I can see that, but this is more like Pascal’s mugging than anything interesting. When the relative uncertainty in probabilities is significantly larger than one, it does not pay to worry about the event. For example, if the mugger threatens you with umptillion gazillion up-arrows in disutility, and you assign her threats 1/gazillion chance of being credible, with the uncertainty in your estimate of that chance being 1 billion percent, you do what most humans already do naturally: shrug and walk away from something that is clearly somewhere in the noise level. The importance of worrying about the universe being truly infinite is so low, it is one of those noise-level events that is fun to ponder for fun after having a few, but not much more than that.
Converting between option preference and a utility number might be wanted even in scenarios where we have different kinds of preferences that we both care about but are distinct. Say that you can create or kill a human being and receive and receive or lose money. A morality that prefers 0 humans killed or created to a human killed regardless of money effect, but still uses money as a tie-breaker seems a relevant option.
If you formulate the number of such a option with a number system that is a single archimedian class (ie is finite) as A + B then there will be some natural number N that A + N B is greater than A + B ie that there will be some amount of money that is preferable to a human life if lifes or money is to be preferred at all. We could do this by treating “life-preferences” and “money-references” as separate utilities but as surreals they can be both be incorporated correctly into a single number (with finite and infinite factors).
In this sense “bros before hoes” implies a sense of infinity in the world.
I’m confused where the impetus to solve the problem comes from. There are no [observable] infinities in the real physical universe.
There aren’t, but not in a way that allows you to conclude the universe is finite
An arbitrarily small chance of an infinite outcome is sufficient to cause your expected utility to be infinity and cause these kinds of issues.
I can see that, but this is more like Pascal’s mugging than anything interesting. When the relative uncertainty in probabilities is significantly larger than one, it does not pay to worry about the event. For example, if the mugger threatens you with umptillion gazillion up-arrows in disutility, and you assign her threats 1/gazillion chance of being credible, with the uncertainty in your estimate of that chance being 1 billion percent, you do what most humans already do naturally: shrug and walk away from something that is clearly somewhere in the noise level. The importance of worrying about the universe being truly infinite is so low, it is one of those noise-level events that is fun to ponder for fun after having a few, but not much more than that.
Converting between option preference and a utility number might be wanted even in scenarios where we have different kinds of preferences that we both care about but are distinct. Say that you can create or kill a human being and receive and receive or lose money. A morality that prefers 0 humans killed or created to a human killed regardless of money effect, but still uses money as a tie-breaker seems a relevant option.
If you formulate the number of such a option with a number system that is a single archimedian class (ie is finite) as A + B then there will be some natural number N that A + N B is greater than A + B ie that there will be some amount of money that is preferable to a human life if lifes or money is to be preferred at all. We could do this by treating “life-preferences” and “money-references” as separate utilities but as surreals they can be both be incorporated correctly into a single number (with finite and infinite factors).
In this sense “bros before hoes” implies a sense of infinity in the world.