Some people have the intuition that there is something fishy about doing standard Bayesian update on evidence E when one couldn’t have observed the absence of E. A standard case here is where the evidence E is being alive, as in firing squad or fine-tuning cases. In such cases, the intuition goes, you should just ignore the evidence.
I had a great conversation with a student who found this line of thought compelling, and came up with this pretty convincing (and probably fairly standard) case that you shouldn’t ignore evidence E like that. You’re stranded on a desert island, and the only food is mushrooms. They come in a variety of easily distinguishable species. You know that half of the species have a 99% chance of instantly killing you, and otherwise having no effect on you other than nourishment, and the other half have a 1% chance of instantly killing you, again otherwise having no effect on you other than nourishment. You don’t know which are which.
To survive until rescue, you need to eat one mushroom a day. Consider two strategies:
Eat a mushroom from a random species the first day. If you survive, conclude that this species is likely good, and keep on eating mushrooms of the same species.
Eat a mushroom from a random species every day.
The second strategy makes just as much sense as the first if your survival does not count as evidence. But we all know what will happen if you follow the second strategy: you’ll be very likely dead after a few days, as your chance of surviving n mushrooms is (1/2)n. On the other hand, if you follow the first strategy, your chance of surviving n mushrooms is slightly bigger than (1/2)(0.99)n. And the first strategy is precisely what is favored by updating on your survival: you take your survival to be evidence that the mushroom you ate was one of the safer ones, so you keep on eating mushrooms from the same species. If you want to live until rescue, the first strategy is your best bet.
Suppose you’re not yet convinced. Here’s a variant. You have a phone. You call your mom on the first day, and describe your predicament. She comforts you and tells you that rescue will come in a week. And then she tells you that she was once stuck for a week on this very island, and ate the pink lacy mushrooms. Then your battery dies. You rejoice: you will eat the pink lacy mushrooms and thus survive! But then suddenly you get worried. You don’t know when your mom was stuck on the island. If she was stuck on the island before you were conceived, then had she not survived the mushrooms, you wouldn’t have been around to hear it. And in that case, you think her evidence is worthless, because you wouldn’t have any evidence had she not survived. So now it becomes oddly epistemically relevant to you whether your mom was on the island before or after you were conceived. But it seems largely epistemically irrelevant when your mom’s visit to the island was.
7 comments:
This is all well and good for the mushroom case, but I think the idea behind 'being alive' intuition is that we would never be alive to even test between the mushrooms in the first place, so no updating can ever take place. Compare the firing squad. The anthropic response to the firing-squad is silly because you observe before and after the shots are fired. However, in the case of fine-tuning, there is no 'before' state to observe.
I don't know if this objection is any good, but I also don't know if this mushroom case dispels it.
That's a good point, but I think the mushroom case can be tweaked to take this into account. Imagine that your life history is this. You begin your existence as a sleepwalker on this desert island, with a good deal of evolved innate knowledge, such as about mushroom statistics. You eat a mushroom, and lie down. In the morning you wake up. It's the beginning of your consciousness. You see bits of mushroom near you, and find bits of mushroom in your teeth, and figure out that you must have eaten it last night, before you became conscious.
Now that you ARE conscious, next time you need to eat a mushroom, clearly you should eat the SAME kind of mushroom. Again, we can calculate strategy outcomes.
Strategy 1: Disregard data about which mushroom you ate and choose at random. Chance of surviving both the first (preconsciousness) night and the second (conscious night): (0.5)(0.5)=0.2500.
Strategy 2: Eat the same mushroom as the night before. Chance of surviving both nights: (0.5)(0.01)(0.01)+(0.5)(0.99)(0.99)=0.4901.
Note, too, that in the case of the call to mom, if it turns out that she ate the mushroom before you were conceived, there wouldn't have been a "before" for you to observe, either.
“Some people have the intuition that there is something fishy about doing standard Bayesian update on evidence E when one couldn’t have observed the absence of E.”
That’s not what makes fine tuning arguments seem fishy. (Or so I suggest…) Updating on such evidence is fine, as long as the probabilities you use were formulated independently of E. In all the mushroom examples, the mushroom stats are given, independent of anything you (or your mom) do. So there’s no problem updating on you (or your mom) being alive. In firing squad, the prior and conditional credences are not given, but you set them before the shots are fired.
Fine tuning is much murkier. You have to try to imagine what ‘prior’ and conditional credences would be reasonable ‘before’ the universe (and you with it!) existed, and without using your (relevant) knowledge of the actual universe. That’s a tall order.
Ian:
Isn't this just the problem of where ur-priors come from?
Yes, precisely.
Ian: That cuts both ways and is a main reason I find arguments about what's "surprising given (a)theism" so maddening.
But if we don't have priors over possible laws of nature, we can't do science (at least not in a Bayesian way).
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