If someone cries out in pain, I have no doubt of their experience. It is this phenomenon, which is not formally meaning, that I am calling "empathy"

Excuse me for taking this apart some more: The first sentence implies that this is an unfailing,

Point taken. It is not unfailing. Why and when it might fail is a question of some interest to, for example, psychologists and to those, as I have suggested, who might concern themselves with how holocausts come about, to name two.

quasi-automatic reaction of you as a human being. But the remainder of your argument suggests that you regret the very fact that empathy is not general, but has to be taught, and can be "manipulated".

Where do I say empathy has to be taught? That it can be manipulated is indisputable, as is its significance in human relations.

A quality which would be inborn/instinctive could not be considered part of ethics, because, as I see it, ethics is about conscious social behavior.

Can you advance anything other than egoism without it?

Now something rather provocative: Is there really a categorical difference between the first, purely emotional reaction on hearing someone cry out in pain on one hand, and witnessing a valuable object (like a brand-new car) going to pieces in a crash, on the other hand?

Obviously, there is. I don't feel empathy for cars, not even Ferraris.

What I want to demonstrate is a warning not to stylize every pinching gut-feeling as empathy.

a) are you assuming I do?

b) you are distinguishing the despair at a lost investment from empathy, for example, for the person pinned behind the wheel. Either we are already agree, or you have answered your own question.

IP