It is common to speak of true beliefs. As an example think of the JTB analyses of knowledge. JTB, that is, justified true belief. One could see “true belief” as a shorthand for “a belief in a true proposition”. This seems to be the case. It is common to call the theory for the JTB analysis of knowledge, but when writing down the three necessary and sufficient conditions, one does not write “has a true belief” but “p is true”.
But perhaps it is a good idea to allow for some or all beliefs to be true/false while still maintaining that it is propositions that are the primary truth bearers. A reason not to think so is again parsimony similar to the case of allowed sentences to be true too. Suppose that it is a good idea anyway.
What are the truth-conditions for beliefs?
First we may note that there seems to be no problem with ambiguity as there is with sentences as truth bearers. Perhaps there are ambiguous beliefs. We will suppose that there are none. We may, then, introduce these simple truth-conditions for beliefs:
A belief is true iff the proposition believed in is true.
A belief is false iff the proposition believed in is false.