Well, let get these technical stuff out of the way:
Ok, moral realism is the ontological claim that there are "moral facts" that makes moral proposition true.
This proposition could be a mental representation, intention etc. For our purpose, they are all truthbearers.
To say that a proposition "P is true", is to say P is a truthbearer, and "is true" is known as a truth predicate.
According to our best theory for the assignment of truth predicated is Russell ` s explication between propositions and facts. To say that P is true is to say there exist a fact that makes P true. For our case, the "Moral facts" is what makes a moral proposition true.
Now, this technical use of "facts", "truth predicate" and propositions has a long history, and generally accepted by philosophers. The pros of this approach is the objectivity of what we mean by a proposition, namely, it `s corresponding fact. So to say that P is a proposition, or truthbearers of some sort, is to commit to the existence of a fact F, where "facts" are supposed to have some sort of mind-independent existence.
Russell theory of logical atomism is based an the relation between truthbearers, and the follow ontological claims: 1. there exist facts, 2. there exist relations between facts. With 1&2 postulated, according to russell, A proposition P that is true is suppose to refer to 1, or 2. The pros of this approach is the objectivity of what we mean by a proposition.
The con is the ontological commitment onces we accept this view about propositions, and truthbearer.
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I wonder how many understand?
In case no one understand:http://www.unc.edu/~gsmunc/Papers/Moral%20Realism.pdf