Even thornier problems arise when one tries to define absolute utility by adding up the utility of all individuals. Although counting humans is pretty reliable to date, with the thorniest edge cases still being relatively uncontroversial (twins who are conjoined at the brain and share a thalamus; they’re 2 people), but if there are ever any morally relevant digital individuals (which I hope there will be!), the edge cases will get much worse.
The easy answer to this question is that you cannot in general do this, and this is a basic point of utility theory, in which experiences can’t always be added up meaningfully.
This is very different from a lot of other domains, where you can add up different quantities meaningfully, but here, there is no reason to expect this to happen, and indeed it’s impossible in general, because utility functions are only defined up to affine transformations, and you can change a number arbitrarily, as long as other numbers are changed.
(We usually just change one variable, or a small set of them, but it doesn’t change this fact.)
The easy answer to this question is that you cannot in general do this, and this is a basic point of utility theory, in which experiences can’t always be added up meaningfully.
This is very different from a lot of other domains, where you can add up different quantities meaningfully, but here, there is no reason to expect this to happen, and indeed it’s impossible in general, because utility functions are only defined up to affine transformations, and you can change a number arbitrarily, as long as other numbers are changed.
(We usually just change one variable, or a small set of them, but it doesn’t change this fact.)
More here:
https://www.lesswrong.com/posts/cYsGrWEzjb324Zpjx/comparing-utilities
Also, how is Brouwer getting a claim that all functions are continuous, when there are known functions that are discontinuous?
He has to be assuming something, but I can’t yet work out what the assumptions are.