The Self Indication Assumption Works As Well As Effective Contraception
But I was wrong about why!
I recently made a dumb error!
I know, hard to believe. Many affirm the doctrine of Bentham’s Bulldogamite infallibility, according to which my articles are infallible—theopnustos, many have said. The fact that I seemingly made an error and am now changing my mind may seem to pose a puzzle for Bentham’s Bulldogamite infallibility, though I’m sure people can reconcile being perfectly wise with seeming to change my mind. In all seriousness, however…
In a recent article, I made the following argument. Given that you exist, you have a reason to think that your parents didn’t use extremely effective contraception. I gave the following case which I’ll know give a name:
Procreation coinflip worldwide: In 1970 a coin was flipped. If it came up heads then everyone in the world would have had to use extremely effective contraception. If it came up tails, they wouldn’t. Given that you exist, I submit that you should think the coin probably came up tails. But why?
I argued that the only explanation of why this is so is that the self-indication assumption (SIA) is right—that’s the theory according to which, given that you exist, you should think there are more people because the existence of more people makes it likelier that any particular person would exist. But I missed an obvious reply: the person who rejects SIA can reason in the following way: the odds my parents would get pregnant are higher if they didn’t use contraception than if they did. Therefore, given that they got pregnant, I have strong evidence that they didn’t use contraception.
But from this, I think we can still construct a powerful argument. Let’s first note that there’s a powerful reason to accept SIA’s judgment in Procreation coinflip worldwide—this seems like:
Procreation conflip local: In 1970 a coin was flipped. If it came up heads then your parents would have decided to use extremely effective contraception. If it came up tails, they wouldn’t. Given that you exist, I submit that you should think the coin probably came up tails.
These are relevantly alike. After all, the only difference between the cases is in whether the coinflip also affected other people’s reproductive decisions. But obviously, the odds you should give to the coinflip described in the scenario coming up heads should be unaffected by other people’s procreative decisions. Here’s another case:
Procreation conflip local one super-prolific family: There are extremely long-lasting beings named Bob and Randi. They birthed everyone in the world. In 1970 a coin was flipped. If it came up heads then Bob and Randy would have decided to use extremely effective contraception. If it came up tails, they wouldn’t.
Suppose in this case that you don’t know your birth rank. If Bob and Randi used extremely effective contraception, they would have had only 50 children. If they didn’t, they’d have had a few billion children. I claim that given that you exist, you should think the coin came up tails. After all, even on non-anthropic grounds, we can see that this result is right. Whichever particular sex act resulted in your creation would be very unlikely to result in Randi’s pregnancy if the coin came up heads. Thus, you know that some sex act, say sex act N, resulted in Randi being pregnant. The odds of that are much higher if the coin came up tails than if it came up heads, so you get strong evidence that the coin came up tails (for if something that happens is more strongly predicted on one hypothesis than another, it occurring is evidence for the first hypothesis over the second).
But this case seems relevantly like:
Bob’s coin toss: Bob is a immensely powerful Godlike being. He tossed a coin and created a few billion people if it came up tails and 50 if it came up heads.
I submit that this case is relevantly like Procreation conflip local one super-prolific family. Whether Bob produces children through sex with Randi or through his own Godlike powers should be irrelevant to how you reason about the odds of your existence conditional on his act. If I know that either 50 or 10 billion people were created, the odds I should give to each of them shouldn’t depend on how they were created—whether through intercourse or the creation of a powerful being.
But Bob’s coin toss is a judgment basically only held by SIA. Given that SIA says that you should think there are more people, given that you exist, only it makes sense of a judgment like Bob’s coin toss. In fact, this essentially just is the famous presumptuous philosopher counterexample to SIA, wherein SIA instructs you to think there are a lot of people given that you exist.
So from these modest judgments, one can arrive at a conclusion amenable only to SIA. This gives, I think, a pretty good reason to accept SIA.
> Bob’s coin toss
The correct answer is to update in favor of Tails if you know that you were randomly selected to be created and not update otherwise. If there was no random sampling involved, if Bob was planning to create you no matter what, then your existence tells nothing about the outcome of the coin toss - you simply observe event "At least one person was created", not "I was randomly selected from N attempts".
However, SIA just assumes that you are always randomly sampled. This is sometimes true. But not always. You need to actually investigate the casual history that led to your existence to know which case is which. Therefore SIA is wrong in a general case.
You should have addressed my example from the comments to the previous post:
On Tails only your biological parents are infertile since 1970, on Heads everyone in the world except your parents is infertile since 1970.
It is an actually interesting case where SIA contradict common sense and so it allows us to distinguish between two types of reasoning about such problems.
As you say, regardless of anthropics, in the the super-prolific case I have reason to favor tails. One reason for this is that the probability of Randi getting pregnant at all (or carrying through to term, or whatever) is higher on the tails outcome than on the heads outcome*. In the divine case, the existence of the causal processes that successfully lead to even a single example of a human being created are the same. The causal process is just "God decides to directly create at least one person," and that has probability 1 of happening/succeeding on both coin outcomes, given omnipotence. Of course, you can modify the scenario so that God's actions might fail to create anyone based on more intermediary processes, but then we can appeal to a similar sort of non-anthropic evidence as in the other example.
* This still only gives me absurdly weak evidence for tails, since the probability of at least one pregnancy happening on heads and tails are both pretty close to 1. But I don't see a problem with this.