Rejecting premise 1, completeness is essentially a nonstarter in the context of morality, where the whole project is premised on figuring out which worlds, actions, beliefs, rules, etc., are better than or equivalent to others. You can deny this your heart of heartsāI wonāt say that you literally cannot believe that two things are fundamentally incomparableābut I will say that the world never accommodates your sincerely held belief or conscientious objector petition when it confronts you with the choice to take option A, option B, or perhaps coin flip between them.
This isnāt central to your post, but Iām commenting on it because itās a very common defense of completeness in EA and I think rejecting completeness has very important implications:
I donāt buy this argument. If youāre forced to choose between A and B, and you pick A, this isnāt enough to show you think A is ābetterā with respect to some particular normative view v ā e.g., some lexical threshold consequentialism. You might have simply picked arbitrarily, or you might have chosen based on some other normative criteria you put some weight on.[1]
And incomparability differs from indifference in that, if you consider A and B incomparable, you might also consider āA + $1ā and B incomparable. To me this property seems pretty intuitive in many cases, like this one from Schoenfield (in the context of relative probabilities, not betterness):
You are a confused detective trying to figure out whether Smith or Jones committed the crime. You have an enormous body of evidence that you need to evaluate. Here is some of it: You know that 68 out of the 103 eyewitnesses claim that Smith did it but Jonesā footprints were found at the crime scene. Smith has an alibi, and Jones doesnāt. But Jones has a clear record while Smith has committed crimes in the past. The gun that killed the victim belonged to Smith. But the lie detector, which is accurate 71% percent of the time, suggests that Jones did it. After you have gotten all of this evidence, you have no idea who committed the crime. You are no more confident that Jones committed the crime than that Smith committed the crime, nor are you more confident that Smith committed the crime than that Jones committed the crime.
[paraphrased:] But now you learn, actually 69 eyewitnesses claim Smith did it, not 68. The proposition that Smith did it has been mildly sweetened. So, should you now think that Smith is more likely to have done it than Jones?
There are some philosophical wrinkles involved in making this idea rigorous, which I hope to do in a forthcoming post. But see here for a bit of a preview.
This isnāt central to your post, but Iām commenting on it because itās a very common defense of completeness in EA and I think rejecting completeness has very important implications:
I donāt buy this argument. If youāre forced to choose between A and B, and you pick A, this isnāt enough to show you think A is ābetterā with respect to some particular normative view v ā e.g., some lexical threshold consequentialism. You might have simply picked arbitrarily, or you might have chosen based on some other normative criteria you put some weight on.[1]
And incomparability differs from indifference in that, if you consider A and B incomparable, you might also consider āA + $1ā and B incomparable. To me this property seems pretty intuitive in many cases, like this one from Schoenfield (in the context of relative probabilities, not betterness):
More on this here and here.
There are some philosophical wrinkles involved in making this idea rigorous, which I hope to do in a forthcoming post. But see here for a bit of a preview.
Iād be pretty interested to hear why those who disagree-voted disagree.