It doesn't depend on N if N is consistent between options A and B, but it would if they were different. It would make for an odd hypothetical scenario, but I was just saying that it's not made completely explicit.

I'm making a point about human psychology. The value of a life obviously does not change.

Although, I suppose theoretically, if the concern is not over individual lives, but over the survival of the species as a whole, and there are only 500 people to be saved, then picking the 400 option would make sense.

I think that rephrasing improves it.

Or, for all we know, there are only 400 lives to be saved in the first instance. Saving 400 out of 400 is different than saving 400 out of 7 billion. The context of the proposition makes a difference, and it's always best to be clear and unambiguous in the paramaters which will necessarily guide ones decision as to which choice is the best.

Rationality doesn't require that you not feel the emotions, it just requires that you avoid letting them bias you towards one conclusion over another. You should follow the evidence to determine the level of guilt of the perpetrator. There is no causal link from how you feel about the event to how it actually happened. I'd have to say that in terms of interpreting the event, there is no room to "agree to disagree" if all the facts are understood and agreed upon. Certainly there's room to feel differently about it based on your own relative situation, but it has no bearing on the interpretation of the event.

The way I see it, emotions and reason serve two complimentary functions. Emotions tell you your goal, what you want. Reason tells you how to get there. Your emotions may say "Go south!" and reason may say "There is an obstacle in my path. In order to reach my destination, I need to first make a detour." If you allow your emotions to override your sense of reason, you'll try to go south and plow straight into the wall, and that lack of reason will hinder your ability to achieve your desired ends. If you think that reason is the way and emotions are the enemy and thus undervalue your emotions, you'll wander around aimlessly, as you'll have no sense of where it is you actually want to go. If one were truly Spock-like, and bad events failed to result in negative affect, there would be no reason to think of them as bad and thus no logical reason to avoid them. (Here you could argue that, well, if it affects other people negatively, that would be reason. But in that case you're assuming empathy--that when bad things happen to others, it makes you feel bad, which is an emotional response.)

To some extent this is true. Strong emotions do have the power to shut down activity in the executive centers of the brain. There's a physiological basis for the idea of "seeing red" when you're angry. However, you can also train yourself to stop your emotional reactions in their tracks, think about them, and change them. You can choose not to be angry, but you likely need education and training to do so, and you may not be successful 100% of the time. But you can certainly improve dramatically.

It does benefit you to feel sad because your brother died, though not exactly directly. The reason you feel sad is because you were attached to him. You would not feel sad if he were a random, namless (to you) stranger. Having that attachment is beneficial, even if the consequent emotion is not. But the two are inextricably tied together, and the prospect of sadness at the loss is part of what keeps you wanting to look after each other.

The question of rationality in emotions is better considered in the framework of Rational Emotive Behavior Therapy. An emtion is irrational if it results from an irrational belief, one that is dogmatic, rigid, inflexible. When you recognize this and replace the irrational belief with the rational one, the irrational emotion tends to be replaced by a rational one.

In the example of the goblin, the anger is not a direct result of the goblin tying your shoes together, but of your beliefs about the goblin tying your shoes together. Common anger-inciting beliefs are "he shouldn't have done the" or "I can't stand that he did that." But why shouldn't he have done that? Is there some law stating goblins can't tie shoes together that was violated? Can you not stand that? Will you expire on the spot if that happens? No, what you really ought to realize is that "it's unfortunate and inconvenient that the goblin tied my shoes together." And when you think that thought, the anger typically turns into mild irritation or disappointment.

In the case of losing a brother, being sad and mourning is a normal, natural, and healthy response. If you went around thinking "I can't live without him" or "I can't stand that he died" you're going to upset yourself irrationally and likely end up unduly depressed. If you replace those thoughts with "It's very sad that my brother died, but I can tolerate it and life will still go on" you will likely be sad and mournful, but then move on with your life as most people do when they lose loved ones.

Yes. This is called Rational Emotive Behavior Theory, and it was developed by Albert Ellis.

My point was that it's misleading to those trying to interpet it directly into a logical statement, which is what Eliezer seemed to be trying to do. I'm sure there are lots of people who could read that sentiment and understand the meaning behind it (or at least a meaning; some people interpret it differently than others). It's certainly possible to comprehend (obviously, otherwise I wouldn't have been able to explain it), but the meaning is nevertheless in an ambiguous form, and it did confuse at least some people.