So, the rejection of false propositions does not cause a serious problem for the theory of propositional functions in Russell.
According to Paul, the mental proposition existing obiective in our intellect is the significatum ultimum et adaequatum of false propositions (In Cat., cap. de priori, fol. 136vb).
One important branch of medieval logic developed in treatises called De obligationibus dealt, roughly speaking, with how an increasing set of true and false propositions might remain coherent.
Strikingly, then, in the propositions-as-types doctrine, a type, or set, simply is the type, or set, of proofs of a proposition, and, reciprocally, a proposition is just the type, or set, of its proofs.
A proposition consisting of the conjunction of two false propositions cannot be true.
In his letter, the pope merely requested Tempier to investigate rumors of false teaching, whereas the latter responded by drawing up a list of 219 false propositions.
It is, however, one thing for a proposition or set of propositions to be false, another altogether for it to be necessarily false.
"Now — two sets of false eyelashes".
The idea is to have a function, which given a proposition and a world yields a set of propositions instead of a single proposition.
On this view, to say that a proposition coheres with a specified set of propositions is to say that the proposition is consistent with the set.
