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Monthly Archives: May 2012

Logical Fallacies As Weak Bayesian Evidence: Post Hoc Ergo Propter Hoc

So I already have two posts that go over the notion that logical fallacies aren’t necessarily fallacies of probability. The issue with logical fallacies is that in deduction, the conclusion has to follow necessarily from the premises. But we don’t live in a world of deductive certainty; we live in a world of uncertainty: the world of probability.

The thing about post hoc ergo propter hoc is that it is an inductive inference. That being the case, post hoc fallacies should be easily explained using probability theory, thus Bayes’. Thinking about this fallacy intuitively (that is, using quick Bayesian format), it seems that this fallacy is an instance of the Base Rate fallacy. Of course, given that some cause is the reason for some effect, the cause has to come before the effect (unless you live in the world of quantum physics, which none of us do).

This means that the conditional probability, or success rate, of a post hoc argument would necessarily be 1.00, or P(B Happened After X | B Caused By X) = 1.00. But the argument itself is trying to prove P(B Caused By X | B Happened After X); the cause is the hypothesis and what happens is the evidence. Sure, given that god answers prayer there’s a 100% chance you would get a job after praying for it. But that’s a Base Rate fallacy; we are not trying to establish P(Get A Job After Praying To God | God Answers Prayers) but P(God Answers Prayers).

One hundred percent of all effects (in the macro world) are preceded by their causes. Concluding that because the conditional probability is 100% that it means that it is actually the reason is, like I said, a Base Rate fallacy, because we aren’t taking into account the prior probability.

But there’s a second factor that has to be taken into account: The alternative hypothesis. Or, what about an effect that just happens after the “cause” by chance or some other cause? In other words the false positive rate? This, surely, must also be a high number but it doesn’t necessitate 100% certainty like the success rate that denominates post hoc logic. Given this, it seems that the Likelihood Ratio, or dividing the success rate by the false positive rate, returns a very very low quotient. If the success rate is 100%, and the false positive rate is 98%, then this is only a Bayes’ Factor of 1.02 decibles. This means that if we had a 50/50 spread between the hypothesis and the alternative, the post hoc ergo propter hoc logic in this example would only increase our probability to 50.5%.

If we go back to my original example P(Get A Job After Praying To God | God Answers Prayers), we would have to include the alternative hypothesis. There are various alternatives, but let’s just go with P(Get A Job After Praying | Economy Improves). Of course, there’s not a 100% chance that you would get a job when the economy improves, but an improving economy in and of itself has a much higher prior probability than the existence of god. Therefore, in this case, the prior probability of P(God Answers Prayers) doesn’t get much of a boost due to the small difference between P(Get A Job After Praying To God | God Answers Prayers) and P(Get A Job After Praying | Economy Improves).

So post hoc ergo propter hoc is weak (possibly very weak) probabilistic evidence. It’s not strong enough evidence to rest an entire argument on; you would need much more evidence. Or you would need an argument or situation where there is a huge disparity between the success rate and false positive rate, which most post hoc ergo propter hoc arguments never attempt to ascertain.

The god hypothesis, of course, also suffers due to its lack of falsifiability.

 

Wrath of the Titans!

2 Peter 2.4

For if God did not spare angels when they sinned, but sent them to hell, putting them in chains of darkness to be held for judgment

You’re probably wondering what this short verse has to do with Greek mythology and/or some recent movies. It might become a bit more clear if I write it in the original language it was penned in:

εἰ γὰρ ὁ θεὸς ἀγγέλων ἁμαρτησάντων οὐκ ἐφείσατο, ἀλλὰ σειροῖς ζόφου ταρταρώσας παρέδωκεν εἰς κρίσιν τηρουμένους,

ei gar o theos aggelon amartesanton ouk efeisato, alla seirois zofou tartarosas paredoken eis krisin teroumenous

There we go, the offending word: The verb form of the word Tartarus, which the author of 2 Peter is using to mean “cast into hell”. How’s that for syncretism? Both Hades (Matt 11.23) and Tartarus are mentioned in the NT. Of course, someone might counter with the fact that many English words also derive from Greek — like hysteria (womb) or energy (en ergos:: in work) — and this doesn’t mean that we have some syncretism with Greek mythology (our Western religions have syncretism with Greek mythology for other reasons).

