A pessimistic thought about epistemic rationality

The more I think about relatives of the Doomsday Argument and my insect argument, the more I become suspicious of both the self-sampling and the competing self-indication assumptions.

Both assumptions require one to assign non-zero probabilities to metaphysically impossible hypotheses about where I am located in spacetime, such as the hypothesis that I was born in the 19th century, the hypothesis that I am a non-human or the hypothesis that it is now a Wednesday. It is usual in the discussion of these hypotheses not to worry much about such issues of metaphysical impossibility. The thought is that we are doing epistemology, not metaphysics.

Moreover, it seems reasonable to assign a credence 1/10 to the proposition that the hundredth digit of π is 3 when one hasn’t calculated that digit, even though one knows that the proposition is either necessarily true or necessarily false.

Perhaps my Aristotelian meta-epistemology can help, though. What if the right way to assign credences is not some abstract “rational” way to do so, but rather the human way—the way that our human nature calls us on us to? Our human nature specifies how we should function within a certain broad range of conditions. But outside of that range, human nature may not specify how we should function. Our nature specifies normal human locomation in earth gravity, but specifies nothing about what normal human locomation out in space should be like. Likewise, our nature specifies normal human credential behavior in many circumstances, but need not specify human credential behavior in outlandish cases like Doomsday.

Of course this raises the very hard question of which cases are within the range of cases where our nature specifies credential behavior and which are not.

An argument that insects are not conscious

Suppose insects are conscious. There are at least about a billion insects per human being. So, if insects are conscious, we should be surprised to find ourselves not being an insect. But if insects are not conscious, there is no surprise there. So, it seems, observing that we are not insects gives us very strong evidence that insects are not conscious.

But this just doesn’t seem to be a good argument… Perhaps the self-sampling thesis—the thesis that we should count ourselves as randomly selected from among observers—needs to be restricted to intelligent and not merely conscious observers? But isn’t that restriction ad hoc? If we're doing such restricting, maybe we should restrict even more finely, say to observers at our exact level of intelligence?

Doomsday, numbered cards and firing squads

The stuff in this post is surely in the literature, but it's more fun to think it through oneself than to dig in the literature.

The Doomsday Argument holds that our position in the birth-order of humanity supports hypotheses on which we are roughly in the middle of the birth-order over hypotheses on which we occupy a more extreme position in the birth-order. Here's a back of the envelope calculation. Let's say that about 100 billion people have ever lived. Then we should expect that only about 100 billion people will live. If population stabilizes at 10 billion, that means that the earth's population will probably turn over only about ten times, and hence the human race will die out within 1000 years (life expectancy might go up to 100 years).

As a proxy for the complications of the full Doomsday Argument, consider a simplified version. The Demiurge flips a fair coin. If it's heads, he creates a single person. If it's tails, he creates a sequence of 100 people, a new person every 20 years. You come into existence, learn these facts from the Demiurge, and also learn that you're number one in humanity's birth order. By the Doomsday Argument, this should give you reason to prefer the hypothesis that the Demiurge got heads on his flip. And indeed there is a very nice Bayesian rendering of this. The probability that you're first given heads is one. The probability that you're first given tails is 1/100, since you could equally well have been anywhere in the sequence. So your position in the sequence strong supports heads. Indeed, if the prior probability for heads is 1/2, Bayes' theorem says your final probability for heads is about 0.99.

Birth order complicates intuitions a little. There are worries of essentiality of origins: could you have been anywhere else in the birth order? There is some reason to think that such considerations are irrelevant as what matters is epistemic and not alethic modality, but to rule them out, let's vary the case a little. The Demiurge tosses the coin. On heads, he creates one person on one planet. On tails, he creates 100 people, each on a different planet. And then after creating each person he takes a deck of cards numbered from 1 to the number of people (i.e., a deck containing just a single card labeled 1, or a deck of cards from 1 to 100), and gives one card to each person. You are apprised of all these facts and you see that you have a card labeled 1. You think: getting card 1 is very unlikely on tails, but is certain on heads, so probably the Demiurge tossed heads. The cards obviously correspond to birth order. It is clear that if the Doomsday Argument is sound, this argument is inductively good. The reasoning is exactly parallel.

