Contra Circovic on SIA
The self-indication assumption is the best view of anthropics
Introduction
Milan Ćirković has a paper titled Is Many Likelier Than Few? A Critical Assessment of the Self-Indication Assumption. In it, he argues against the self-indication assumption, claiming that the only thing it has going for it is that it explains why the doomsday argument fails. I think this is wrong—not only is SIA the only view that avoids doomsday-style results, it’s what you get when you apply straightforward probabilistic reasoning to your own existence. In a paper which I just finished writing, I argued that the main objection to SIA—the presumptuous philosopher case—is totally bunk, and that SIA is the only way to avoid various grotesquely counterintuitive paradoxes. I thought it would thus be fun to address Ćirković’s piece arguing against SIA. I won’t address every point, but I’ll address the main ones.
1 Crazy results
Ćirković is not moved by the standard sorts of paradoxes opposing SSA (which can be shown to follow from any alternative to SIA) including UN++:
It is the year 2100 A.D. and technological advances have enabled the formation of an all-powerful and extremely stable world government, UN++. Any decision about human action taken by the UN++ will certainly be implemented. However, the world government does not have complete control over natural phenomena. In particular, there are signs that a series of n violent gamma ray bursts is about to take place at uncomfortably close quarters in the near future, threatening to damage (but not completely destroy) human settlements. For each hypothetical gamma ray burst in this series, astronomical observations give a 90% chance of it coming about. However, UN++ raises to the occasion and passes the following resolution: It will create a list of hypothetical gamma ray bursts, and for each entry on this list it decides that if the burst happens, it will build more space colonies so as to increase the total number of humans that will ever have lived by a factor of m. By arguments analogous to those in the earlier thought 6 experiments, UN++ can then be confident that the gamma ray bursts will not happen, provided m is sufficiently great compared to n.
This is the only case he lists, but I’ll list a few others to show just how unintuitive it is to accept the broad Doomsday-style reasoning. One that’s original to me is:
Future Graham’s Number: there is some machine that will ensure a future of Graham’s number years, containing more than Graham’s number observers unless the next 100 hands in some particular poker game all contain royal flushes.
Another comes from Bostrom and is called serpent’s advice:
Eve and Adam, the first two humans, knew that if they gratified their flesh, Eve might bear a child, and if she did, they would be expelled from Eden and would go on to spawn billions of progeny that would cover the Earth with misery. One day a serpent approached the couple and spoke thus: “Pssst! If you embrace each other, then either Eve will have a child or she won’t. If she has a child then you will have been among the first two out of billions of people. Your conditional probability of having such early positions in the human species given this hypothesis is extremely small. If, one the other hand, Eve doesn’t become pregnant then the conditional probability, given this, of you being among the first two humans is equal to one. By Bayes’s theorem, the risk that she will have a child is less than one in a billion. Go forth, indulge, and worry not about the consequences!”
A final case is called Lazy Adam:
Assume as before that Adam and Eve were once the only people and that they know for certain that if they have a child they will be driven out of Eden and will have billions of descendants. But this time they have a foolproof way of generating a child, perhaps using advanced in vitro fertilization. Adam is tired of getting up every morning to go hunting. Together with Eve, he devises the following scheme: They form the firm intention that unless a wounded deer limps by their cave, they will have a child. Adam can then put his feet up and rationally expect with near certainty that a wounded dear – an easy target for his spear – will soon stroll by.
Ćirković has two responses to these cases. The first is that he denies there’s anomalous causation. He says that backwards causation sometimes occurs, so there’s nothing special about this case. This is similar to a response Bostrom gives, wherein he denies that any backwards causation is going on at all.
I was sort of baffled reading these responses. The problem for SSA is not that there’s any anomalous causation—though that might also be a problem, though sorting out whether there’s anomalous causation gets quite technical quite fast. The problem is that Adam plainly shouldn’t be confident that a deer would drop dead at his feet, that Eve won’t get pregnant, and the person in the Future Graham’s Number case shouldn’t expect to get royal flushes. Making a bunch of offspring only if one’s spouse gets pregnant is not a safe form of birth control, no matter how many offspring it would be!
Next, he claims:
The second relevant issue is that there is a sort of semantic confusion here. When Olum (2001) states that SIA “agrees with our intuition that the chance of an event (e.g., the earth being hit by an asteroid) should not depend on the event’s consequences (e.g., humanity being wiped out)” he seemingly ignores what he has written only a few pages earlier, that “there are different kinds of probability”. There he explicitly distinguishes between objective physical probabilities, and the subjective ones following from our ignorance. In the asteroid case, we are obviously dealing with the latter, since it is far from clear that we understand all factors playing a role in the occurences of catastrophic impacts in earth's history.
A few points:
The main puzzle is that SSA implies crazily that Adam can be confident a deer will drop dead at his feet, that Eve won’t get pregnant, that the person in the UN++ case can be confident that a supernova won’t be destructive because of the UN++’s breeding plan, and that the person in the Future Graham’s Number case can be confident that they’ll get a bunch of royal flushes in a game that hasn’t been played yet.
SSA gives bad advice. If the objective probability of, for instance, Eve getting pregnant is 80%, then if one keeps running the experiment, Adam will be wrong 80% of the time. That means that SSA is a wrong theory of anthropics.
