Monday, March 17, 2008

How Probable is God?

The design arguments that have become popular in the last few years have invoked some impressive claims about probability that have an authoritative air to them. Many people who share the intuition that “this all couldn’t have possibly have happened by chance” find these arguments quite compelling.

Robin Collins, in God, Design, and Fine Tuning, claims: The existence of the fine-tuning is not improbable under theism. The existence of the fine-tuning is very improbable under the atheistic single-universe hypothesis. And in his version of the design argument, Richard Swinburne argues that it is exceedingly unlikely that there would be a lawlike universe of matter composed of simple parts that could just happen by random chance. But such a universe is what we would expect to find if there were a designer God who values beauty, simplicity, and who wishes to create a challenging environment for his human creations.

In order to make use of the Bayesian probability calculus, which these arguments do, part of what figures into the equation is something called a person’s prior probabilities. In order to attach a probability to some outcome that is unknown, Bayes theorem requires that I attach some value to the probable outcomes as I see them. Bayesian calculations are subjective in this fashion. In the design arguments above, we are asked to agree that the likelihood that the universe could have come out like it is without God is very, very low. It doesn’t seem like such a thing could have happened by chance or without some purposeful plan in the hands of a powerful being, does it?

But our subjective sense of likelihood here is really all that we have. We don’t have any real distribution data concerning universes that would let us say that 95% of the time in cases we have studied, universes with stable carbon molecules were designed by God. And only in a tiny number of cases of the millions of universes we have studied do life favorable conditions happen by chance. If we had those numbers, then it would clear a lot of things up. But we have one universe—the one we live in. And each of us only has the confines of our own mind in which to make a call about the probability or improbability of a life friendly universe by chance. No doubt for many people, when they consider the possibility that all of the physical laws just happened to line up the way they did by chance, or God did it, they find the latter much more likely. See my earlier post, Bogus Probability Judgments and God for an analysis of the false dilemma that is getting smuggled past us here.

In this sort of case, though, assigning a low probability to a random chance origin and a high chance probability to the God origin really just amounts to expressing your personal level of surprise about one and your comfort with the other. It has no objective bearing on the truth. As a previous poster put it, “if these are where these supposed "probabilities" are coming from, then it is equivalent to "some people subjectively suppose it's a very unlikely probability that the universe is as it is without our God to make it so."”

All of these probability claims seem impressive, but in the end, all they amount to is a person’s measure of their surprise that something would be true. So Collins’ claim, "On the God hypothesis, the fine tuning we observe in the universe is highly probable," really says little more than "I would find it very surprising that God doesn't exist in a world with these physical features."

The problem here is that one's subjective measure of surprise, to put it mildly, just doesn't count for jack. Medieval priests would have been exceedingly surprised to find out that the bubonic plague was caused by a bacteria, not by evil demon possession or the corruption of sin. On their view, this sentence seems justified: "On the sinners-are-punished hypothesis, the health problems we observe in plague victims would be very likely." Therefore, the plague is caused by sin. Copernicus’ contemporaries were exceedingly surprised and assigned a very low probability to his claim that the Earth orbits the sun. I know lots of people are very surprised to find out that the Gambler’s Fallacy is a fallacy. Many ancient people would assign a very low probability to the claim that the earth is spherical, not flat. And so on.

Since authors like Collins and Swinburne are using terms like "probability" lots of people are more impressed with the arguments than they should be. But what becomes clear when the details of Bayes Theorem come out is that the arguments are flagrantly circular. The existence of God is exceedingly probable because I find the non-God alternatives to be very improbable, therefore, the existence of God is exceedingly probable.


Eric Sotnak said...

Have you ever noticed that when it suits their purposes, theists are often very willing to make confident pronouncements about what God would or wouldn't do, or how things must be if God exists, etc. But when things seem not to go their way, they fall back on the mysteriousness or inscrutability of God? The general argument forms seem to go something like this:

If God exists, we can explain X because X is just what we would expect if God exists.

We can't infer that God doesn't exist from Y because God is so inscrutable that we can't say that Y is what we would expect if God doesn't exist.

Anonymous said...

God and Rev. Bayes

Anonymous said...

One thing to point out, besides the fact many people throw around probability incorrectly, but in the area of statistics we have to keep in mind the only real alternative is a frequentist approach (parametric testing can be used to, but it applies to unique cases of non-distributions). The frequentist inference is limited, however, to the design of the analysis, to put it simply. If there can be a distribution derived from data, then we can use our statistical methods. Bayesian inferences, on the other hand, can be applied to conditional statements that have nothing to really do with distributions. It is in this view we have to keep in mind the utter subjectivity of the claims.

Now, what makes Bayesian inferences useful is the fact we can take "educated guesses" from people who actually know what they're talking about. When we lack data, it is good to be able to rationalize what kind of probability we might expect. It is in this way that expert opinion can be utilized in an analysis, even though it is not technical in any sense of data (and the differences once we have data really show Bayesian to be no better than frequentist models).

I would not want people to walk away from this thinking Bayesian inferences or conditional probabilities are incorrectly applied outside of distribution (of frequency) data, but what appears to also be in short supply is justification for priors. I think McCormick's closing statements really brought that point home with the circularity that seems apparent in these monotheistic arguments. It's ultimately like trying to make an inductive argument without a knowledge-set (data) and making an inference anyway by referencing itself. It's not reasoning!

Anonymous said...

The way I see it.
There are only 3 possible outcomes for a universe.

1. Matter is attracted to itself.
2. Matter is neutral to its self.
3. Matter is repelled by its self.

In the latter 2 cases this universe could not form into complex forms.

Since Matter is attracted to its self, complex things can form.
Science explains how this happens.

So the odds are really 1 in 3 if the 3 options are are equal, not that extraordinary in my opinion.

The probability of a God existing seems much more unlikely.

Since the universe exists and nothing can be destroyed, only change form, seems more likely the universe has always existed in some form or another.

Even if there is a God, I see no reason why such God would take a personal interest in humans.