But the difference is that Greek mythology was still believed by a great many people when pseudo Peter wrote this epistle. If he was walking around he might have heard some Greeks explicitly talking about Tartarus as though they really believed it existed as it does in Greek mythology; he couldn’t have not known what it meant, unlike how modern speakers of English don’t know what “psycho” or “pneumonia” or “sycophant” originally meant. I imagine if more people knew what sycophant originally meant and implied, feminists would have a field day.

 
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Posted by on May 23, 2012 in greek

 

Self-Contradictions In Hoffmann’s Latest Essays

So R. Joseph Hoffmann has published three essays arguing against mythicism. I don’t have a bone to pick with mythicism, but I do have bone to pick with bad arguments. Especially self-contradictions.

Here is the bit of self-contradiction that demonstrates that they see Bayes’ Theorem as some manner of sorcery instead of modeling correct thinking when dealing with uncertainty:

But I think the basic factuality of Jesus is undeniable unless we (a) do not understand the complexity of the literature and its context, or impose false assumptions and poor methods on it; (b) are heavily influenced by conspiracy theories that–to use a Humean principle—are even more incredible than the story they are trying to debunk; or (c) are trying merely to be outrageous.  To  repeat Morton Smith’s verdict on Wells, the idea that Jesus never existed requires the concoction of a myth more incredible than anything to be found in the Bible.

The use of any single “theorem” to deal with the values discussed here beggars the credible.

(speaking of poor methods…)

Did anyone notice it? No? It was his reference to a Humean principle. The same Humean principle that is a Bayesian principle, which he then denigrates at the beginning of the very next paragraph. Ironically, if Bayes’ Theorem doesn’t apply, then neither does Hume’s argument that he appeals to since they are the same thing.

David Hume and Thomas Bayes were contemporaries. Hume used logic to arrive at his conclusion, while Bayes used math to arrive at his formula (which necessiates Hume’s conclusion.). If math doesn’t apply, then neither does logic; Bayes is no less applicable to historical questions than a logical syllogism.

If someone thinks that when doing historical analysis, extraordinary claims requires extraordinary evidence, they are a Bayesian. If someone thinks that falsifiable historical hypotheses are better than unfalsifiable historical hypotheses, then they are a Bayesian. Bayes theorem models all correct probabilistic thinking. If historians are dealing with uncertainty, and using probabilistic language, they should know the rules of probability.

Stephanie Fisher writes:

[Bayes’ Theorem] is completely inappropriate for, and unrelated to historical occurrence and therefore irrelevant for application to historical texts

Of course, she is wrong. Unless we have 100% confidence in every single argument and evidence in history, then probability theory will necessarily apply. It doesn’t matter if you are using percentages to the nth decimal place since it’s not about mathematical accuracy but about making sure your conclusions (which are necessarily probabilistic statements in history) follow from your premises (which are also probabilistic statements). Even if you use educated (or even uneducated) guesses, you still have to follow the rules of probability so that your conclusion follows from your premises.

I reiterate: If historians are using probabilistic statements and educated guesses, they still have to know the rules of probability. To say that probability theory doesn’t apply is to say things like Occam’s Razor and falsifiability don’t apply. And if falsifiability doesn’t apply, then that’s not even pseudoscience. That’s religion.

So the self-contradiction, the irony, is that Hoffmann (and Fisher) contradict themselves when they claim that Bayes theorem doesn’t apply. It does apply, you just don’t understand it. Sure, you can use Bayes’ theorem incorrectly just like you can use formal logic incorrectly, but the sweeping statement that it doesn’t apply is to shut yourself out of correct thinking. The contradiction I’ve hopefully pointed out is that they already use Bayesianism intuitively when they think correctly, even for mundane everyday things. They just need to use it more explicitly when doing scholarship, which is Carrier’s point.

Does Hoffmann really think that he needs mathematical precision to the nth decimal place to conclude that if a student of his misses a week of class that the student was probably goofing off instead of having been abducted by aliens? I would hope not: Welcome to Bayesianism.

