All Theories Of Anthropics Are Presumptuous

Some just presume more plausible things than others

The most common objection to SIA is the following, from Bostrom’s book Anthropic Bias:

The Presumptuous Philosopher 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 world is very, very big but finite and there are a total of a trillion trillion observers in the cosmos. According to T2, the world is very, very, very big but finite and there are a trillion trillion trillion observers. The super-duper symmetry considerations are indifferent between these two theories. Physicists are preparing 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! (whereupon the philosopher runs the Incubator thought experiment and explains Model 3).”

Lots of people seem to think that SIA implying that you have good reason to think that the philosopher is reasoning correctly is a decisive mark against it. And worse, if we took this seriously, it would have actual implications in the real world favoring, for instance, the many worlds interpretation of quantum physics simply because it implies that there are more people. Anthropics, if we adopt SIA, can’t just be brushed aside as a purely theoretical inquiry—it would change how we do our science and what we believe about the world.

But every view of anthropics will have to be presumptuous in this sense. In fact, we can show that everyone will have to be presumptuous. To see this, suppose one is a halver in sleeping beauty. Suppose that if the coin comes up tails they’ll be awoken on Monday and Tuesday. If they’re awoken and discover that it is Monday, they should be 2/3 confident that the coin got heads then, because they were initially 50/50 and got new evidence that’s twice as strongly predicted on the hypothesis that the coin came up heads. But we can make this more extreme. Suppose that there are days labeled 1,2,3,4…10^100. If the coin comes up tails she’ll be awoken each of the days, each time with no memory of the previous ones. If the coin comes up head, she’ll be awakened only on day 1.

There are two main views about what Beauty should conclude in such a scenario (Bostrom tentatively describes a third view that’s a bit more complicated which I’ll set aside for now, as it implies that same kind of presumptuous as thirding). On thirding, upon waking up, one should be very confident that the coin came up tails. Even if scientists run blood tests and tell them that there vitals are more consistent with having been awoken once than multiple times, they should still be confident for the evidence is so strong. Thirders therefore should be quite presumptuous, even in the face of scientific disagreement.

But so should halvers. To see this, suppose that Beauty wakes up and learns that it’s day 1. Halvers would say she should now be almost absolutely certani that the coin came up heads—she was 50/50 and then she learned that it’s day 1 which is much more strongly predicted on the hypothesis that the coin came up heads. Here, Beauty should still be presumptuous.

Note here that I’m only describing what follows from the various views. Of course, in the real world one should be uncertain and thus not have their credences be in accordance with either theory. Here, I’m just describing that both theories have presumptuous outputs.

In fact, those who disagree with the presumptuous philosopher must have their own presumptuousness problem. The presumptuous philosopher verdict says that one should be maximally certain, upon finding out that they exist, that the universe is infinitely large. Suppose then that one finds out that they exist, but are part of the leftmost quadrant of the universe. There are two hypotheses:

1. The universe is infinitely big.

2. The universe is small.

The presumptuous philosopher can follow the evidence where it leads—the left quadrant evidence cancels out that a bigger universe makes it more likely that they’ll exist somewhere. In contrast, even after gathering overwhelming scientific evidence for the first theory, the denier of the presumptuous philosopher verdict will deny it on the basis of their prior philosophical commitments.

Finally, SSA, the main rival to SIA, implies extremely presumptuous results. It implies you can know you won’t get pregnant by having sex if you’re one of the first humans and you getting pregnant would result in lots of people. It even implies that you should presume solipsism because it implies that the reference class is small enough that you’d be guaranteed to be drawn from it. It implies the presumptuousness I gave in a previous article:

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.

When criticizing the presumptuous philosopher verdict, there’s often a lurking background assumption that one shouldn’t make empirical predictions from philosophy. Doing so is reminiscent of Aristotle trying to figure out the number of teeth women had a priori. But this is the wrong way to think of it.

Philosophical conclusions do often make empirical predictions. That moral realism is true, for instance, implies that if God existed and we spoke to him, he’d say that moral realism is true. That contradictions are impossible makes a radical empirical prediction—that we could search the entire universe and we’d never find a true contradiction. We could scan every centimeter of the universe and we’d never find a rock that is not a rock, a person that is not a person, a star that is not a star. How presumptuous! Who are philosophers to make radical empirical predictions about the world?

Furthermore, anthropics is not an a priori inquiry. SIA defenders don’t claim that an infinitely big world is a priori more likely based on simplicity or elegance or anything in the vicinity. Rather we claim that you have a piece of data that is infinitely unlikely on the hypothesis that there are finite agents—namely, that this version of you exists. That’s extremely an extremely unlikely chance event. Most ways reality could be don’t involve them containing you—certainly not this version of you rather than someone else with similar qualitative features but a different identity and some different features. In fact, if we’d followed the advice of SIA, we’d have consistently been right historically!

It’s true that there are many cases where people make incorrect predictions based on purely philosophical inquiry. But the solution is to simply…not conclude things based on bad reasons. As long as philosophy can teach us some things, and those things it teaches us will sometimes have empirical content, philosophy will sometimes teach us things about the world!