. He explicitly advocates a dualistic and spiritual vision of man, rejecting “monism” (the idea that humans are simply physical material) and saying that Darwinism and “so-called `scientific’ monism, materialism” were “shallow and therefore injurious systems” … “which have nevertheless in the nineteenth century produced so much confusion of thought”. He then says that as a result of such “errors” … “theists become in the twinkling of an eye atheists, a strikingly common thing in the case of Jews …”.
Thus to the Nazis Darwinism was something they largely rejected and opposed. As with many Christians they opposed Darwinism because it saw man as an evolved ape, whereas they saw man as God’s special creation, and they opposed Darwinism because it was materialist, stripping mankind of the spiritual dimension, and because it did not give man a moralistic destiny.

That is why, in a list of books they banned from the Third Reich libraries, the Nazis listed:

“Writings of a philosophical and social nature whose content deals with the false scientific enlightenment of primitive Darwinism and Monism (Haeckel).”

“Monism” is the idea that mankind is solely material, with no spiritual soul.


Gunther Hecht, who represented the National Socialist’s Department of Race-Politics (Rassenpolitischen Amt der NSDAP), issued a monitum:

“The common position of materialistic monism is philosophically rejected completely by the volkisch-biological view of National Socialism. . . . The party and its representatives must not only reject a part of the Haeckelian conception — other parts of it have occasionally been advanced — but, more generally, every internal party dispute that involves the particulars of research and the teachings of Haeckel must cease.”

To equate atheism and the Theory of Evolution to Nazism and the Holocaust is a grave, abject, and abhorrent historical error. It's actually Creationism that contributed heavily to the Holocaust. This doesn't mean that Creationism is false, it just means that Creationism actually has the moral failing that it projects onto Darwinism.
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Posted by on November 17, 2011 in apologetics, atheism, history


Extraordinary Claims Require Extraordinary Evidence

The first step towards wisdom is not to know that you know nothing. The first step towards wisdom is to know that, placing yourself in the totality of human history, any proposition you currently hold is much more likely to be wrong than it is to be correct; especially any unexamined proposition.

The article I read that made me crystallize that axiom of mine is this article by Isaac Asimov: The Relativity of Wrong. This article implies a philosophy of “less wrong” throughout, which has sort of become my guiding catchphrase: to be “less wrong” about everything I engage in. I'm guessing that this is where the Less Wrong blog got its title (of course, I only became aware of the Less Wrong blog courtesy of Luke at Common Sense Atheism's “Reading Yudkowsky” series, which he started posting November of last year; a number of years after I read that Asimov article).

Here is a snippet from Asimov's article (the article isn't very long, but…):

My answer to him was, “John, when people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together.” The basic trouble, you see, is that people think that “right” and “wrong” are absolute; that everything that isn't perfectly and completely right is totally and equally wrong.  However, I don't think that's so. It seems to me that right and wrong are fuzzy concepts…

The Big Question

Anyway, to the point. Does a personal god or gods exist? Like I just wrote, almost every other proposition that a human selected at random from the totality of the existence of the human species was wrong. What causes rain? Why does the sun travel across the sky? What causes disease? How do plants grow? Just about any random question that you can think of had a wrong answer for a lot longer than it has a correct answer. And adhering to “less wrong” philosophy, we still do not have the “correct” answer; we only have the less wrong answer.

For the vast majority of human history, people have believed in gods. Not every single person or every single community, but the vast majority of them have posited the existence of god(s) or some supernatural being(s). Based solely on the prior exemplified in my first two sentences, it is highly unlikely that a god or supernatural beings are the correct explanation for whatever phenomena we are attributing to them.

The most convincing line of evidence that most people use to verify the existence of their god is when they have an experience they can't explain, and thus conclude that their god or the supernatural is the best explanation for said event. However, these people never take into account any competing hypothesis that might also explain the unexplainable experience. You also always have to keep in mind the prior probability for some hypothesis. Again, the probability of you having the correct explanation for something is exceedingly low because you live in the continuum of all of humanity. And the vast majority of all humans who have ever lived have had the wrong explanation.

