Full Idea
We use the same that-clause ('that snow is white') to specify the contents of both a person's utterances and of their beliefs, because it is the same proposition.
Gist of Idea
The same proposition provides contents for the that-clause of an utterance and a belief
Source
E.J. Lowe (Introduction to the Philosophy of Mind [2000], Ch. 4)
Book Reference
Lowe,E.J.: 'Introduction to the Philosophy of Mind' [CUP 2000], p.73
A Reaction
Certainly to say 'he believes that we should declare war' seems to refer to something non-linguistic, but it doesn't demonstrate that anything concrete or real is being referred to. It may be an abstract account of dispositions and desires.