Premature death paradox

by bfinn2 min read13th Apr 202021 comments


ParadoxesWorld Modeling

There seems to be a paradox about premature death. (Or at least, I am confused about it - perhaps due to ignorance of philosophy of death, or some related paradoxes, e.g. about time.)

Thinking e.g. of COVID-19, what makes potentially fatal illnesses bad is not that they kill people, or increase the chance of dying. For throughout the past and future, everyone has always died, and always will die, precisely 1.0 times (a contingent fact, but nonetheless the most accurately known physical constant in the universe, somehow). So nothing can increase the chance of dying (which is already 100%), and we all die eventually of something.

What seems bad, though, is when an illness causes premature death - dying too soon, before one's time. But when is that?

Everyone dies prematurely

Life expectancy tables report that at birth, in the UK (or US) you have a life expectancy of 81 years. So dying before 81 would be premature; if you died aged 20 or 50, people would say you'd died young, before your time.

But when you get to 81, it's not your time either - for you then have a life expectancy of as much as 8.5 more years, living to 89.5. And if you reach 89.5 years, you can then expect to live on to 94, etc. Even at age 100 you have a life expectancy of 2.1 further years.

So whatever age you die at, your death is always premature - for your life expectancy at that age is invariably greater than the time you continue to live for (= 0 years).

Maybe this is part of the reason death seems like a raw deal. For however old you are when you die, you certainly could have lived longer (by at least a nanosecond). Because there is no upper limit for age: no age which you have a non-zero probability of reaching, but a zero probability of exceeding (another contingent fact about the universe we oddly seem to be certain of).

But the raw deal is even worse. Suppose you die at age x; and the life expectancy at that age is e further years. Then of all the people in the world aged x, you are the very first to die - for you die immediately, whereas they all continue living (for at least a nanosecond), and indeed on average they live e further years that you missed out on.

Moreover, all those who are younger than x also continue living, and even those older than x do too (for at least a nanosecond). So you not only died before everyone the same age as you, but also before everyone younger, and even everyone older! You're the unluckiest person alive! (Or at least, the unhealthiest.)

No-one dies prematurely

Perhaps the confusion is about the concept of life expectancy: e doesn't tell you how long you will live, but how long people in general aged x live, on average. So it's not personalized to your situation. The more we know about your health & circumstances, the more we can improve on this estimate to make it specific to you. And if we knew everything about you, we could make an extremely accurate, perhaps even exact, tailored prediction.

So let's try it: at the age in question - x (your death) - your tailored prediction (which oddly we can make without knowing anything about you) is that your life expectancy is precisely 0.0 years.

But then in what sense did you die prematurely? Given this actual, individual life expectancy, it's clear that you haven't missed out at all - even if you were aged only 20. You lived exactly the expected number of years, and died when your time came - not a nanosecond before, nor after.

So at first it looked like people always die prematurely; now it looks like they never do.

Is the confusion then just that we didn't know enough to make an individually tailored life expectancy prediction for you in advance, so rely instead on life expectancy tables? But they're so unreliable; when your time comes, why do the tables invariably overestimate? (No wonder death seems too soon!) Can't we just correct them?

I'm partly joking, but there seems to be a real paradox here. Is it a known one? Or more than one paradox? It feels a bit like one of Zeno's; and also a bit like the unexpected hanging/test.

[added:] Also it feels like there may be a confusion between credence and chance (i.e. subjective & objective probability) when calculating life expectancy, and/or confusion about the appropriate reference class of people.