Suppose we add propositional quantifiers in the language of propositional logic. So, for example, we can write $\forall\!p\,(p\lor\neg p)$ to express the proposition that every proposition is either true or false. This, I take it, is a special case of second-order logic. Now suppose that due to some (say, philosophical) reasons we want to distinguish between the two kinds of propositions, and that we want to extend/revise our formal system as well, in a way that captures two kinds of propositions. What comes to my mind is to add a new sort to the language, so we have two sorts of propositions.
For example, let $\langle\rangle\!/\!1$ and $\langle\rangle\!/\!2$ stand for our two sorts of propositions. Suppose also we superindex variables with these symbols to indicate their sorts (e.g., $p^{\langle\rangle\!/\!1}$ is a sort-${\langle\rangle\!/\!1}$ variable). We revise our primary logic in a way that these sorts are accommodated. For instance, we allow Boolean connectives to now take arguments from each sort, and in our term-formation rules we say that, e.g., both $\forall p^{\langle\rangle\!/\!1}\phi$ and $\forall p^{\langle\rangle\!/\!2}\phi$ are well-formed formulas whenever $\phi$ is.
Now my question is this: Would this sortifying the space of propositions keep things second-order? What does 'order' in sorted languages even mean?