The Argument from First-Order Ethical Beliefs for Moral Realism

As far as I can tell, the argument from ordinary language
originated with John Post, but has also been defended by Quentin Smith.  The argument begins with the observation that
“our first-order ethical beliefs imply that ethical sentences have truth-value
and sometimes correspond to moral facts that obtain independently of our
beliefs about whether they obtain” (p. 158). 
For example, when the average person says, “Rape is morally wrong,” they
typically do not mean that rape is wrong for them but okay for rapists.   On the contrary, they mean that rape is
morally wrong for everyone.  Or,
similarly, it violates ordinary usage to say, “It all comes down to a personal
decision in the end as to whether it is wrong to torture newborn babies for the
fun of it.”  More formally, we may say:

(1)  
Ordinary ethical sentences and commonsense first-level
moral beliefs imply moral realism (or “Moral realism tacitly seems to be true
in ordinary commonsense moral attitudes”).

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