 
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Posted by on May 22, 2012 in Bayes

 

Flesh Eating Bacteria and Probability

It’s well known that doctors are bad at probability:

Here’s a story problem about a situation that doctors often encounter:

1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?

[…]

Next, suppose I told you that most doctors get the same wrong answer on this problem – usually, only around 15% of doctors get it right. (“Really? 15%? Is that a real number, or an urban legend based on an Internet poll?” It’s a real number. See Casscells, Schoenberger, and Grayboys 1978; Eddy 1982; Gigerenzer and Hoffrage 1995; and many other studies. It’s a surprising result which is easy to replicate, so it’s been extensively replicated.)

On the story problem above, most doctors estimate the probability to be between 70% and 80%, which is wildly incorrect.

That’s why it is in your best interest to learn some probability theory so that you don’t die! Not knowing probability might increase your probability of death; look at the tail end anecdote in this story:

She said that many doctors have a mantra: “If you hear hooves outside your window, chances are it’s a horse and not a zebra,” meaning that you should first consider the obvious explanation. “Our point is, physicians need to be trained to look at necrotizing fasciitis as a horse and not a zebra.”

If you suspect the disease, ask doctors to rule it out. Batdorff cited the case of “a gentleman whose wife said to the emergency room staff ‘could this be the flesh-eating bacteria? They said no. And it was. And he died.”

There’s a lot right with this quote but one thing wrong. No, flesh eating bacteria shouldn’t be thought of as a horse. It’s still a zebra; meaning that it’s still less common than other infections.

But the sound advice — the best advice — is to ask doctors to rule out the more serious (though less probable) possibility. That’s not probability in and of itself, but decision theory. More to the point, ask doctors to do a high success rate/low false positive rate test to rule out the possibility. Like I wrote in the post right before this one: Disconfirming evidence is better than confirming evidence. If flesh eating bacteria give certain symptom 100 out of 100 times, this doesn’t mean you actually have the disease. That, again, is the Prosecutor’s or Base Rate fallacy.

Ask for disconfirming evidence. And don’t just accept “no” from a doctor like in the last sentence of the quote, because like I said, doctors suck at probability just like the rest of us. And that ignorance of probability might cost you a lot of money in repeated doctor’s visits… or cost you your life.

 
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Posted by on May 17, 2012 in Bayes

 

Bayes’ Theorem and Falsifiability (2)

I thought I’d attempt another go at explaining Bayes’ theorem and falsifiability.

In a previous post, I went over a hypothetical scenario where there are only two possible ways of getting a headache: One was by brain tumors and the other was by head colds. In this hypothetical scenario, the number of people in the world with brain tumors was equal to the number of people in the world with head colds; head colds are responsible for headaches in 50 out of 100 people and brain tumors are responsible for headaches in 100 out of 100 people.

Given all of that information, if you wake up with a headache, what is the probability that you have a brain tumor, and what is the probability that you have a head cold?

Let’s assume that the prior probability for both (H1 and H2) is 10%. Our Bayes’ theorem would be:

P(H1 | E) = P(E | H1) * P(H1) / [P(E | H1) * P(H1)] + [P(E | H2) * P(H2)] + [P(E | ~H) * P(~H)]

= 1.00 * 0.1 / [1.00 * 0.1] + [0.5 * 0.1] + [0 * 0.8]
= 0.1 / [0.1] + [0.05]
= 0.1 / 0.15
= .6666

So the probability of having a brain tumor, upon getting a headache, went up from 0.1 to 0.6666. Thinking otherwise, that since 100 out of 100 people with brain tumors have headaches therefore you have a 100% chance of having a headache, is the Prosecutor’s Fallacy. The probability of having a head cold, also, went up from 0.1 to 0.3333.

