My question boils down to this. Are there "moral facts"? In what sense, if any, are they true/false? From what do they derive their authority?
Let me outline some positions one could take in response: ethicists make a broad distinction between cognitivism, the position that moral statements have objective truth values, and non-cognitivism, the position that they do not. Cognitivism encompasses moral realism, or the belief that there are genuine, objective moral facts and that these facts inhere in the universe (somehow). On the other hand, non-cognitivism denies that a sentence like "Abortion is right/wrong" has the same kind of meaning as a sentence like "The earth is round"; rather than being evaluable as true or false, moral sentences either have no meaning, or have some other completely different meaning. E.g., an emotivist would hold that moral statements express personal approval or disapproval (like "Boo killing!", "Yay honesty!"), not facts.
Note that it's possible to be a cognitivist without being a moral realist. For example, a moral relativist will probably be a cognitivst, because s/he believes that there are moral facts and propositions; however, for the relativist, these moral facts differ depending on context or society, and they reflect subjective attitudes rather than objective features of the world. (Making moral relativists also ethical subjectivists). Moral realists hold the opposite. Another cognitivist but non-realist view is error theory, which all moral propositions are false, because (for example) all moral propositions presuppose moral facts which do not actually exist.
Because this was a boring and potentially confusing list, I have also attached a flow-chart to identify yourself among the categories listed above:
--Note to pedantic computer scientists: this is not a technically correct flow-chart. It's readable though, ain't it?
I have the impression that most people on this forum will identify themselves as non-cognitivists or cognitivists who do not hold that moral facts are objectively true (such as error theorists, or ethical subjectivists). I'd be interested to hear reasons why, arguments for/against, though.