As I wrote in a previous post, this resorting to the supernatural for an explanation is a type of Prosecutor's Fallacy: Confusing P(E | H) with P(H | E). Sure, given that supernatural beings exist it would be an explanation for your experience; P(E | H) might be relatively high. But P(H) itself is already insanely low. And what about the probability of having that experience in the first place? What about the probability of having that experience given some other competing hypothesis? Some other competing hypothesis that has a higher prior probability that can also explain the experience? Worse yet, if P(E | ~H) is higher than P(E | H), then that experience is actually evidence against your hypothesis.

What if P(~H) is something like a physiological hiccup? I would say that the probability of a physiological hiccup is much higher than the probability of a god or supernatural being existing. Especially given that the vast majority of humans are imperfect and thus physiological hiccups would be the (relative) norm. So I would think that a physiological hiccup might explain the unexplainable experience better than the existence of the supernatural. Of course, this is a very specific claim; it doesn't mean that the supernatural doesn't exist, it just means that the supernatural isn't a better explanation for your particular experience than a physiological hiccup.

Why Apply Bayes (Math) To Religion And History?

Bayes is all about making your assumptions explicit. It's also about taking into account other competing hypotheses that can explain the same evidence or event. But what's the best thing about Bayes, that is somewhat implicit? Each “test” that we have, with us being imperfect beings, we know can't be 100% accurate. There will be false positives and false negatives. The rate of these false positives/negatives is something we need to be acutely aware of when making decisions based on new evidence.

What happens when our false positives rate is too high? The “test” becomes worthless, or in some cases the test might be actually more useful for refuting a hypothesis – as in the case with Oliver's blood. In the case with some religious experience being evidence for the hypothesis that god(s) or the supernatural exists, we should pay extra attention to our rate false positives. But I don't know any religious people who take into account “false positives” of religious experiences. They seem to follow a methodology of counting the hits and ignoring the misses; a sort of selection bias. Their only corroboration of their religious experience is their own unreliable feeling of certainty. Again, what is the success rate of your feeling of certainty? Have you documented when your feeling of certainty was wrong; as in, what's your rate of false positives?

Many people, however, are intimidated by Bayes because it's math, and math can get confusing very quickly. But as I showed in the Monty Hall problem, you don't really need to do any complicated math. If you see that the denominator in the Likelihood Ratio is larger than the numerator, then what you're looking at probably isn't evidence for your hypothesis. Or, if you know that the probability of seeing the evidence at all, P(E), is equal to the probability of seeing the evidence assuming your hypothesis is true, P(E | H), then you know that the evidence really has no affect on your initial probability; the evidence actually exists independently of your hypothesis. And then, even if you think that the evidence at hand is highly likely assuming your hypothesis is true, it doesn't mean that your hypothesis actually is true because the prior probability of your initial hypothesis might be insanely unlikely to begin with. Assuming otherwise is the Prosecutor's Fallacy (i.e. confusing P(E | H) with P(H | E); never assume your hypothesis is true and then conclude that your hypothesis is true).

Carl Sagan's saying “extraordinary claims require extraordinary evidence” is a Bayesian saying. An extraordinary claim, as in a highly unlikely P(H), requires extraordinary evidence, that is, a highly unlikely P(E). Moreover, H has to be extremely well connected to E. That is, there has to be an extremely low rate of false positives – a high P(E | H). If P(H) is low, and P(E) is low, then P(E | H) will have to be HUGE in order to make a dent in P(H | E). And that's only if E actually occurred. If E places some weight on H and E is absent, then this absence is evidence against H. If not, then you have to admit that E has no affect on H at all and is independent of H. Ironically, religious experiences are actually pretty common, so this makes P(E) a relatively large number in the case of E being a religious experience (like seeing a frozen waterfall). Which in turn would make no dent in your prior: P(H), the prior probability of the existence of god or the supernatural will be damn close to P(H | E), the hypothesis that god and/or the supernatural exists given a religious experience. Again, to explain the logic and math behind this, let's go over the Prosecutor's Fallacy again.

