Bayes, Sober, dice, intelligent design

I’m teaching Bayes’ theorem this week in my discrete math course, and that reminds me of an interesting puzzle related to the “argument by design” for God’s existence. The argument goes something like this: the probability that the universe would, by pure chance, have the physical constants “fine-tuned” in such a way as to allow intelligent life is spectacularly small. The probability that God would create the universe in this way, though, seems pretty high. So, according to Bayes, whatever prior degree of belief we might have in the existence of God should be much amplified by the fact that the universe is so hospitable to human life.

Objection to this argument: if the physical constants of the universe weren’t fine-tuned to permit our existence, we wouldn’t be here to notice! So the observation that the constants are fine-tuned carries no information, and shouldn’t be allowed to affect our beliefs.

Objection to the objection: Then suppose you were blindfolded in front of a firing squad, you hear twenty shots ring out, and you find yourself alive and unharmed. Quite naturally, you’re drawn to the conclusion that the firing squad must have missed you on purpose. Now a philosopher wanders by and objects: “But if you’d been killed, you wouldn’t be here to make that observation, so the fact that you survived carries no information and shouldn’t affect your beliefs about the intentions of the firing squad!”

At this point your confidence in philosophers would be shaken.

Elliot Sober handles this version of the argument by design, along with many others, and their corresponding objections and counter-objections, in a very thorough and clearly-written paper (.pdf file). So rather than try to unravel this knot in a blog post, I’ll give you one more puzzle.
Suppose you roll a die 20 times and get

6-4-1-5-1-2-1-3-3-1-6-2-4-1-5-1-3-2-4-5

A person sitting next to you now pipes up and says, “Well, there you have it, very strong evidence of the existence of God.”

You: “How so?”

Person: “Any God I can conceive of would certainly have arranged for those dice to fall 6-4-1-5-1-2-1-3-3-1-6-2-4-1-5-1-3-2-4-5. So the probability of that outcome, conditional on God’s existence, is 1, while the probability conditional on God’s nonexistence is 6^(-20). So you and I both have to drastically increase our degree of belief that God exists.”

How similar is this to the argument by design for God’s existence? To the firing squad argument that the shooters must have missed on purpose? Which of the three arguments are right and which are wrong?

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3 thoughts on “Bayes, Sober, dice, intelligent design

  1. Dirty Davey says:

    A quick response before reading the paper–in the firing squad example, the obvious issue is that you KNOW there is an intentional decision being made, one way or the other: each of the 20 people either chooses to shoot at you (and either hits you or misses) or chooses to miss you (we may be able to presume not-you is a big enough target that such shooters will not hit you accidentally). The likelihood of survival can easily be calculated if you know the skill of the shooters.

    And of course, the conclusion the potential victim draws wouldn’t be that different from the conclusion drawn by the commandante who gave the “fire” command, right?

  2. Steve says:

    Yeah, that’s where I came in too: we are predisposed from what we know about firing squads (the squads are made of people, kinda like Soylent Green) toward explanations for unlikely events that rely on the squad members’ intention, since we already know that the squad members have intentions (that they are people). Better parallel: not a firing squad but an avalanche…

  3. […] to see more in Bayes’s theorem than a mere probability inversion, see here and there and there again for examples, a focus that actually confuses—to some extent—the theorem [two-line proof, […]

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