## Saturday, February 20, 2010

### Privileged priors and God

On Less Wrong, someone thought up a new kind of fallacy, called "privileging the hypothesis".
Suppose that the police in Largeville, a town with a million inhabitants, are investigating a murder in which there are few or no clues - the victim was stabbed to death in an alley, and there are no fingerprints and no witnesses.

Then, one of the detectives says, "Well... we have no idea who did it... no particular evidence singling out any of the million people in this city... but let's consider the possibility that this murder was committed by Mortimer Q. Snodgrass, who lives at 128 Ordinary Ln."
I would describe this fallacy as "questionable choice of prior probabilities".

Prior probabilities are something you need to consider if you wish to compare hypotheses with Bayesian statistics.  The prior probability of a hypothesis is the probability you assign before you consider the relevant evidence.  Prior probabilities are fundamentally arbitrary.  It's supposed to indicate your personal degree of belief.  Therefore, you can pick whatever numbers you like, and so can I.

And yet, some choices of prior probabilities are just more reasonable than others.  In the example of Largeville, we can reasonably say that there is a prior probability of one in a million that Mortimer Q. Snodgrass is the murderer.  Or perhaps we'd choose a higher probability, because we want to exclude young children.

But the detective has a much less reasonable choice of prior probabilities.  By simply pointing Mortimer out, the detective has biased our investigation significantly.  Because we have trouble conceptualizing numbers as small as one in a million, we can't help but overestimate the probability that Mortimer is the murderer.  The detective has wrongly privileged the hypothesis that Mortimer is the murderer.

For fun, here's a gratuitously controversial example of "privileging the hypothesis": God.  Specifically, let us consider the cosmological argument for God (ie God was required for the universe to exist).

If we accept the cosmological argument, then we can conclude that something ("the first cause") allowed for the universe to exist.  We can also conclude (depending on which kind of cosmological argument we're using) that the first cause is eternal, non-contingent, and so forth.  But there's not really anything that requires the first cause to be a god, much less God with a capital G.

I propose that the first cause, if it exists, can be all sorts of things.  The vast majority of those things are not deities, indeed the vast majority don't even have consciousness or intentionality.  But we still know it as the cosmological argument for God.  The hypothesis that the first cause is God is a wrongly privileged hypothesis.

Furthermore, I discourage the use of "god" when it does not refer to any of the gods of major religions.  When we talk about a god, it could be all sorts of things.  But most religious people instantly think of their own god.  By simply using the same word, "god", we inadvertently privilege the hypothesis that the god in question is the god of a major religion.

(via The Thinker)