An objection to objectivism
"Empirical judgments admit empirical verification through some sort of observational method. The same doesn't seem to be true in the case of morality. With a moral judgment it seems difficult to know what method we would use to settle the issue. How do we figure out who's right about the issue? It doesn't look like we can observe the world and find the moral facts in the same way that we can with the empirical facts."
A possible response by the objectivists to the objection
"Objectivists could argue that sometimes we do use empirical observation to determine what's right and wrong. What's right and wrong is determined by what maximizes overall happiness. And we can go out and measure different policies as to whether they promote or don't promote overall happiness. That's something that you can observe."
An objection to relativism
"The basic challenge for the relativist is to explain the possibility of moral progress. If the relativist's view is right, somebody in the past said slavery is morally okay and that could be true, relative to that culture. Whereas somebody now says slavery is morally wrong. That could be true relative to our culture. There is a sort of difference in opinion, but there's no progress in opinion. Because there are different cultures."
A possible response by the relativists to the objection
"Relativists could argue that different cultures overlap [ˌəʊvəˈlæp] and so we can see for example, the slavery in America in the 18th century as part of our cultural heritage [ˈhɛrɪtɪʤ] now. You could see that culture is overlapping with our culture and so there is moral disagreement there because there's cultural overlap. It's not two radically different cultures."
An objection to emotivism
"The basic challenge of emotivism is to explain how we can reason to our moral views. If emotivism is right, then our moral opinions are just emotive reactions. They are not reasoned responses to questions about morality. So, changing your mind through reason is really hard for the emotivist to explain."
A possible response by the emotivists to the objection
"Emotivists could say: look, some of our evaluative reactions to things are in the space of reasons. They are the sorts of things we can reason to. For example, if you prefer a to b, and b to c, but you prefer c to a, there is something wrong with your preferences. They're irrational. That seems like I need to change my preference about a and c somehow."
SOURCES
'Introduction to Philosophy' course (the University of Edinburgh)
https://www.coursera.org/learn/philosophy