This is an exciting question.
As someone who has always has to resist the urge to nihilism, I will try to argue with you.
The question is not whether right and wrong exist in a tangible way to each individual person, or even in a systemic, shared way throughout a society or culture. The question is whether there is a right and wrong that exists immutibly and independent of the human experience. Is there a sense that my right and wrong can be held superior to someone else's contradictory sense of right and wrong?
I don't think that abortion is always morally wrong, but plenty of people not only think I'm incorrect, but that my opinion there is reprehensible. There is plenty of moral debate on this subject (and on plenty of similarly difficult questions) but my opinion is that neither side can ever be proven to be absolutely correct. Every moral argument is always based on some fundamental premise or assumption, and these assumptions invariably spring from some deeply felt conception of "right and wrong" that can neither be proved or disproved. It is prior to logic. In what sense does that right and wrong exist independent of the people who believe in it? At any rate, I accept that your argument shows that everyone but the craziest psychopath lives their lives under a moral principle guided by a private conception of right and wrong.
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