The thing is, in this scenario you could not have a headache and still have a head cold. Since 50 out of 100 people get headaches due to head colds, it could go either way. Both a headache and a non-headache could be evidence of a head cold; that is the essence of being unfalsifiable. One observation is no more or less probable than the other — exclusive — observation. On the other hand, not having a headache is pretty strong evidence that you don’t have a brain tumor. Not having a headache falsifies the brain tumor hypothesis; absence of evidence is evidence of absence. But, again, you could have a headache and not have a brain tumor even if brain tumors cause headaches 100% of the time; there’s still a 33.33% chance that you have a head cold. So one can see the dangers behind confirmation bias. Falsifying, disconfirming evidence is a lot better than confirming evidence.

Let’s up the ante.

Say your friend has two die. One has six sides numbering 1 – 6 and the other is a trick die that has a 1 on all faces. She rolls one of the die at random and it ends up with a 1. What is the probability that the die that she rolled was the normal 6 sided one or the trick die?

For the normal 6 sided die, our probability distribution is P(One | Normal) + P(Two | Normal) + P(Three | Normal) + P(Four | Normal) + P(Five | Normal) + P(Six | Normal) = 1.00. If it is a fair die, then the probability for P(One | Normal) = 1/6 or .1667.

For the trick die, our probability distribution is P(One | Trick) = 1.00.

We can then go through Bayes’ to see what the probability is for her rolling each:

P(Normal | One) = P(One | Normal) * P(Normal) / [P(One | Normal) * P(Normal)] + [P(One | Trick) * P(Trick)]
= .1667 * .5 / [.1667 * .5] + [1.00 * .5]
= .0834 / [.0834] + [.5]
= .0834 / .5834
= .1429

P(Trick | One) = P(One | Trick) * P(Trick) / [P(One | Trick) * P(Trick)] + [P(One | Normal) * P(Normal)]
= 1.00 * .5 / [1.00 * .5] + [.1667 * .5]
= .5 / [.5] + [.0834]
= .5 / .5834
= .8571

So upon rolling a 1, the probability that she rolled the normal sided die is .1429 and the probability that she rolled the trick die is .8571. There is still some ambiguity here, but if you were a betting person you should bet on her having rolled the trick die. But due to falsifiability, if she had rolled any other number then we would have 100% confidence that she rolled the normal die. Again, disconfirmation is stronger than confirmation.

Let’s try another example, this time approximating people’s confidence in their unfalsifiable hypotheses by increasing the prior probability in favor of the unfalsifiable hypothesis. Let’s also introduce a 50 sided die and a prior of 90% in favor of picking the 50 sided die. The probability of her having rolled the 50 sided die and getting 1 between a 50 sided die, a 6 sided die, and the trick die to choose from is:

P(Fifty| One) = P(One | Fifty) * P(Fifty) / [P(One | Fifty) * P(Fifty)] + [P(One | Trick) * P(Trick)] + [P(One | Six) * P(Six)]
= .02 * .9 / [.02 * .9] + [1.00 * .05] + [.1667 * .05]
= .018 / [.018] + [.05] + [.0083]
= .018 / .0763
P(Fifty | One) = .2358

P(Six| One) = P(One | Six) * P(Six) / [P(One | Six) * P(Six)] + [P(One | Trick) * P(Trick)] + [P(One | Fifty) * P(Fifty)]
= .1667 * .05 / [.1667 * .05] + [1.00 * .05] + [.02 * .9]
= .0083 / [.0083] + [.05] + [.018]
= .0083 / .0763
P(Six | One) = .1092

P(Trick| One) = P(One | Trick) * P(Trick) / [P(One | Trick) * P(Trick)] + [P(One | Six) * P(Six)] + [P(One | Fifty) * P(Fifty)]
= 1.00 * .05 / [1.00 * .05] + [.1667 * .5] + + [.02 * .9]
= .05 / [.05] + [.0083] + [.018]
= .05 / .0763
P(Trick | One) = .6550

Upon rolling a 1, the 50 sided die has a .2358 probability of having being rolled, the 6 sided die has a .1092 probability of having been rolled, and the trick die has a .6550 probability of having been rolled. Even given a prior probability of 90% that your friend would pick the 50 sided die. This is the problem with positing hypotheses that can equally explain multiple exclusive outcomes, even if there is a high initial probability of that hypothesis being true. If we had a 100 sided die, and a 90% chance of picking that die, upon rolling a 1 there would only be a .1337 probability that the 100 sided die was picked, in contrast to a .7426 probability that the trick die was picked. A 200 sided die would do worse. 300, even worse. Etc.