The Prosecutor's Fallacy (Again)

Say someone wins the lottery. This would be our evidence or event, P(E). Someone comes up to the lotto winner and says “Aha! You cheated! The probability of winning the lotto is low (true) so that means that you must have cheated!”. The person is claiming that P(E | H) is high. Why is this a fallacy to conclude that the person cheated? Because the prior probability of cheating period is also extremely low. Our P(E) as I said, is the probability of the event happening, in this case it's winning the lottery. Our prosecutor might be right, that given that you cheated, the probability of winning the lottery is high; P(E | H) might be really high. But we can't assume our hypothesis is true and then conclude that it's true; we need to know what P(H) is as well.

So in the case of the Prosecutor's Fallacy, our Bayes formula is this:

P(H | E) = P(E | H) * P(H) / P(E)
P(H | E) = [probability of winning the lottery given that you cheated] * [prior probability of cheating period] / [probability of winning the lottery]

So if we look at Bayes, we can see that we have high * low / low. In this case, if P(E) was equal to P(H), then these two cancel each other out and indeed our P(H | E) is equal to P(E | H). That would be no Prosecutor's Fallacy. But let's think about this: I read stories of people winning the lottery at least once a year. I've never read any stories of anyone winning the lotto because they cheated, nor have I read any stories of people even attempting to cheat. So even if P(E), the event of winning the lottery, is like 1 in a million, P(H) has to be lower than that. With P(H) being lower, this will bring down P(E | H) even if it's like .99. Dividing this by P(E) will only make a relatively small dent in P(H | E); it won't update our prior probability P(H) enough to make it significant.

So Bayes in this case would generally look like this:

P(H | E) = high * lower / low

The two “lows” are close to canceling each other out, but not enough to make the jump from prior probability (lower) to posterior probability that huge, i.e. not enough to make P(E | H) equal to P(H | E). Which is a jump we need it to do to make it a compelling argument.

Again, there's no complicated math going on here. It's just the concept of dividing big numbers by small numbers to get a bigger number, dividing a small number by a big number to get a smaller number (as in the case of Oliver's blood), or dividing numbers that are pretty close to each other to make a not-so-big number (as in the Monty Hall problem).

This has a real world applicability, too. Don't trust your doctor's diagnosis? Ask them what the success rate, P(E | H), and false positives rate, P(E | ~H), is for some test or symptom. Then find out what the prior probability, P(H), is for that disease (that is, the number of people in the total population who have that disease). Then do the math yourself; a lot of crappy doctor diagnoses have elements of the Prosecutor's Fallacy in them, and waste a lot of the patient's money. If a breast cancer test has an 80% success rate, this does not mean that you have an 80% chance of having breast cancer if you get a positive result. As I keep saying, this is P(E | H) and not P(H | E), equivocating between the two is the Prosecutor's Fallacy. You always want to find P(H | E). P(E | H) is one piece of the puzzle that gives you P(H | E).

The Resurrection of Jesus: Ordinary or Extraordinary?

When we talk about the resurrection of Jesus, is this an ordinary claim or an extraordinary claim? There are actually two issues at hand when we talk about this. One, is whether Jesus actually came back from the dead. The other, is whether we would have stories of Jesus coming back from the dead. Jesus actually rising from the dead is an extraordinary claim, however having stories about someone rising from the dead are comparatively mundane. We know they are relatively mundane because we have many other stories in antiquity of other pagan gods and demi-gods coming back from the dead. One of the most famous cities in Western civilization was supposedly founded and named after a guy who was born from a virgin, ascended to heaven, and resurrected from the dead: Romulus, who supposedly founded Rome. There were other pagan gods like Adonis, Hercules, Asclepius, Osiris, Bacchus, Inanna, and Zalmoxis who all came back from the dead in some fashion (i.e. some form of “divine re-embodiment”, 1 Cor 15.35-54). So P(E) in this case would be a lot higher than in the lottery example.

