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MugaSofer comments on Humans are utility monsters - Less Wrong
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The actual reality does not have high level objects such as nematodes or humans.
Before one could even consider an utility of a human (or a nematode) 's existence, one got to have a function that would somehow process a bunch of laws of physics and state of a region of space, and tell us how happy/unhappy that region of space feels, what is it's value, and so on.
What would be the properties of that function? Well, for one thing, an utility of a region of space would not generally be equal to sum of utilities of parts, for the obvious reason that your head has bigger utility when it haven't been diced into perfect cubic blocks and then rearranged like a Rubik's cube.
This function could, then, be applied to a larger region of space containing nematodes and humans, and process it in some way which would clearly differ from any variety of arithmetic utilitarianism that adds or averages utilities of nematodes and humans, because, as we have established above, the function is not distributive over regions of spacetime, and nematodes and humans are just regions of spacetime with specific stuff inside.
What I imagine that function would do, is identify existence of particular computational structures of interest in the region of space, and there are many such structures inside a human head that do not exist in any region of space occupied by nematodes, which have a much smaller set of structures with extra nematodes not adding any new structures (unlike humans who, due to distinct memories and the different ways their brains are arranged, do add new structures, linearly up to a fairly large number).
So even a very large region of spacetime full of nematodes and one human can have it's utility decreased a lot more by random rearrangements of the atoms (quarks, what ever the bottom level is - does not matter) constituting a human than by random rearrangements of the atoms constituting nematodes.
edit: that is, as long as there's enough nematodes to cover the entire nematode experience space (which is quite small), increases in their number won't add to computational structure of the whole region. Something that's not true for people, up to a really very large number of people.
I'm not entirely sure what the point of this comment was, but in that case, surely the problem occurs when said chunks die? I mean, if they magically kept working the same way, linking telepathically with the other chunks and processing information perfecty well, I don't see why they wouldn't be just as valuable, albeit rather grisly looking.
Finding out that the chunks will die (given the laws of physics as they are) is something that the function in question got to do. Likewise, finding out that they won't die with some magic, but would die if they weren't rearranged and the magic was applied (portal-ing the blood all over the place).
You just keep jumping to making an utility that is computed from the labels you already assign to the world.
edit: one could also subdivide it into very small regions of space, and note that you can't compute any kind of utility of the whole by going over every piece in isolation and then summing.
edit2: to be exact, I am counter-exampling the f(ab)=f(a)+f(b) (where "ab" is a concatenated with b) with f(ab)!=f(ba) and a+b=b+a .
More broadly, mathematics1 has been very useful in science, and so ethicists try to use mathematics2 . Where mathematics1 is a serious discipline where one states assumptions and progresses formally, and mathematics2 is "there must be arithmetical operations involved" or even "it is some kind of Elvish" . (while mathematics1 doesn't get you very far because we can't make many assumptions)