Orthonormal, you're rehashing things I've covered in the post. Yes, many reasonable discounting methods (like exponential discounting in the "proximity argument") do have a specific step where the derivative becomes negative.
What's more, that fact doesn't look especially unintuitive once you zoom in on it; do the math and see. For example, in the proximity argument the step involves the additional people suffering so far away from you that even an infinity of them sums up to less than e.g. one close relative of yours. Not so unrealistic for everyday humans, is it?
What's more, that fact doesn't look especially unintuitive once you zoom in on it; do the math and see. For example, in the proximity argument the step involves the additional people suffering so far away from you that even an infinity of them sums up to less than e.g. one close relative of yours. Not so unrealistic for everyday humans, is it?
It's intuitive to me that everyday humans would do this, but not that it would be right.
In line with my fine tradition of beating old horses, in this post I'll try to summarize some arguments that people proposed in the ancient puzzle of Torture vs. Dust Specks and add some of my own. Not intended as an endorsement of either side. (I do have a preferred side, but don't know exactly why.)
Oh what a tangle. I guess Eliezer is too altruistic to give up torture no matter what we throw at him; others will adopt excuses to choose specks; still others will stay gut-convinced but logically puzzled, like me. The right answer, or the right theory to guide you to the answer, no longer seems so inevitable and mathematically certain.
Edit: I submitted this post to LW by mistake, then deleted it which turned out to be the real mistake. Seeing the folks merrily discussing away in the comments long after the deletion, I tried to undelete the post somehow, but nothing worked. All right; let this be a sekrit area. A shame, really, because I just thought of a scenario that might have given even Eliezer cause for self-doubt: