"What's the worst that can happen?" goes the optimistic saying. It's probably a bad question to ask anyone with a creative imagination. Let's consider the problem on an individual level: it's not really the worst that can happen, but would nonetheless be fairly bad, if you were horribly tortured for a number of years. This is one of the worse things that can realistically happen to one person in today's world.
What's the least bad, bad thing that can happen? Well, suppose a dust speck floated into your eye and irritated it just a little, for a fraction of a second, barely enough to make you notice before you blink and wipe away the dust speck.
For our next ingredient, we need a large number. Let's use 3^^^3, written in Knuth's up-arrow notation:
- 3^3 = 27.
- 3^^3 = (3^(3^3)) = 3^27 = 7625597484987.
- 3^^^3 = (3^^(3^^3)) = 3^^7625597484987 = (3^(3^(3^(... 7625597484987 times ...)))).
3^^^3 is an exponential tower of 3s which is 7,625,597,484,987 layers tall. You start with 1; raise 3 to the power of 1 to get 3; raise 3 to the power of 3 to get 27; raise 3 to the power of 27 to get 7625597484987; raise 3 to the power of 7625597484987 to get a number much larger than the number of atoms in the universe, but which could still be written down in base 10, on 100 square kilometers of paper; then raise 3 to that power; and continue until you've exponentiated 7625597484987 times. That's 3^^^3. It's the smallest simple inconceivably huge number I know.
Now here's the moral dilemma. If neither event is going to happen to you personally, but you still had to choose one or the other:
Would you prefer that one person be horribly tortured for fifty years without hope or rest, or that 3^^^3 people get dust specks in their eyes?
I think the answer is obvious. How about you?
It occurred to me to add something to my previous comments about the idea of harm being nonlinear, or something that we compute in multiple dimensions that are not commensurate.
One is that any deontological system of ethics automatically has at least two dimensions. One for general-purpose "utilons," and one for... call them "red flags." As soon as you accumulate even one red flag you are doing something capital-w Wrong in that system of ethics, regardless of the number of utilons you've accumulated.
The main argument justifying this is, of course, that you may think you have found a clever way to accumulate 3^^^3 utilons in exchange for a trivial amount of harm (torture ONLY one scapegoat!)... but the overall weighted average of all human moral reasoning suggests that people who think they've done this are usually wrong. Therefore, best to red-flag such methods, because they usually only sound clever.
Obviously, one may need to take this argument with a grain of salt, or 3^^^3 grains of salt. It depends on how strongly you feel bound to honor conclusions drawn by looking at the weighted average of past human decision-making.
The other observation that occurred to me is unrelated. It is about the idea of harm being nonlinear, which as I noted above is just plain not enough to invalidate the torture/specks argument by itself due to the ability to keep thwacking a nonlinear relationship with bigger numbers until it collapses.
Take as a thought-experiment an alternate Earth where, in the year 1000, population growth has stabilized at an equilibrium level, and will rise back to that equilibrium level in response to sudden population decrease. The equilibrium level is assumed to be stable in and of itself.
Imagine aliens arriving and killing 50% of all humans, chosen apparently at random. Then they wait until the population has returned to equilibrium (say, 150 years) and do it again. Then they repeat the process twice more.
The world population circa 1000 was about 300 million (roughly,) so we estimate that this process would kill 600 million people.
Now consider as an alternative, said aliens simply killing everyone, all at once. 300 million dead.
Which outcome is worse?
If harm is strictly linear, we would expect that one death plus one death is exactly as bad as two deaths. By the same logic, 300 megadeaths is only half as bad as 600 megadeaths, and if we inoculate ourselves against hyperbolic discounting...
Well, the "linear harm" theory smacks into a wall. Because it is very credible to claim that the extinction of the human species is much worse than merely twice as bad as the extinction of exactly half the human species. Many arguments can be presented, and no doubt have been presented on this very site. The first that comes to mind is that human extinction means the loss of all potential future value associated with humans, not just the loss of present value, or even the loss of some portion of the potential future.
We are forced to conclude that there is a "total extinction" term in our calculation of harm, one that rises very rapidly in an 'inflationary' way. And it would do this as the destruction wrought upon humanity reaches and passes a level beyond which the species could not recover- the aliens killing all humans except one is not noticeably better than killing all of them, nor is sparing any population less than a complete breeding population, but once a breeding population is spared, there is a fairly sudden drop in the total quantity of harm.
Now, again, in itself this does not strictly invalidate the Torture/Specks argument. Assuming that the harm associated with human extinction (or torturing one person) is any finite amount that could conceivably be equalled by adding up a finite number of specks in eyes, then by definition there is some "big enough" number of specks that the aliens would rationally decide to wipe out humanity rather than accept that many specks in that many eyes.
But I can't recall a similar argument for nonlinear harm measurement being presented in any of the comments I've sampled, so I wanted to mention it.
But I thought it was interesting and couldn't recall seeing it elsewhere.
I mentioned duplication. That in 3^^^3 people, most have to be exact duplicates of one another birth to death.
In your extinction example, once you have substantially more than the breeding population, extra people duplicate some aspects of your population (ability to breed) which causes you to find it less bad.
... (read more)