A few months ago, I had an appointment on my calendar marked "Death". A friend had asked me earlier for help figuring out why she was afraid of death. At first I thought that surely philosophers must have addressed this question, so with my education I ought to be able to provide something relevant and illuminating. But all I could think of was attempts to cure the fear of death, not attempts to explain it.

When I asked my former classmates, they had the same problem. Unless our memories are defective, or unless we simply aren't as widely read as we think, this is an embarrassment for philosophy, a failure to be curious about a fundamental question. I asked a librarian friend for help, and she turned up some resources, but these were mostly empirical in nature - descriptions of how fear of death is expressed in our and others' cultures, not a causal explanation of why we fear it.

So I used the last tool in my box. I offered to ask her some clarifying questions and engage in dialogue for an hour. By the end, my thinking on death was clearer too, and I realized that a true understanding of how to think about one's own death ought to involve answers to these questions:

• Should I expect to die?
• How should I compare being dead with being alive?

Valar Morghulis?

Death seems pretty likely. No human in reliably recorded history has been observed to live past the age of 200 years. But there's good reason to doubt that you should expect to die at all. I'm not talking about the singularity, or medical miracles - I'm talking about Sleeping Beauty, and Schrödinger's Immortal Cat.

The Sleeping Beauty problem illustrates a situation where probabilities appear different from the inside and the outside:

Suppose Sleeping Beauty volunteers to undergo the following experiment, which is described to her before it begins. On Sunday she is given a drug that sends her to sleep, and a coin is tossed. If the coin lands heads, Beauty is awakened and interviewed on Monday, and then the experiment ends. If the coin comes up tails, she is awakened and interviewed on Monday, given a second dose of the sleeping drug that makes her forget the events of Monday only, and awakened and interviewed again on Tuesday. The experiment then ends on Tuesday, without flipping the coin again.

Beauty wakes up in the experiment and is asked, "With what subjective probability do you believe that the coin landed tails?"

First, some easier questions. Suppose that before the experiment, Sleeping Beauty were offered the opportunity to bet a dollar on whether the coin would come up heads. If she bets on heads at even odds, then the expected value of the bet is zero - if the experiment is repeated, then on average she'll win a dollar half of the time, and the other half of the time she'll lose a dollar.

Now, suppose the experimental design instead involves offering to make that bet each time Sleeping Beauty wakes up? She knows in advance that she'll wake up inside the experiment, and that the probability of the coin coming up heads is 50%.

If Sleeping Beauty accepts the same bet at even odds, the expected value of the bet is negative. Half the time the coin comes up heads, so she is woken up once, bets on heads, and wins a dollar. The other half the time, she is woken up twice, twice bets on heads, and loses two dollars. She has a 50% chance of winning one dollar, and a 50% chance of losing two dollars, so if the experiment were repeated many times, on average she'd lose fifty cents each time.

Having just woken up, Sleeping Beauty should bet as if the probability of the coin having come up heads was 1/3, and tails 2/3.

Probability isn't betting odds by definition, but probability theory was developed largely through explaining how wagers work, so it would be really weird if they diverged.

But if you accept the betting odds Sleeping Beauty should use as the true probability, this means that the likelihood that something happened is determined, not just by previous known facts and new observations, but by how many times you expect observations to be made in each possible outcome. This is called the Self-Indication Assumption.

It is not obvious how to apply this, but it seems plausible that this should discount, if not eliminate, the probability of scenarios under which you die.

In the Schrödinger's cat thought experiment, a cat in a black box lives if and only if a quantum particle has some property. Since quantum mechanics is inconsistent with a single true interpretation before particle is measured, it is also inconsistent with the cat being alive, or being dead, and only becomes one or the other when the particle is measured. There are a few different ways of dealing with this counterintuitive situation, but under the many worlds interpretation of quantum mechanics, the period of uncertainty is the period in which two possible worlds are entangled with one another, and the measurement severs the bond.

Quantum Immortality suggests something similar. If you believe that there is both a world in which the cat is alive, and a world in which the cat is dead, then it should in principle be possible to perform a sort of quantum "Russian Roulette" on a human, in which case there will always be an actual future world containing that human' consciousness, with 100% probability.

Should that human believe that they risk death, if they will definitely have the experience of living in some possible world, and never have the experience of being dead (because that is not an experience)?

 

How should I compare being dead with being alive?

Well, in one sense you clearly can. If you're alive, you're not dead. Dead is what we call it when you're not alive any more. At any time, being alive can have a positive value (if you like it), a negative value (if you wish you were dead), or a neutral one (in which case it's no better or worse than being dead). So my first inclination was to think that my friend was right to fear death, because it's less good than being alive, and things being less good is bad.

There is a common philosophical argument against the fear of death, famously made by Epicurus:

Death is not present when you are, and you are not present when death is. You will never with death, so you have nothing to fear from it.

I used to think this was silly - you can fear a loss even if you don't fear the state of death. But for some people, it seems that death is scarier than you would expect from adding up the fear of losing each hour of their life, put together. I led my friend through a thought experiment, asking how scared she would be of skipping one hour of life, a day, a year, and so on, until we were talking about losing all her remaining time - and this wasn't scary to her at all. She was more afraid of being dead than she was of her life, never having any more experiences. It seemed like she was experiencing a fear qualitatively different from the fear of not being alive anymore.

 

Double Counting

Let's say you are trying to figure out whether to buy something. And you reason in the following manner:

The price is $100. So if I don't buy the thing, I have an extra $100. But if I do buy the thing,  it costs me $100. That's a $200 difference between +$100 and -$100, so I should only buy it if it's worth more than $200 to me.

The problem here is that you counted the cost twice - both on the positive side, and again on the negative side. I think that some people do something similar when thinking about death. They think of the benefit of life as being above some neutral baseline, but try to think of death as similarly being below the neutral baseline of life. This leads to thinking of death as not just a failure to have good things, but the presence of equal and opposite bad things. If your brain is doing this, then your thinking will in fact be improved by reminding yourself that death is in fact the neutral reference class. Count the lost life, but don't then count death as an independent harm.

Just because it's stuck in my head now, I'm going to share one of my college's school songs. We sang it in translation:

There is a reaper men call Death

And God has given him power

The blade he is whetting,

Sharp, sharper it's growing,

Soon will he be mowing,

All must fall before him.

Beware, o lovely flower.

Here's the full original and a less poetic translation, from the original German original (what else?). And here's what it sounds like: