"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?
Mitchell, I acknowledge the defensibility of the position that there are tiers of incommensurable utilities. But to me it seems that the dust speck is a very, very small amount of badness, yet badness nonetheless. And that by the time it's multiplied to ~3^^^3 lifetimes of blinking, the badness should become incomprehensibly huge just like 3^^^3 is an incomprehensibly huge number.
One reason I have problems with assigning a hyperreal infinitesimal badness to the speck, is that it (a) doesn't seem like a good description of psychology (b) leads to total loss of that preference in smarter minds.
(B) If the value I assign to the momentary irritation of a dust speck is less than 1/3^^^3 the value of 50 years' torture, then I will never even bother to blink away the dust speck because I could spend the thought or the muscular movement on my eye on something with a better than 1/3^^^3 chance of saving someone from torture.
(A) People often also think that money, a mundane value, is incommensurate with human life, a sacred value, even though they very definitely don't attach infinitesimal value to money.
I think that what we're dealing here is more like the irrationality of trying to impose and rationalize comfortable moral absolutes in defiance of expected utility, than anyone actually possessing a consistent utility function using hyperreal infinitesimal numbers.
The notion of sacred values seems to lead to irrationality in a lot of cases, some of it gross irrationality like scope neglect over human lives and "Can't Say No" spending.
I'm not sure why surreal/hyperreal numbers result in, essentially, monofocus.
Consider this scale on the surreals:
Let's say you're a perfectly rational human (*cough cough*). You naturally start on the Omega^2 scale, with a certain finite amount of resources. Clearly, the worth of an omega of human lives is worth more than your own, so you do ... (read more)