and such that its truth or falsehood depends only upon the truth or falsehood of p , q , r , … It might seem at first sight as though there were other functions of propositions besides truth-functions; such, for example, would be “A believes p ”, for in general A will believe some true propositions and some false ones: unless he is an exceptionally gifted individual, we cannot infer that p is true from the fact that he believes it or that p is false from the fact that he does not believe it. Other apparent exceptions would be such as “ p is a very complex proposition” or “ p