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The Real Problem With Theistic Evolution

05 Mar

Theistic evolution. What can I say about this that hasn’t already been said? Not much. Most biologists are either annoyed or appalled by the mention of it. No one believes in theistic evolution because it makes sense. They believe in it because, to use an overwraught phrase, it lets them have their cake and eat it too.

The evidence for evolution is overwhelming. Endogenous Retroviruses? Succession in the fossil record? Ring Species? Nested Hierarchies? Broken vitamin C gene in primates? Whales with hipbones and bones for legs? Birds with teeth? Approximately 98% genetic similarity between chimps and humans; the genetic difference between rats and mice being 15 times that of humans and chimps? Approximately 128 mutations per human zygote? All of those things make better sense in an biological/inheritance (i.e. evolutionary) framework than any other framework. So where does this leave god, in this case, the Christian god? If he isn’t necessary for the existence of humanity, then what other place is god necessary? Evolution makes the Christian god an unecessary hypothesis; the Christian god is a third wheel. There is observationally no difference between evolution with a god and without a god guiding the process. But the Christian god has to be there anyway, because, well, if he’s not then people like Richard Dawkins are right. And we can’t have that!

So theistic evolution is a political decision. It’s not a logical conclusion based on evidence. It’s the choice used by, in this case, liberal Christians to claim to be open minded about the evidence for evolution — to the chagrin of the fundamentalists — but yet also keep their god in the mix.

Of course, since I’m thinking like a Bayesian, allow me to retort.

Let’s assume, for the sake of example, that the number of people on the planet right now with a brain tumor was the same as the number of people on the planet with a head cold. Brain tumors cause headaches in 99 out of 100 people, head colds cause headaches 30 out of 100 people. If you wake up one morning with a headache, are you now in the population of people with a brain tumor or the population of people with a head cold? How likely is it that you are in one population or the other?

Hopefully you know the answer to that.

Now, the point here is to emphasize that some hypotheses can only account for one observation, while other hypotheses can account for multiple observations. If the two hypotheses have the same prior probability of being true, the hypothesis that can only explain the current evidence gets the bonus when placed in conjunction with the hypothesis that can explain multiple types of evidence.

Probability is a lot like energy, it has to be conserved. The hypothesis that places all of its probability capital on only explaining one type of evidence will win when juxtaposed with the hypothesis that can explain multiple lines of evidence (assuming that the prior probability for both is the same). Because the hypothesis that attempts to explain multiple lines of evidence spreads itself thin when saying that it can explain multiple lines of evidence. There’s a limited amount of probability to spread around since it all has to add up to 100%. Or, P(E | H) + P(~E | H) = 1.00.

So theistic evolution. If the prior probabilities for atheism and theism were equal, which hypothesis better explains evolution? Theists, taken as a whole, assert that their god can account for evolution and non-evolution (creating humanity by other means). So the theism hypothesis can account for both types of evidence (if, indeed, those were the only two options). On the other hand, the atheist hypothesis can only account for humanity via evolution. It cannot explain any other way for humans to have come about.

In the case of the head cold (if you didn’t click on the link), to find the Likelihood Ratio, you divide the success rate of the brain tumor by the success rate of the head cold. This would be 99 out of 100 divided by 30 out of 100. Or .99 / .3. This number, the Likelihood Ratio, is 3.3 decibles. Let’s run through this using Bayes’:

E = headache

P(HTUMOR) = .4
P(HCOLD) = .4

P(E | HTUMOR) = .99
P(E | HCOLD) = .3

P(HTUMOR | E) = P(E | HTUMOR)*P(HTUMOR) / [P(E | HTUMOR)*P(HTUMOR)] + [P(E | HCOLD)*P(HCOLD)]
= .99 * .4 / [.99 *.4] + [.3 * .4]
= .396 / [.396] + [.12]
= .396 / .516
= .767

Or:

P(HCOLD | E) = P(E | HCOLD)*P(HCOLD) / [P(E | HCOLD)*P(HCOLD)] + [P(E | HTUMOR)*P(HTUMOR)]
= .3 * .4 / [.3 * .4] + [.99 * .4]
= .12 / [.12] + [.396]
= .12 / .516
= . 233

So on the event of having a headache, the probability of it being a tumor went up from .4 to .767, yet the probability of it being a cold went down from .4 to .233**   

In this case, atheism is the brain tumor and theism is the head cold. Evolution is the headache. Which one is more likely, assuming an equal probability for atheism and theism? Exactly.

But why is theism the head cold? Because P(E | H) + P(~E | H) = 1.00. If theism can account for both evolution and non-evolution (if those were the only two options) then it becomes P(Evolution | Theism) + P(NonEvolution | Theism) = 1.00. Conversely, atheism would be P(Evolution | Atheism) + P(NonEvolution | Atheism) = 1.00. Atheism puts all of its weight behind evolution so P(Evolution | Atheism) is basically 100%, whereas theism has to split its probability capital between P(Evolution | Theism) and P(NonEvolution | Theism). If not, then you are effectively saying that the Christian god could only have created humanity by evolution and no other means, which would be the implication by asserting P(Evolution | Theism) is high like P(Evolution | Atheism). Thus, P(Evolution | Atheism) > P(Evolution | Theism), and we have a situation similar to the brain tumor and head cold in this example i.e. assuming prior probabilities are equal.

——
** this is assuming that headaches are only caused by tumors or head colds, since all of the P(H)s added together have to add up to 100%. Since the tumor and cold hypotheses in this example only account for 80%, the remaining 20% would be allocated to P(~H). If not assuming that only tumors and colds account for headaches, we would add + [P(E | ~H) * P(~H)] in the denominator to account for all other hypotheses in this example. But if P(E | ~H) were 0, or that only tumors and colds cause headaches, then the last bracket isn’t needed. Of course, in reality head colds vastly, vastly outnumber brain tumors so this is for example only.

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Posted by on March 5, 2012 in Bayes

 

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