I should emphasize that this doesn’t count if the data aren’t mutually exclusive.

How much mutually exclusive data can an all powerful god, philosophical zombies, solipsism, being a brain in a vat, the world being created last Thursday, etc. explain? How many sides would God Dice have? In an effort to prevent their god from being proven wrong, believers have given their god dice every side imaginable.

Bayesian Judo (falsifiability) will always win over goalpost moving (unfalsifiability). A god that can be proven wrong is more probable than a god that can’t be proven wrong.

 
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Posted by on May 15, 2012 in Bayes

 

Jerry Coyne: The correlation between religiosity and well-being among U.S. states

Dr. Jerry Coyne, biologist and author of Why Evolution Is True, wrote a fantastic blog post that shows the correlation between income inequality and religiosity in countries around the world. Coyne gave a talk about evolution, religion, and science, and societal dysfunction where he argues that lack of acceptance of evolution is linked to high religiosity, which itself is linked to poor societal health. A commenter crunched some numbers for specifically the United States:

[Dr.] Harry [Roy, professor of biology at Rensselaer Polytechnic Institute in New York] found some relevant data in the United States, crunched the numbers, and did a statistical analysis. He left comments and a link to the analysis, after my post. And he’s kindly done a bit more analysis and allowed me to reproduce it here. What he found is precisely the same relationship among states (using the HDI) as I found among countries: American states with lower HDIs are more religious.

First, a portrait of American religiosity taken from a 2009 Gallup poll:

As we know, the south is really religious (just go there if you doubt that!), and the northeast and west coast states much less so.

And below is a national map of the Human Development Index (HDI) from Wikipedia. This index is a measure of societal well being that differs from the “Successful Societies Scale” (SSS) that I used in my talk at Harvard. The HDI uses a set of traits that differ from those used in the SSS: the former amalgamates three traits (life expectancy, education, and income), while the latter combines 25 traits, including corruption, income disparity, child mortality, access to medical care, suicide rates, and so on. Unlike the SSS, under which the U.S. ranks very low among first-world nations, the HDI places the U.S. at the top when the index is not adjusted for inequality among residents, but falls much lower when adjusted for inequality (see the Wikipedia article on the HDI at link above). The disparity may be due to the inclusion of income inequality in the adjusted HDI; income inequality is highly positively correlated with religiosity across 71 nations.

The south is not so great here, the northeast (and two states on the west coast) are better. That suggests a relationship between religiosity and well being as measured by the HDI.

After crunching the data, Dr. Roy produced this correlation between the religiosity of the 50 states and their ranking on the HDI:

As you see, we have the same negative relationship between well-being and religiosity that we saw for different countries of the West. The correlation here is r= – 0.66897, and the probability (“p”) that this correlation would arise by chance is p = 0.00000012. (A value of p less than 0.05 is conventionally used to show a significant relationship.) This relationship, then, is not only striking but very highly significant in a statistical sense. Harry put a least-squares regression line through the data; its slope is also highly significant.

The only thing to determine is if religion is the cause or the effect of income inequality. There could also be some other variable(s) that is/are driving both indicators. But whatever the cause, it stands to reason that your best bet for a good, healthy society to live in is one that accepts evolution! Now why would god do that?

 
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Posted by on May 13, 2012 in economics/sociology

 

Neil DeGrasse Tyson on Atheism

I’m pretty sure most people have seen NDT’s video on why he doesn’t call himself an atheist. (If you haven’t, here it is).