But now consider a firing squad variant. One hundred people, including you, are blindfolded, and a different crack shot in the squad is assigned to each. The dictator tosses a coin. If it's heads, one of the shooters loads his gun with a blank and the others load a bullet. If it's tails, they all load their guns with blanks. They fire. You notice you're still alive. Then the dictator takes a deck of cards, numbered from 1 to the number of survivors, and hands them out randomly to the survivors. You look at your card before you look around for other survivors--perhaps smoke swirls around you and you can't see further than your card--and it has the number one on it. The exact parallel to the Doomsday Argument then would say that you have very strong evidence that the dictator tossed heads, since it would be unlikely that you'd see the number one card if there were 100 survivors.

But notice that if that's how you're thinking, you're neglecting a crucial piece of evidence: your survival. Yes, the number one card favors the heads hypothesis. But the earlier observation that you survived favors the tails hypothesis. Your probability of survival on heads is 1/100, and on tails it is 1. In fact, the two pieces of evidence cancel out perfectly. For consider the combined piece of evidence: you survive and get the number one card. The probability of this on heads is: (1/100)(1) = 1/100. The probability of this on tails is: (1)(1/100) = 1/100. So the overall evidence is neutral between the two hypotheses. Your probability of heads remains 1/2 as before the experiment.

If the Demiurge case with the deck of cards is analogous to the firing squad case, then in the Demiurge case we should say that overall you have no evidence for heads or tails. The diagnosis of what went wrong in the reasoning about the Demiurge case then is that the evidence of your existence was neglected. If it were taken into account, it would have canceled out with the evidence of the card number. And by the same token, in the Demiurge and birth order case, the evidence of your existence and the position in the birth order cancel out. And hence by parallel the Doomsday Argument fails.

Is the firing squad case analogous to the Demiurge case? The one potentially relevant difference between the two cases is that the firing squad case is about survival while the Demiurge case is about coming into existence. Does that matter? I don't know. But whether it matters or not, I do actually have an intuition that in the Demiurge case we should take into account the evidence of your existence. On tails, intuitively, you have 100 times greater chance of coming into existence. That precisely cancels out with the fact that on tails any one of the persons who comes into existence has a 1/100 chance of getting the number one card. And hence on balance no evidence is provided.

I am weird

The Doomsday Argument says that we should expect to be typical people: this is the "self-sampling assumption". Hence, we should expect to be roughly in the middle of humanity's birth order. But since the population has grown exponentially, being in the middle of humanity's birth order implies being close to the end of the world. Hence, the end is nigh.

But I have evidence against the self-sampling assumption. The self-sampling assumption predicts that I am typical. But I am not: I am weird.

Animal consciousness

Sometimes I come up with an argument such that I can't tell for sure if it's more a joke or a really interesting argument. The following is a case in point:

1. (Premise) If some non-human earthly animals are conscious, all normal mammals are conscious.
2. (Premise) There have ever been several orders of magnitude more non-human mammals than humans.
3. (Premise, plausibly a consequence of 2) If all normal mammals are conscious, I should very strongly expect not to experience reality as a human.
4. (Premise) I experience reality as a human.
5. So, probably, not all normal mammals are conscious. (By 3 and 4)
6. So, probably, no non-human earthly animals are conscious.

As for (1), if some non-human earthly animals are conscious, a line must be drawn as to where consciousness is found. There are two main plausible places to draw such a line: (a) humans versus other animals, and (b) animals with sophisticated brains versus other animals. If we draw the line in the second place, all normal mammals will be conscious. As for (2), I don't have data as to how many mammals there are on earth. I saw an unreferenced "400 million" online, and a referenced somewhat smaller estimate for the number of birds (and I could run the argument with birds, too, I think). There are apparently roughly as many rats and mice in the world as humans. And there have been non-human animals for millions of years before there were humans.

I think the difficult philosophical question is whether (3) is true and what sense can be made of it.

I am more inclined to see this argument as a joke, or maybe as a challenge to figure out how anthropic arguments work.