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Bayes’ Theorem and the Existence of God, Part 2

11 Mar

So this is part 2 of using Bayes’ Theorem to see where I end up when I start with a high (.977) prior probability of the Christian god’s existence and add up all of the evidence for the existence of the Christian god (besides the Why I’m Not a Christian reasons). In the first part I first assumed that this is an analysis between the average person’s conception of the Christian god (all powerful, all good, all knowing, etc.), represented by H, and a non-all powerful god / atheism, represented by ~H. For the sake of sanity I am leaving out the god of the sophisticated theologians/philosopher’s god, the god(s) of Hinduism, Native American deities, animism, etc.

Next I looked at the relationship that religious experiences and cultural language have with the existence of the Christian god. It looks like there is no necessary correlation with religious experiences / cultural language and the existence of the Christian god, since non-Christians and even atheists have religious experiences. That is, people would have religious experiences whether the Christian god existed or not.

In this post I’ll look at some other arguments.

Our Privileged Planet

So we are still at .977 probability that the Christian god exists. What is another argument that convinces people that the Christian god exists? It’s usually some form of the “I don’t know how things work, therefore god” argument. Or, things are so complicated that only an intelligent designer could have built all of this. So on and so forth.

I already addressed this argument in a couple of posts, but I’ll rehash it here again.

The first aspect of this argument is how lucky we are that we live on planet Earth, which is the perfect distance from the sun to support life. The popular (and mistaken) Christian form of this, seen in lots of forwarded emails and drive by postings on Internet forums, is that if the Earth were one inch (or one mile or one kilometer or something) closer to the sun we would fry and if we were one inch (mile, etc.) away from the sun we would freeze to death. Of course, this can’t be correct on its face because the Earth’s orbit is not a perfect circle; it moves between 91 and 94 million miles from the sun over the course of a year. The Earth is closest to the sun in what is arguably one of the coldest months in the Northern Hemisphere (January).

But even all that is besides the point from a probability perspective. All stars have a Goldilocks Zone where liquid water can form, and it’s only a matter of probability that a star would have planets orbiting within that zone. The problem with the Christian god is that he’s supposed to be all powerful so we have no a priori reason for the Christian god to choose a planet that is within the Goldilocks Zone to create life. He could use perpetual miracles to make liquid water on Jupiter or Mercury if he wanted to.

So if we were to watch the Solar System form, before seeing which planets would end up green and which planets would end up barren, what probability would you place on life arising on any of those planets assuming the Christian god? What probability would you place on any of those planets assuming some other god or no god at all?

The success rate for Christianity for this problem is:

P(EMercury | H) + P(EVenus | H) + P(EEarth | H) + P(EMars | H) + P(EJupiter | H) + P(ESaturn | H) + P(EUranus | H) + P(ENeptune | H) = 1.00.

So if one were to say that P(EEarth | H) 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(EEarth | H) in reality would be 1/8, or .125.

(to be fair I’m not including asteroids or moons since even though the Christian god has no restrictions on creating life on Titan, including all of those satellites would diminish the probability further) On the other hand, either assuming a non-all powerful god or atheism, life is limited to coming about on Goldilocks Zone planets. What, then, would you place the probability of life coming about on any one of the eight planets assuming some other non-all powerful god or no god at all (these two options are included in ~H)? We wouldn’t have an even distribution like in the case of the Christian god, but a more bell-curve like distribution peaking on the Goldilocks Zone planet(s). In our Solar System it would peak on Earth, have a bit of probability on Mars and Venus, and the rest of the planets would have a negligible probability.

So I would estimate that P(EEarth |~ H) would be closer to .9, with the planets on the outskirts of the GZ 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.

Evolution

Evolution, the dreaded E word. Even though I already wrote about this two posts ago, I’ll do so a bit here again, but from a different perspective. Let’s say that there was no evidence for evolution, what would we conclude about the Christian god?

To back up a moment, according to theistic evolutionists, the Christian god can account for both evolution and no evolution. This means that P(Evolution | Christian God) + P(No Evolution | Christian God) = 1.00. In this case, I’m not including the Christian god in the larger category of “Intelligent Designers” which could possibly include aliens or humans from the future, The Matrix, or something. Even if life on this planet were created by aliens, those aliens themselves were probably evolved. So this is taking the question of evolution from a reductionist standpoint; the first intelligent life coming about through evolution.

So this analysis will be limited to the Christian god and atheism. Atheism can only account for evolution. Non evolution doesn’t make sense in an atheistic framework due to reductionism. Reductionism inferring that intelligence has to come from non-intelligence. ** So, atheism would look like this P(Evolution | Atheism) + P(No Evolution | Atheism) = 1.00. When we put the two side by side, theistic evolution can explain both while atheistic evolution can only explain one. Who knows how theists would spread their probability between the two explanations, but atheism can only put the vast majority of its probability capital on P(Evolution | Atheism).

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.

