I really don’t see why I can’t say “the negative utility of a dust speck is 1 over Graham’s Number.”
You can say anything, but Graham’s number is very large; if the disutility of an air molecule slamming into your eye were 1 over Graham’s number, enough air pressure to kill you would have negligible disutility.
or “I am not obligated to have my utility function make sense in contexts like those involving 3^^^^3 participants, because my utility function is intended to be used in This World, and that number is a physical impossibility in This World.”
If your utility function ceases to correspond to utility at extreme values, isn’t it more of an approximation of utility than actual utility? Sure, you don’t need a model that works at the extremes—but when a model does hold for extreme values, that’s generally a good sign for the accuracy of the model.
An addendum: 2 more things. The difference between a life with n dust specks hitting your eye and n+1 dust specks is not worth considering, given how large n is in any real life. Furthermore, if we allow for possible immortality, n could literally be infinity, so the difference would be literally 0.
If utility is to be compared relative to lifetime utility, i.e. as (LifetimeUtility + x / LifetimeUtility), doesn’t that assign higher impact to five seconds of pain for a twenty-year old who will die at 40 than to a twenty-year old who will die at 120? Does that make sense?
Secondly, by virtue of your asserting that there exists an action with minimal disutility, you’ve shown that the Field of Utility is very different from the field of, say, the Real numbers, and so I am incredulous that we can simply “multiply” in the usual sense.
Eliezer’s point does not seem to me predicated on the existence of such a value; I see no need to assume multiplication has been broken.
I think that latter statement is equivalent to this:
V = Virgin Birth
G = God appears and proclaims ~V
P(V|G) < 1
∴P(V) < 1
But that argument is predicated on P(G) > 0. It is internally consistent to believe P(V|G) < 1 and yet P(V) = 1, as long as one also believes P(G) = 0, i.e. one is certain that God will not appear and proclaim ~V.