What do you mean by “wrong”, in the moral sense?

I’ve been reading through the recent discussions on morality here, and I wanted to ask about how people are using the word “wrong”. Something I’ve read here (I don’t recall the specific post or comment) discussed how someone could be rationally wrong, say thinking 2+2=5, and that’s equivalent to being morally wrong, say committing an unprovoked violent act. Now, I won’t pretend that I don’t agree with both statements, but the word “wrong” to me is referring to different things in my mind. In the first case, it means the answer, assuming base 10, etc., is incorrect. Whether or not math has some platonic reality outside of people’s minds, or is a construction we have, in that system, the answer isn’t correct, given all the other points that are assumed to be true. When it comes to the wrongness of a violent act, however, it’s completely different. I think it’s wrong to inflict pain for no reason. I don’t have a list of axioms of why that’s the case, and I don’t think I need one.

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