The basic idea of objectivism
"Our moral judgments are the sorts of things that can be true or false, and what makes them true or false are facts that are generally independent of who we are or what cultural groups we belong to. They are objective moral facts. For instance, if someone thought genocide is not morally abhorrent, we think he just must be mistaken. We think that this idea is wrong for any culture or people."
Differences and similarities between relativists and objectivists
"Like the objectivist, the relativist thinks our moral judgments are the sorts of things that can be true or false. But, unlike the objectivist, the relativist thinks that the truth or falsity of our moral judgment is only relative to something that can vary from person to person. Relativist believes that moral judgments are not objectively true or false."
Relativism
Subjectivism [səbˈʤɛktɪvɪzm] (an extreme form of relativism).
Cultural relativism (a less strong form of relativism).
Subjectivism
"The basic idea behind subjectivism says our moral judgments are indeed true or false, but they are only true or false relative to the subjective feelings of a particular person, the person who makes them. So, it's almost like when I say X is bad, I'm saying I morally disapprove of X."
Cultural relativism
"The basic idea behind cultural relativism is that our moral judgments are indeed true or false, but they are only true or false relative to the culture of the person who makes them. So, a judgment like X is bad, morally bad, morally wrong might be thought of as almost like I am saying X is disapproved of or forbidden by my culture. You can see that one person is saying polygamy is morally dubious, it could be true for him because in his culture it is morally dubious, whereas a person saying polygamy is morally dubious it is false for him because it's not morally dubious in his culture."
Emotivism
"The basic idea in emotivisim is that our moral judgments are not the sorts of things that can be true or false, neither objectively true or false, nor true or false relative to some person's feelings or some culture. They are the direct expression of our emotive reactions to the world."
Connection between morality and our motivations to act
"Subjectivism can explain the way our moral judgments are intimately tied up with how we are motivated to act. So, if I dislike something I will be motivated to avoid it or not to promote it. Or if I like something or approve of something I will be motivated to promote it
The emotivists, like the subjectivists, can explain the tight connection between some moral judgments and our motivations to action, because we are often motivated to act based on the way we feel about things."
SOURCES
'Introduction to Philosophy' course (the University of Edinburgh)
https://www.coursera.org/learn/philosophy