I just want to put a spotlight on a recent Facebook post of his where he wrote:

Thanks for all your candid comments on this wall regarding my short atheism-agnosticim clip on “Big Think”. I found them illuminating for their breadth as well as their depth. I note a few other possibly unexpected things about me: Not only do I not embrace labels, you will never see me debating people on the subjects of UFOs, Religion, Alternative Health practices, Astrology, or Pseudoscience in general. My speeches at TAM 6 & 9 were given reluctantly (I don’t normally attend). I don’t sign petitions. I don’t write to, or lobby congress (although I am happy to testify when asked). I don’t lead or participate in rallies. I don’t picket. And I don’t publicly align with organized causes. Meanwhile, labels and causes have, now and then, aligned themselves with me. In any case, I’m rather specific about how I invest my energies. As an educator, I have found that people are more receptive to learning when they know you don’t have an agenda, and when they determine that your goal is to teach them how to think rather than what to think. Such is the universe I have created for myself

I have to agree 100% with his reasoning, both in the video and his quote here. Because of the current juncture in history, “atheism” is a cause; an identity. And it needs to be, because the adjective “atheist” has been one of the longest lived insults in the history of the human race and that has to change. The fact of the matter is that NDT is an atheist, he just chooses not to apply that label to himself because the people who do that usually have some agenda. And being associated with that agenda he argues would hinder his primary goal as an educator.

Agnostic is in another class altogether so creating a dichotomy between the two is nonsensical. Agnosticism can be a reason for atheism, but it could also be a reason for theism. The way I see it, the way you live your life determines your brand of theism or atheism (or deism or polytheism or misotheism etc.). If you go about your life as though a god exists, then you’re a theist. If you go about your life as though no god exists, then you’re an atheist. You can be agnostic about either proposition, but what you do more accurately reflects your “real” beliefs more than what you say.

What you do will always be more powerful than what you believe. Which is why I think the biggest crime against the human spirit is to reject someone, not because they treat you badly, but because they believe the “wrong” thing.

As a counterpoint to bring up an issue where “agnostic” makes sense, I’m agnostic about whether Jesus existed or not. The existence or non-existence of Jesus makes absolutely no bearing on how I go about my life, so how I act wouldn’t be a good gauge for what I think in regards to that guy’s historicity.

So yeah, even though he might not like it, I consider NDT to be on “my team”: Team atheism (the same is true of Bart Ehrman, sorry lol). But it’s not only because NDT is an atheist, but because we went to the same high school (of course about 20 years apart) 😉

 
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Posted by on May 11, 2012 in atheism

 

The Marcionite God Is Compatible With Evolution


Marcion (Μαρκίων) of Sinope (modern Turkey)

If you look at my posts about Bayes’ Theorem and the existence of god (parts 2 and 3) you’ll notice that the probability of the Christian god goes down due to it being asserted that he has a role in evolution and the creation of the universe. If you don’t feel like slogging through those posts, here are the relevant arguments.

On life arising on Earth as opposed to other planets:

So if one were to say that P(Earth | H [i.e. Chrisian God]) is .99, then one is in effect saying that it would be very unlikely, or .01 probability, for the Christian god to create life on any other planet. What exactly is limiting the Christian god at this point? Why couldn’t the Christian god create life on Mercury if he wanted to? It seems to me that since all things are possible with the Christian god, we would have to distribute our probability evenly between the eight planets. We can’t have .99 for each planet because .99 * 8 is much greater than 1.00. Like I said in a previous post, probability is like energy. It has to be conserved. When everything is added up it has to equal 1.00.

P(Earth | H) in reality would be 1/8, or .125.

[…]

So I would estimate that P(Earth |~ H) would be closer to .9, with the planets on the outskirts of the [Goldilocks Zone] getting a decent chunk like .04, and the remaining five planets splitting up the .02. This is in fact what astrophysicists do when looking for planets outside of our Solar System. They concentrate on looking for planets that are within that star’s GZ and then concluding that those are the planets that have a high probability of water and thus a high probability of life (compared to other planets outside of the GZ). Methodological Naturalism for the win, I suppose!

So our formula to update our prior of .977 looks like this:

P(H | E) = P(E | H) * P(H) / [P(E | H) * P(H)] + [P(E | ~H) * P(~H)]
= P(Life on Earth | Christian God) * P(Christian God) / [P(Life on Earth | Christian God) * P(Christian God)] + [P(Life on Earth | NonChristian God, Atheism) * P(NonChristian God, Atheism)]
= .125 * .977 / [.125 * .977] + [.9 * .023]
= .1221 / [.1221] + [.0207]
= .1221 / .143
= .8551

So our prior was bumped down from .977 to .8551. If there were no GZ planets (i.e. P(E | ~H) would be basically zero) and there was life on a planet anyway, then even if P(E | H) was .125, this would increase our prior probability from .977 to basically 1.00; we would have almost absolute certainty of the Christian god’s existence, according to the assertions of Christians.

