I am not sure that we disagree here / expect we are talking about slightly different things. I am not expressing any view on fanaticism issues or how to resolve them.
All I was saying is that infinites are no more of a problem for utilitarianism/ethics than large numbers. (If you want to say “infinite” or “TREE(3)” in a thought experiment, well either works.) I am not 100% sure, but based on what you said, I don’t think you disagree on that.
So what? What thought experiment does this lead to that causes a challenge for ethics? If infinite undefined-ness causes a problem for ethics please specify it, but so far the infinite ethics thought experiments I have seen either:
Are trivially the same as non-infinite thought experiments. For example undefined-ness is a problem for utilitarianism even without infinity. For example think of the Pascal’s mugger who offers to create “an undefined and unspecified but very large amount of utility, so large as to make TREE(3) appear small”
Make no sense. They require assuming two things that physics says are not true – let us assume that we know with 100% certainty that the universe is infinite and let us assume that we can treat those infinites as anything other than limits in a finite series. This make no more sense than though experiments about what if time travel was true make sense and are little better than what if “consciousness is actually cheesy-bread”.
Maybe I am missing something and there are for example some really good solutions to Pascal’s mugging that don’t work in the infinite case but work in the very large but undefined cases or some other kind of thought experiment I have not seen yet in which case I am happy to retract my skepticism.
I would say both “very large unknown positive number x”—“very large unknown positive number y” and inf—inf are undefined. However, whereas the value of 1st difference can in theory be determined by looking into what is generating x and y, the 2nd difference cannot be resolved even in principle.
inf—inf can sometimes be resolved under certain assumptions with richer representations of infinite outcomes, e.g. if both infinities are the result of infinite series over a common ordered index set (e.g. spacetime locations by distance from a specific location, moral patients with some order), you can rearrange the difference of series as a series of differences. This doesn’t always work, because the series of differences may not always have a limit at all.
inf—inf can sometimes be resolved under certain assumptions with richer representations of infinite outcomes, e.g. if both infinities are the result of infinite series over a common ordered index set
Right, but I would classify these cases as resolving “very large unknown positive number x”—“very large unknown positive number y”. It looks to me that infinite series are endless in the sense that we cannot point to where they end, but they do not contain infinity.
For example, the natural numbers 1, 2, … go on indefinetely, but any single one of them is still finite, so I would say they can be represented by 1, 2, …, N, where N is a very large unknown number. From the point of view of physics, I am pretty confident we could assume N = TREE(3)^TREE(3)^TREE(3)^TREE(3)^TREE(3)^TREE(3)^TREE(3)^TREE(3)^TREE(3)^TREE(3) while explaining exactly the same evidence.
I am not sure that we disagree here / expect we are talking about slightly different things. I am not expressing any view on fanaticism issues or how to resolve them.
All I was saying is that infinites are no more of a problem for utilitarianism/ethics than large numbers. (If you want to say “infinite” or “TREE(3)” in a thought experiment, well either works.) I am not 100% sure, but based on what you said, I don’t think you disagree on that.
Doesn’t infinity make aggregating utilities undefined, in a way that’s not true for just very large numbers? Maybe I’m missing something here though.
So what? What thought experiment does this lead to that causes a challenge for ethics? If infinite undefined-ness causes a problem for ethics please specify it, but so far the infinite ethics thought experiments I have seen either:
Are trivially the same as non-infinite thought experiments. For example undefined-ness is a problem for utilitarianism even without infinity. For example think of the Pascal’s mugger who offers to create “an undefined and unspecified but very large amount of utility, so large as to make TREE(3) appear small”
Make no sense. They require assuming two things that physics says are not true – let us assume that we know with 100% certainty that the universe is infinite and let us assume that we can treat those infinites as anything other than limits in a finite series. This make no more sense than though experiments about what if time travel was true make sense and are little better than what if “consciousness is actually cheesy-bread”.
Maybe I am missing something and there are for example some really good solutions to Pascal’s mugging that don’t work in the infinite case but work in the very large but undefined cases or some other kind of thought experiment I have not seen yet in which case I am happy to retract my skepticism.
Hi Linch,
I would say both “very large unknown positive number x”—“very large unknown positive number y” and inf—inf are undefined. However, whereas the value of 1st difference can in theory be determined by looking into what is generating x and y, the 2nd difference cannot be resolved even in principle.
inf—inf can sometimes be resolved under certain assumptions with richer representations of infinite outcomes, e.g. if both infinities are the result of infinite series over a common ordered index set (e.g. spacetime locations by distance from a specific location, moral patients with some order), you can rearrange the difference of series as a series of differences. This doesn’t always work, because the series of differences may not always have a limit at all.
See:
https://forum.effectivealtruism.org/posts/N2veJcXPHby5ZwnE5/hayden-wilkinson-doing-good-in-an-infinite-chaotic-world
https://link.springer.com/article/10.1007/s11098-020-01516-w
Right, but I would classify these cases as resolving “very large unknown positive number x”—“very large unknown positive number y”. It looks to me that infinite series are endless in the sense that we cannot point to where they end, but they do not contain infinity.
For example, the natural numbers 1, 2, … go on indefinetely, but any single one of them is still finite, so I would say they can be represented by 1, 2, …, N, where N is a very large unknown number. From the point of view of physics, I am pretty confident we could assume N = TREE(3)^TREE(3)^TREE(3)^TREE(3)^TREE(3)^TREE(3)^TREE(3)^TREE(3)^TREE(3)^TREE(3) while explaining exactly the same evidence.
Saved to watch later. Thanks for sharing!