So if we were to formulate Jesus' resurrection in Bayesian terms, our P(H) is the hypothesis that Jesus rose from the dead. Our P(E) is the event/evidence of having stories of Jesus rising from the dead, like the Gospels. Our P(E | H) would be the probability of having stories about Jesus rising from the dead given that Jesus rose from the dead. Our formula might look like this:

P(H | E) = high * low / high

In this case, we have something different than the lottery example. Instead of the prior probability, P(H), and the probability of the event, P(E) being close to each other it turns out that P(E) is closer to P(E | H) so these two terms are closer to canceling each other out. Which means that our prior probability's move to posterior probability will be a very small jump. P(H) is pretty close to P(H | E). The extraordinary claim of Jesus' resurrection only has a relatively ordinary claim of stories about Jesus' resurrection. We would need something more extraordinary to support the claims of Christians. As it happens, there's probably another reason why we would have stories about Jesus' resurrection that in themselves would have a higher prior probability and an equivalent P(E | H).

As I explained above, religious experiences are also pretty mundane due to human imperfection. So our Bayes formula is still denominated by a relatively high P(E). Again, our posterior probability only slides a couple of percentage points in favor. But not enough to make a good argument; not enough to argue from a high probability.

At this point, some apologists might claim that the success of Christianity in the Roman Empire is an extraordinary event or evidence. I actually don't think this is so; Christianity's growth rate is almost exactly the same as the growth rate of Mormonism. Mormon's experienced persecution just like the early Christians did. So if Christianity is true due to its growth rate, then so is Mormonism. However, even Christianity's success can be explained in more pragmatic terms: Christianity succeeded – in a pagan environment – because it successfully emulated pagan ideals. Even though the Gospels superficially quote from the LXX, even though the body of Christianity is cloaked in Judaism, the soul of Christianity is Greek tragedy. A quote that Neil Godfrey has in that post:

What one learned from the classical tradition was what it meant to be a respected person in the larger context of the Greek cosmos, a world controlled by the jealousy of the gods and the vicissitudes of Fate. One learned piety towards the gods, to respect the rights of others, especially the unfortunate, the suppliant, and the stranger. But what one learned above all was how to face the ultimate test, unjust suffering, the inevitable suffering unto death, with courage and integrity. The texts display a remarkable sophistication on this point

This sounds an awful lot like Christianity's ideals and worldview. Substitute the jealousy of the gods with the jealousy of Satan and there seems to be a match, it would seem as though this was the mentality behind the early Christian martyrs, and why their deaths were compelling to interested pagans. As I explained in a previous post arguing for Christians borrowing the Eucharist ceremony from Mithraists, this might just be one more thing that Christians inherited from their cultural matrix.

This is one of the reasons why people claim that the U.S. was founded on Christian ideals. They say this because the U.S. was founded on pagan Greek ideals (like rationalism, equality, and democracy) and confuse this with Christianity, which itself was ensouled with pagan Greek ideals.

So again, the success of Christianity would also be a relatively high P(E), a relatively ordinary claim. What would work for Christianity would be a truly extraordinary claim, a low P(E) coupled with a high P(E | H); a high likelihood ratio. Moreover, this P(E | H) would have to be higher than P(E | ~H) or the probability of seeing the evidence given some other competing hypothesis. In all of these cases, I think that P(E | ~H) is pretty close to P(E | H) but that's just a hunch.

Religious claims don't seem to have the extraordinary evidence that Bayes requires for their extraordinary claims. And if you agree that extraordinary claims require extraordinary evidence, then this lack of evidence is indeed evidence of absence.


Posted by on November 14, 2011 in Bayes