On evolution:

So given evolution, and assuming equal distribution between theistic evolution and theistic non-evolution (I don’t have any a priori reason why the Christian god would pick evolution over non-evolution or vice versa), we would have the following Bayesian update to our prior probability of .8551:

P(Christian God | Evolution) = P(Evolution | Christian God) * P(Christian God) / [P(Evolution | Christian God) * P(Christian God)] + [P(Evolution | Atheism) * P(Atheism)]
= .5 * .8551 / [.5 * .8551] + [.99 * .1449]
= .4276 / .4276 + .1435
= .4276 / .571
= .7487

Now, given no evolution, we would have the following Bayesian update to our prior probability of .8551:

P(Christian God | No Evolution) = P(No Evolution | Christian God) * P(Christian God) / [P(No Evolution | Christian God) * P(Christian God)] + [P(No Evolution | Atheism) * P(Atheism)]
= .5 * .8551 / [.5 * .8551] + [~0 * .1449]
= .4276 / .4276 + ~0
= ~1.00

So if there were no evolution, then the evidence for the Christian god goes up from .8551 to approximately 1.00. I have to stress that in reality no evolution would simply be evidence against atheism. Surely the Greek gods or some other supernatural force could have created life on Earth if there indeed was no evidence for evolution, and that would have to be included in the H of ~1.00. This is the reason why P(No Evolution | Atheism) is only approximately zero and not zero. ~H was supposed to be both atheism and some other, non-all powerful god(s) besides the Christian god.

But as it stands, evolution is the most likely explanation for the emergence of human beings on Earth. And evolution does indeed favor atheistic evolution over Christian theistic evolution.

Now our prior probability for the existence of the Christian god is .7487 and the prior probability for the existence of a non-Christian god(s) or atheism is .2513.

On the creation of this universe as opposed to some other universe:

According to this apologetics website the probability of the current arrangement of our universe’s constants is the equivalent of picking one red dime out of a pile of 1037 dimes. Or, P(Current Universal Constants) = 0.0000000000000000000000000000000000001.

[…]

Back to our Total Probability formula:

0.0000000000000000000000000000000000001 = P(Current Universal Constants | Christian God) * .7412 + P(Current Universal Constants | Non Christian God, Atheism) * .2588.

0.0000000000000000000000000000000000001 = ???? * .7412 + P(Current Universal Constants | Naturalism, Atheism) * . 2588.

It looks like the equation has to be P(Current Universal Constants | Non Christian God, Atheism) > P(Current Universal Constants | Christian God) in such a manner that makes the Total Probability equal to 0.0000000000000000000000000000000000001. Since P(Current Universal Constants | Christian God) is basically zero — the majority of the probability capital goes into P(Other Universal Constants | Christian God) — this means that P(Current Universal Constants | Non Christian God, Atheism) is equal to a miniscule amount more than P(Current Universal Constants). At this point, it might as well be equal to P(Current Universal Constants).

Since P(Current Universal Constants | Christian God) is basically, zero, this means that the probability of the Christian god’s existence given the current universal constants is also basically zero. It’s not actually zero because zero isn’t a probability. I’d like to say that I’m the first one to make that argument, but it already looks like other people have come to a similar conclusion about the fine-tuning argument.

You can see that the probability of the Christian god’s existence takes a hit with all of these arguments; the reason it takes a hit is because the Christian god is unfalsifiable. But what happens if no one ever asserted that the Christian god was responsible for the creation of the universe or life on Earth?

That just so happens to be the description of the Marcionite god.

According to Marcion, his good god was an alien. Previously unknown to humanity before the descent of Jesus from heaven, this god had no hand in the creation of humanity or the universe. All of that was on the hands of the Jewish god. Marcion’s god just sort of “happened” onto humanity and felt sorry for us and decided to offer unconditional eternal life to those who believed in him.

