What is the difference between moral realism and moral cognitivism?

Moral cognitivists hold that when we make a moral judgment, such as ‘Lucy ought to pay back the money she borrowed’, we are stating a belief. The importance of this is that beliefs can be true or false: either it is true that Lucy ought to pay back or it isn’t (note that being moral cognitivists does not commit us to anything specific about what the right thing to do is). Moral cognitivists can be contrasted to moral non-cognitivists. The latter hold that when we make this kind of judgement we are expressing an emotional state or a desire. The non-cognitivist would hold that what we are really doing when we make such a judgment is saying something like ‘hooray for paying back money!’ Such statements can be neither true or false. Note that the statement ‘Anne desires that Lucy pay back the money’ can be true or false, but the desire itself (unlike belief) cannot be.

Moral realists hold there really are moral properties and facts that exist in the world independently of our judgements of them. So, when we judge that Lucy ought to pay back the money she borrowed, this judgment is actually true or false. Moral anti-realists deny that such properties and facts exist. It is important to realise that being a moral realist does not commit one to any view on what makes it the case that (say) it is true that Lucy ought to repay the money – this is the subject matter of normative ethics – but only that it is capable of being true or false.

In order to really draw out the distinction between A and B, it is useful to present an example of a case where something is A but not B (or vice versa). In this case, we can explain that you can be a moral non-cognitivist without being a moral realist by holding that when we make moral judgments we are holding beliefs (cognitivism) but, in fact, all our moral beliefs are false because nothing in the world exists which could make these beliefs true (anti-realism). The error theory of thinkers like John Mackie is an example of such a stance. However, all realists must be cognitivists, since if there really are moral facts and properties, then it must be possible to have beliefs about those facts and properties.