I think you're letting the notation confuse you. It would imply that, if A,B,C,D where e.g. real numbers, and that is the context the "<"-sign is mostly used in. But Orders can exist on sets other then sets of numbers. You can for example sort (order) the telephone book alphabetically, so that Cooper < Smith and still there is no k so that k*Cooper>Smith.

This is fairly confusing...in the telephone book example, you haven't defined * as an operator. I frankly have no idea what you would mean by it. Using the notation kA > D implies a defined multiplication operation, which any reader should naturally understand as the one we all use everyday (and hence, we must assume that the set contains the sort of objects to which our everyday understanding of multiplication normally applies).

Now, this doesn't mean that you are wrong to say that, on all such sets, kA > D does not follow necessarily from A < B < C < D for some k. It does not obtain, for instance, when A = 0. It also wouldn't obtain on the natural numbers modulo 8, for A=2 and D=5 (just to take one example -- it should be easy to create others). But neither of these have any relation to the context in which you made your claim.

So, the question is, can you find a plausible set of definitions for your set that makes your claim relevant to this conversation?

Ben, that's not about additivism, but indicates that you are a deontologist by nature, as everyone is. A better test: would you flip a lever which would stop the torture if everyone on earth would instantly be automatically punched in the face? I don't think I would.

I'm fairly certain I would pull the lever. And I'm certain that if I had to watch the person be tortured (or do it myself!) I would happily pull the lever.

It was this sort of intuition that motivated my earlier question to Eliezer (which he still hasn't responded to). I'd be interested to hear from any of the people advocating torture over specks, though: would you all be willing to personally commit the torture, knowing that the alternative is either (a) a punch in the face (without permanent injury/pain/risk of death) to every human on the planet, or (b) in a universe with 3^^^3 people in it, a speck in everyone's eye?

I suspect that the most people would refuse to pick up the blowtorch in either case. Which is very important -- only some very exotic, and very implausible, metaethical theories would casually disregard the ethical intuitions of the vast majority of people.

Eliezer: would you torture a person for fifty years, if you lived in a large enough universe to contain 3^^^3 people, and if the omnipotent and omniscient ruler of that universe informed you that if you did not do so, he would carry out the dust-speck operation?

Seriously, would you pick up the blow torch and use it for the rest of your life, for the sake of the dust-specks?