There’s no reason why the same sort of logic couldn’t apply in the context of evolution; the Marcionite god just happened upon an already evolved humanity and the subsequent divine passion play would pan out. Since it is never asserted that the Marcionite god had a hand in creation or evolution, he doesn’t take any hits in probability in comparison to the (orthodox) Christian god.

In short, a non-creator god is compatible with evolution. One of the reasons I think Marcion’s theology is one of the most logical iterations of Christianity.

 
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Posted by on May 10, 2012 in Bayes, marcion

 

Lord and God

Quotes from Philo’s lucubrations about why the LXX has both lord and god as a description of the god of the Jews:

Questions and Answers in Genesis (57) Why God places a cherubim in front of the Paradise, and a flaming sword, which turned every way, to keep the way of the tree of life?. The name cherubim designates the two original virtues which belong to the Deity, namely, his creative and his royal virtues. The one of which has the title of God, the other, or the royal virtue, that of Lord

Questions and Answers In Genesis (51) Why is he said to have built an altar to God, and not to the Lord?. In passages of beneficence and regeneration, as at the creation of the world, the sacred writer only refers to the beneficent virtue of the Creator, by which he makes everything in its integrity, and he implies this by concealing the royal name of Lord, as one which bears with it supreme authority; therefore now also, since what he is describing is the beginning of the renewed generation of mankind, he borrows for his description the beneficent virtue, which bears the name of God; for he used the kingly attribute, which declares his imperial power, by which he is called Lord, when he was describing the punishment inflicted by the flood.

Who Is The Heir of Divine Things? (205) And the Father who created the universe has given to his archangelic and most ancient Word a pre-eminent gift, to stand on the confines of both, and separated that which had been created from the Creator. And this same Word is continually a suppliant to the immortal God on behalf of the mortal race, which is exposed to affliction and misery; and is also the ambassador, sent by the Ruler of all, to the subject race. (206) And the Word rejoices in the gift, and, exulting in it, announces it and boasts of it, saying, “And I stood in the midst, between the Lord and You;” neither being uncreate as God, nor yet created as you, but being in the midst between these two extremities, like a hostage, as it were, to both parties: a hostage to the Creator, as a pledge and security that the whole race would never fly off and revolt entirely, choosing disorder rather than order; and to the creature, to lead it to entertain a confident hope that the merciful God would not overlook his own work.

 
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Posted by on May 10, 2012 in Adonai, greek, Hashem, josephus

 

Malleable Observations

Dr. Mano Singham makes an excellent observation (heh) about people’s recollection of observations:

As a scientist who interacts a lot with the general public, I am often asked to explain phenomena that lay people have observed. I used to take those observations at face value and was often stumped at coming up with an explanation because of the inconsistent elements the observations seemed to contain. But I have found from experience that what people tell me they ‘saw’ is not purely raw observational data but that when you go back and actually repeat the situation, the observations are different from what was originally reported and that much of the paradoxical elements go away.

This raises an important point. In investigating and explaining any phenomenon, we first have to check if what we saw was ‘real’.

The problem is that our brain’s first reaction is dominated by what Daniel Kahnemann in his excellent book Thinking Fast and Slow (2011) calls ‘System 1′ thinking. What happens is that when people ‘see’ something, their brain immediately kicks in and they try to makes sense of what they saw by subtly shaping the data to fit into a plausible narrative. It is this manipulated data that they are convinced they saw and which they then report later. Reporting it cements the distorted version even further into their memory making them even more convinced of its truth. Magicians use this feature of our brains to fool us into thinking that we saw something that was more amazing than it really was.

This has obvious implications for people’s recollection of their religious experiences. What if your experience isn’t as dramatic as you remember it, because your thief massaged the data to create a sensible narrative and you simply remembered the thief’s story and not the unadulterated experience? Without attempting to repeat the experience, how would you know? Remember, your thief is always awake, and especially loves to take charge when the wizard is asleep or is preoccupied by something else (like stress or depression). And worst of all, the narrative created by the thief is wholly dependent upon your (subconscious) background knowledge.

 
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Posted by on May 7, 2012 in cognitive science

 
 
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