Integral vs differential ethics, continued

My own resolution to the "repugnant conclusion" is that the goodness of a population isn't a state function: you can't know if a population is better than another simply by looking at the well-being of each currently existing person right now. Instead, you have to know the history of the population as well as its current state.

I suspect much of the problem is that humans aren't very good at consistency nor calculation. Scope insensitivity (and other errors) cause us to accept steps that lead to incorrect results once aggregated. If you can actually define your units and measurements, I strongly expect that the sum of the steps will equal the conclusion, and you will be able to identify the steps which are unacceptible (or accept the conclusion).

I'd advise against the motivated reasoning that "if you don't like the conclusion, you have to find a step to reject", but rather the "I notice I'm confused that I have different evaluations of the steps and the aggregate, so I've probably miscalculated."

And if this is the case (the mismatch is caused by compounded rounding errors rather than a fundamental disconnect), then it seems unlikely to be a useful solution to AI problems. Unless we fix the problems in our calculation, not just use the method we've proven doesn't work.

The Puzzle of the Self-torturer talks about transitive and intransitive preferences.

I would re-frame the issue slightly; the process that philosophy/ethics goes through is something more like this:

If given A, B, and C we get D, and if not-A is unacceptable and not-B is unacceptable and not-C is unacceptable and D is unacceptable, then we do not fully understand the question. So lets play around with all the possibilities and see what interesting results pop up!

Playing around should involve frequent revisits to the differential and integral inspections of the argument; if you are doing just one type of inspection, you are doing it wrong.

But in the end you might come to a solution, and/or you might write a very convincing sounding paper on a solution, but the assumption isn't that you have now solved everything because your integrating or differentiating is nicely explicable. It is highly debatable whether any argument in ethics is more than an intuition pump used to convince people of your own point of view. After all, you cannot prove even the basic fact that happy people are good; we simply happen to accept that as a warrant... or, in some cases, make it our definition of 'good'.

It is worth considering the possibility that all these ethical arguments do is try to make us comfortable with the fact that the world does not work in our favor... and the correct solution is to accept as a working hypothesis that there is no absolutely correct solution, only solutions that we should avoid because they feel bad or lead to disaster. (To clarify how this would work in the case of the Repugnant Conclusion, the correct-enough solution might involve each population setting its own limits on population size and happiness ranges, and those who disagree having to make their own way to a better population; alternatively, we might define an acceptable range and stick to it, despite political pundits criticizing our decision at every turn, and many people maintaining roiling angst at our temerity.)

In the end, the primary and perhaps only reason we continue to engage in philosophy is because it is foolish to stop thinking about questions simply because we do not have a solution (or an experimental process) that applies.

Do these apply to non-utilitarian theories of ethics?

What are the forms of math called where you can compare numbers, such as to say that 3 is bigger than 2, but can't necessarily add numbers - that is, 2+2 may or may not be bigger than 3?