The truth about truth, so far as propositions are concerned, is a long but simple story. A proposition is true iff

So we have the familiar biconditionals – trivial, necessary, and knowable a priori –

and so on, for all the propositions there are.

Not for all the ‘that’-clauses there are. Some ‘that’-clauses fail to name propositions: for instance because of ungroundedness, or because the embedded sentence is a mere expression of feeling in the syntactic guise of a declarative sentence. Further, some propositions cannot be named by ‘that’-clauses. First, because there is an uncountable infinity of propositions, whereas there are only countably many ‘that’-clauses. Second, because some of the propositions, in fact most of them, cannot be named by ‘that’-clauses of finite length. Third, because some propositions cannot be named at all, not even at infinite length, since we lack names for alien properties that are nowhere to be found in our actual world, and that cannot be reached by any sort of construction or extrapolation or interpolation from this-worldly properties.