Although tempting, debating the meaning of empathy is probably not a beneficial contribution to this HN thread.
But I will say, the initial emotional response (for ex. feeling sad someone was harmed) is largely out of our control. But spending time feeling bad after the fact is a controllable state, and is the basis of a large amount of psychological and behavioral therapy.
But it's beside the point dmix is making and distraction from the central point of this thread. This sort of distraction, subtle changes of topic, is a common way discussions fail. If done deliberately it's also a way to appear to have won an argument.
"Empathy is the capacity to recognize feelings that are being experienced by another sentient [...] being." -- http://en.wikipedia.org/wiki/Empathy