Argument From [Objective] Morality

So this one will be tricky to attempt from a Bayesian point of view. The usual Christian refrain is that morality comes from the Christian god, and if the Christian god didn’t exist, we would all be immoral monsters where rape is acceptable and a bunch of other stuff. They are basically saying that P(Morality | Christian God) = 1.00, which also means that P(No Morality | Christian God) = 0.

The problem is how we define morality, which is why I normally do not get involved in discussions about morality.

But what about the alternative hypothesis P(Non Christian God, Atheism)? What is P(Morality | Non Christian God, Atheism)? Or what is the probability of having morality period, or P(Morality)? What I think most Christians are thinking is that morality itself is extraordinary, or uncommon. Which means that the existence of morality is itself uncommon/extraordinary evidence. That P(Morality) is low. So we can use the same type of model that I attempted with religious experiences.

If P(Morality) = .01, what does this do with the rest of the equation? We already have our prior (.7487) and the alternative (.2513) so we end up with .01 = P(Morality | Christian God) * .7487 + P(Morality | Non Christian God, Atheism) * .2513. The Christian claim is that P(Morality | Non Christian God, Atheism) = 0, so what number must P(Morality | Christian God) be in order to get P(Morality | Christian God) * .7487 + 0 = .01?

.01 = P(Morality | Christian God) * .7487
.01 / .7487 = P(Morality | Christian God)
P(Morality | Christian God) = .0133

I don’t think Christians would agree that the probability of the existence of morality given the existence of the Christian god is only 13.3%. We can try it the other way. If P(Morality | Christian God) = .99, what must P(Morality | Non Christian God, Atheism) be, given that morality itself is extraordinary?

.01 = .99 * .7487 + P(Morality | Non Christian God, Atheism) * .2513
.01 = .7423 + P(Morality | Non Christian God, Atheism) * .2513

It looks like the only way to get the equation to equal .01 is for P(Morality | Non Christian God, Atheism) to be a negative number. Or, a literally impossibly low number. In other words, if the existence of morality is extraordinary, then we wind up with an independence.

In reality though, morality (just like religious experiences) are not extraordinary. Just about all social animals (including primates) have a system of morality. Which means that morality is not uncommon. This would result in a much higher P(Morality). If I were to count up the number of social animals and then count up the number of those social animals with some sort of system of morality, no matter how rudimentary, I would then get the “rate” of morality among social animals. That would be the actual P(Morality). From here it seems that about 90% of animal behavior is “pro-social”. I guess the argument could be made that morality isn’t the same as being pro-social, but again I’m no moral philosopher. So that will be my P(Morality).

Now we have:
.9 = P(Morality | Christian God) * P(Christian God) / [P(Morality | Christian God) * P(Christian God)] + [P(Morality | Non  Christian God, Atheism) * P(Non Christian God, Atheism)]
.9 = .99 * .7487 + P(Morality | Non Christian God, Atheism) * .2513
.9 = .7412 + P(Morality | Non Christian God, Atheism) * .2513
.1588 = P(Morality | Non Christian God, Atheism) * .2513
.1588 / .2513 = P(Morality | Non Christian God, Atheism)
P(Morality | Non Christian God, Atheism) = .632

This also means that P(No Morality | Non Christian God, Atheism) = .368.

So with these numbers – P(Morality | Christian God) = .99, P(Christian God) = .7487, P(Morality | Non Christian God, Atheism) = .632, and P(Non Christian God, Atheism) = .2513 —  Bayes’ Theorem updates P(Christian God) from .7487 to .8235. Checkmate, atheists! lol

Of course, I personally believe that the prior probability of the Christian god is extremely low, since Christianity is a slew of extraordinary claims. So with a low prior probability ( > .01) for the existence of the Christian god,  a probability of morality being .9, and a high probability of morality given the existence of the Christian god, this forces P(Morality | Non Christian God, Atheism) = approx. .89. So with this, it bumps up the probability of the existence of the Christian god negligibly.  

On the other hand, if morality indeed were extraordinary, then this would be exceedingly good evidence for the Christian god, given an also low prior probability of his existence. P(Morality) and P(Christian God), both being “extraordinary”, would cancel each other out. Then this would make P(Morality | Christian God) and P(Christian God |Morality) equal, and if Christians assert that morality can only exist with their god, or P(Morality | Christian God) = .99, then this would also mean that P(Christian God | Morality) = .99. A massive increase in prior probability, this is what is meant when one says “extraordinary claims require extraordinary evidence”.

But, as I said, I assumed a high prior probability for the Christian god for this exercise, and morality itself is not uncommon.

Next Again!

So this concludes this part 2 of my critique of the existence of the Christian god given a high prior probability of his existence. Next up is round three, and I’ll see what other arguments common people give for the existence of the Christian god.
_____________
**Granted, there could be (and are) atheists who believe in psi, but this makes them supernaturalists since they think that life and maybe even the universe is fundamentally mental. A fundamentally mental universe is supernaturalism.

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