Adriano_Mannino comments on Arguments Against Speciesism - Less Wrong
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Sure. However, you raise what is in principle a very solid objection, and so I would like to address it.
Let's say that I would, all else being equal, prefer that a dog not be tortured. Perhaps I am even willing to take certain actions to prevent a dog from being tortured. Perhaps I also think that two dogs being tortured is worse than one dog being tortured, etc.
However, I am willing to let that dog, or a million dogs, or any number of dogs, be tortured to save my grandmother from the same fate.
What are we to make of this?
In that case, some component of our utilitarianism might have to be re-examined. Perhaps dogs have a nonzero value, and a lot of dogs have more value than only a few dogs, but no quantity of dogs adds up to one grandmother; but on the other hand, some things are worth more than one grandmother (two grandmothers? all of humanity?).
Real numbers do not behave this way. Perhaps they are not a sufficient number system for utilitarian calculations.
(Of course, it's possible to suppose that we could, if we chose, construct various hypotheticals (perhaps involving some complex series of bets) which would tease out some inconsistency in that set of valuations. That may be the case here, but nothing obvious jumps out at me.)
What about a random human instead of your grandmother? What if the human's/your grandmother's cognitive capacities were lower than the dog's or the chimp's? – What would a good altruist do?
How do you block the "chain of comparables"?