There is no agreement on whether and in what sense moral propositions can be 'proved.'
Aristotle taught that in each area of inquiry we must seek the
kind of knowledge that is appropriate to that area. What exactly
might knowledge mean in the case of ethics as opposed to, say,
physics or mathematics?
However we define moral knowledge, there are usually ways to argue rationally about the rightness or wrongness (or the goodness or badness) of at least some of our actions. At a minimum, we can use the following techniques:
In order to discover inconsistencies or unacceptable consequences,
it is often useful to consider hypothetical cases. These cases
may be unlikely to occur in real life, but they can still be revealing.
A hypothetical case may reveal that our beliefs have a consequence
we had not noticed. As a result, we may decide to change what we believe.