Intuitively, it seems like the subjective probability of a future event shouldn’t depend on its future consequences. The only reason why one’s subjective probability should differ from the objective probability of some event is if they get some special evidence for the event turning out some way. In other words, they only have reason to deviate if they observe some fact about the world that is more strongly predicted on the hypothesis that the evidence will turn out one way. But by definition, future events that you haven’t observed yet cannot be evidence. So therefore one’s odds of some future event can’t depend on its future consequences, and SSA (and alternatives to SIA more broadly) are false.
I think biting the bullet, as Ćirković does, in the Serpant’s Advice, Lazy Adam, Doomsday Paradox, and UN++ cases is crazy especially given that I think it’s totally unmotivated. SIA would be the best view even without those cases. But let’s explore Ćirković’s other objections.
2 Future possible observers
Ćirković claims that plausible views about time say that every time exists equally. Whether this view about time is right is controversial, and not something I will discuss in detail. He says that this makes the doomsday-style reasoning more reasonable—just as reasonable as saying that there probably weren’t lots of past observers because then we’d have likely been around in the past.
For one, I think it’s extremely implausible that you have any a priori reason to rule out the existence of many past people. It’s true that if there were more people then it would be likelier that you’d be in the past given that you’d exist, but it would be likelier that you’d exist, so the probabilities cancel out. Assuming that there aren’t lots of past people implies:
The presumptuous archeologist: The SSA has drawn their reference class. Archeologists discover overwhelming evidence that there were huge numbers of Neanderthals—quintillions of them—and that they’re in our reference class. On the SSA view, one should reject the overwhelming archeological evidence, because if you’re randomly selected from the reference class, it’s unlikely you’d be one of the chance few who isn’t a Neanderthal.
For another, the relevant thing isn’t about time but causality. It seems weird that the odds you should give to some event occurring will depend on its consequences. And causality is objective in physics (at least, this is what my friend who knows about physics tells me). The Adam and Eve results wouldn’t be any less weird if they occurred while time-traveling, so the people they’re talking about would be in the past. The thing that alternatives to SIA imply, that is hard to believe, is that the odds one should give to some event occurring depend on how many people that event occurring would result in. This result is perfectly consistent with every view of time.
3 Physical theories
Ćirković looks at the odd consequences that SIA would have on our physical theories, favoring ones according to which there are more people, even if we’re more anomalous. But I think on SIA, one should think that every possible person exists for that entails the existence of more people. Given that there are this many people, SIA makes similar predictions to SSA—once you exist, you should favor theories that say most of the people are like you. So I don’t think this is a big problem. It’s true that this means we’ll need some way to do anthropic reasoning with infinities, as Ćirković suggests, but this is something we should already accept.
What view does SIA point one to about the nature of everything. I’ve suggested elsewhere the answer is theism. This is good news if, as I think, you find theism independently plausible. This will give a reason to endorse SIA, for it naturally predicts a plausible view about reality.
4 Teleology
It is possible that I’m getting mixed up about what this section is arguing, as it’s a bit confusing, but I think my interpretation is right. Ćirković seems to argue that SIA implies some odd form of teleology by implying that a world is more likely if it has more people. Why should the universe care about the number of people? But SIA doesn’t imply that. SIA isn’t really about assigning absolute priors, it’s about updating on one’s existence. Upon discovering that I exist, I should think it’s likely that there are more people, because that makes my existence more likely.
In a later section, he says “Isn't it obvious that it is more plausible that a typical planetary system is inhabited by 10^9 than 10^99 observers?” Yes, based only on priors. But when I update on my existence, it’s more likely that the universe has a great many people, for that makes it likelier that it would have me.
5 Presumptuous philosophers
Ćirković gives the following spin-off of Bostrom’s presumptuous philosopher case:
PP3: “It is the year 2100 and physicists have narrowed down the search for a theory of everything to only two remaining plausible candidate theories, T1 and T2 (using considerations from super-duper symmetry). According to T1 the density of intelligent observers is about trillion trillion observers per cubic Megaparsec at present day. According to T2, there are on the average a trillion trillion trillion observers per cubic Megaparsec at present day. The super-duper symmetry considerations seem to be roughly indifferent between these two theories. The physicists are planning on carrying out a simple experiment that will falsify one of the theories. Enter the presumptuous philosopher: “Hey guys, it is completely unnecessary for you to do the experiment, because I can already show to you that T2 is about a trillion times more likely to be true than T1!”
I find Carlsmith’s discussion of the presumptuous philosopher case to be enough to thoroughly diffuse it. But just to discuss his considerations briefly:
Views that deny the presumptuous philosopher result must posit some fundamental difference between dying and not having been created on anthropic grounds.
The presumptuous philosopher result only follows if one is certain about anthropics.
Every view that avoids the strange section 1 results will entail the presumptuous philosopher.
Cirkovic suggests that this implies crazy things in the infinite case too—for it implies we should believe ourselves to be in a universe with greater density of observers. But I think that comparing numerousness in cosmological models shouldn’t have to do with density. On such a view, if everyone in Hilbert’s hotel just moved to the nth prime number, where n is their current room, then Hilbert’s hotel would be less numerous, and SIAers should think they’re now less likely to be in the hotel.
I don’t have a well-worked out way to do anthropic reasoning with infinites of the same cardinality. But I’m confident that density is not relevant.
6 Conclusion
Here, I’ve argued that the arguments Ćirković presents against SIA fail. They all either assume SIA is about priors, ignore the more radical implications that SIA has about ultimate reality containing every possible person, or are in some other way unconvincing. While his paper is interesting and thought-provoking, I think SIA comes out far ahead of every other view of anthropics.